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Add Langley's curve25519 (GH #761, PR# 762)

pull/765/head
Jeffrey Walton 2018-12-11 16:17:56 -05:00 committed by GitHub
parent c1681148a2
commit 77923a291a
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
16 changed files with 1825 additions and 61 deletions
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6
Filelist.txt
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@ -101,6 +101,9 @@ dlltest.vcxproj
dlltest.vcxproj.filters
dmac.h
drbg.h
donna.h
donna_32.cpp
donna_64.cpp
dsa.cpp
dsa.h
eax.cpp
@ -371,6 +374,8 @@ whrlpool.h
words.h
x64dll.asm
x64masm.asm
xed25519.h
xed25519.cpp
xtr.cpp
xtr.h
xtrcrypt.cpp
@ -455,6 +460,7 @@ TestData/skipjack.dat
TestData/squareva.dat
TestData/twofishv.dat
TestData/usage.dat
TestData/x25519.dat
TestData/xtrdh171.dat
TestData/xtrdh342.dat
TestVectors/Readme.txt

1
TestData/x25519.dat Normal file
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@ -0,0 +1 @@
30440320984E4ED42CF68631C0FF27A4AB8D3EA7AFDCFE3C0087A847C4FAD054A9C7756C0420CF293063A1807A96AA89929564B1695AFBEC2546BCD048AACBD6C741CE3B5221

4
bench3.cpp
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@ -29,6 +29,7 @@
#include "ec2n.h"
#include "asn.h"
#include "dh.h"
#include "xed25519.h"
#include "mqv.h"
#include "hmqv.h"
#include "fhmqv.h"
@ -390,6 +391,7 @@ void Benchmark3(double t, double hertz)
ECGDSA<ECP, SHA1>::Verifier spub3(spriv3);
ECDH<ECP>::Domain ecdhc(ASN1::secp256k1());
ECMQV<ECP>::Domain ecmqvc(ASN1::secp256k1());
x25519 x25519ka(Test::GlobalRNG());
BenchMarkEncryption("ECIES over GF(p) 256", cpub, t);
BenchMarkDecryption("ECIES over GF(p) 256", cpriv, cpub, t);
@ -399,6 +401,8 @@ void Benchmark3(double t, double hertz)
BenchMarkVerification("ECDSA-RFC6979 over GF(p) 256", spriv2, spub2, t);
BenchMarkSigning("ECGDSA over GF(p) 256", spriv3, t);
BenchMarkVerification("ECGDSA over GF(p) 256", spriv3, spub3, t);
BenchMarkKeyGen("x25519", x25519ka, t);
BenchMarkAgreement("x25519", x25519ka, t);
BenchMarkKeyGen("ECDHC over GF(p) 256", ecdhc, t);
BenchMarkAgreement("ECDHC over GF(p) 256", ecdhc, t);
BenchMarkKeyGen("ECMQVC over GF(p) 256", ecmqvc, t);

88
cryptest.nmake
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@ -52,59 +52,63 @@
LIB_SRCS = \
cryptlib.cpp cpu.cpp integer.cpp 3way.cpp adler32.cpp algebra.cpp \
algparam.cpp arc4.cpp aria_simd.cpp aria.cpp ariatab.cpp asn.cpp \
authenc.cpp base32.cpp base64.cpp basecode.cpp bfinit.cpp blake2s_simd.cpp \
blake2b_simd.cpp blake2.cpp blowfish.cpp blumshub.cpp camellia.cpp cast.cpp casts.cpp \
cbcmac.cpp ccm.cpp chacha_avx.cpp chacha_simd.cpp chacha.cpp cham_simd.cpp cham.cpp \
channels.cpp cmac.cpp crc_simd.cpp crc.cpp darn.cpp default.cpp des.cpp dessp.cpp \
dh.cpp dh2.cpp dll.cpp dsa.cpp eax.cpp ec2n.cpp eccrypto.cpp ecp.cpp elgamal.cpp \
emsa2.cpp eprecomp.cpp esign.cpp files.cpp filters.cpp fips140.cpp \
fipstest.cpp gcm_simd.cpp gcm.cpp gf256.cpp gf2_32.cpp gf2n.cpp \
gfpcrypt.cpp gost.cpp gzip.cpp hc128.cpp hc256.cpp hex.cpp hight.cpp \
hmac.cpp hrtimer.cpp ida.cpp idea.cpp iterhash.cpp kalyna.cpp \
kalynatab.cpp keccak.cpp keccakc.cpp lea_simd.cpp lea.cpp luc.cpp \
mars.cpp marss.cpp md2.cpp md4.cpp md5.cpp misc.cpp modes.cpp mqueue.cpp \
mqv.cpp nbtheory.cpp neon_simd.cpp oaep.cpp osrng.cpp padlkrng.cpp \
panama.cpp pkcspad.cpp poly1305.cpp polynomi.cpp ppc_simd.cpp pssr.cpp \
algparam.cpp arc4.cpp aria.cpp aria_simd.cpp ariatab.cpp asn.cpp \
authenc.cpp base32.cpp base64.cpp basecode.cpp bfinit.cpp blake2.cpp \
blake2b_simd.cpp blake2s_simd.cpp blowfish.cpp blumshub.cpp camellia.cpp \
cast.cpp casts.cpp cbcmac.cpp ccm.cpp chacha.cpp chacha_avx.cpp \
chacha_simd.cpp cham.cpp cham_simd.cpp channels.cpp cmac.cpp crc.cpp \
crc_simd.cpp darn.cpp default.cpp des.cpp dessp.cpp dh.cpp dh2.cpp \
dll.cpp donna_32.cpp donna_64.cpp dsa.cpp eax.cpp ec2n.cpp eccrypto.cpp \
ecp.cpp elgamal.cpp emsa2.cpp eprecomp.cpp esign.cpp files.cpp \
filters.cpp fips140.cpp fipstest.cpp gcm.cpp gcm_simd.cpp gf256.cpp \
gf2_32.cpp gf2n.cpp gfpcrypt.cpp gost.cpp gzip.cpp hc128.cpp hc256.cpp \
hex.cpp hight.cpp hmac.cpp hrtimer.cpp ida.cpp idea.cpp iterhash.cpp \
kalyna.cpp kalynatab.cpp keccak.cpp keccakc.cpp lea.cpp lea_simd.cpp \
luc.cpp mars.cpp marss.cpp md2.cpp md4.cpp md5.cpp misc.cpp modes.cpp \
mqueue.cpp mqv.cpp nbtheory.cpp neon_simd.cpp oaep.cpp osrng.cpp \
padlkrng.cpp panama.cpp pkcspad.cpp poly1305.cpp polynomi.cpp \
ppc_power7.cpp ppc_power8.cpp ppc_power9.cpp ppc_simd.cpp pssr.cpp \
pubkey.cpp queue.cpp rabbit.cpp rabin.cpp randpool.cpp rc2.cpp rc5.cpp \
rc6.cpp rdrand.cpp rdtables.cpp rijndael_simd.cpp rijndael.cpp ripemd.cpp \
rc6.cpp rdrand.cpp rdtables.cpp rijndael.cpp rijndael_simd.cpp ripemd.cpp \
rng.cpp rsa.cpp rw.cpp safer.cpp salsa.cpp scrypt.cpp seal.cpp seed.cpp \
serpent.cpp sha_simd.cpp sha.cpp sha3.cpp shacal2_simd.cpp shacal2.cpp \
shark.cpp sharkbox.cpp simeck_simd.cpp simeck.cpp simon.cpp \
simon128_simd.cpp simon64_simd.cpp skipjack.cpp sm3.cpp sm4_simd.cpp \
sm4.cpp sosemanuk.cpp speck.cpp speck128_simd.cpp speck64_simd.cpp \
serpent.cpp sha.cpp sha3.cpp sha_simd.cpp shacal2.cpp shacal2_simd.cpp \
shark.cpp sharkbox.cpp simeck.cpp simeck_simd.cpp simon.cpp \
simon128_simd.cpp simon64_simd.cpp skipjack.cpp sm3.cpp sm4.cpp \
sm4_simd.cpp sosemanuk.cpp speck.cpp speck128_simd.cpp speck64_simd.cpp \
square.cpp squaretb.cpp sse_simd.cpp strciphr.cpp tea.cpp tftables.cpp \
threefish.cpp tiger.cpp tigertab.cpp ttmac.cpp tweetnacl.cpp twofish.cpp \
vmac.cpp wake.cpp whrlpool.cpp xtr.cpp xtrcrypt.cpp zdeflate.cpp \
zinflate.cpp zlib.cpp
vmac.cpp wake.cpp whrlpool.cpp xed25519.cpp xtr.cpp xtrcrypt.cpp \
zdeflate.cpp zinflate.cpp zlib.cpp
LIB_OBJS = \
cryptlib.obj cpu.obj integer.obj 3way.obj adler32.obj algebra.obj \
algparam.obj arc4.obj aria_simd.obj aria.obj ariatab.obj asn.obj \
authenc.obj base32.obj base64.obj basecode.obj bfinit.obj blake2s_simd.obj \
blake2b_simd.obj blake2.obj blowfish.obj blumshub.obj camellia.obj cast.obj casts.obj \
cbcmac.obj ccm.obj chacha_avx.obj chacha_simd.obj chacha.obj cham_simd.obj cham.obj \
channels.obj cmac.obj crc_simd.obj crc.obj darn.obj default.obj des.obj dessp.obj \
dh.obj dh2.obj dll.obj dsa.obj eax.obj ec2n.obj eccrypto.obj ecp.obj elgamal.obj \
emsa2.obj eprecomp.obj esign.obj files.obj filters.obj fips140.obj \
fipstest.obj gcm_simd.obj gcm.obj gf256.obj gf2_32.obj gf2n.obj \
gfpcrypt.obj gost.obj gzip.obj hc128.obj hc256.obj hex.obj hight.obj \
hmac.obj hrtimer.obj ida.obj idea.obj iterhash.obj kalyna.obj \
kalynatab.obj keccak.obj keccakc.obj lea_simd.obj lea.obj luc.obj \
mars.obj marss.obj md2.obj md4.obj md5.obj misc.obj modes.obj mqueue.obj \
mqv.obj nbtheory.obj neon_simd.obj oaep.obj osrng.obj padlkrng.obj \
panama.obj pkcspad.obj poly1305.obj polynomi.obj ppc_simd.obj pssr.obj \
algparam.obj arc4.obj aria.obj aria_simd.obj ariatab.obj asn.obj \
authenc.obj base32.obj base64.obj basecode.obj bfinit.obj blake2.obj \
blake2b_simd.obj blake2s_simd.obj blowfish.obj blumshub.obj camellia.obj \
cast.obj casts.obj cbcmac.obj ccm.obj chacha.obj chacha_avx.obj \
chacha_simd.obj cham.obj cham_simd.obj channels.obj cmac.obj crc.obj \
crc_simd.obj darn.obj default.obj des.obj dessp.obj dh.obj dh2.obj \
dll.obj donna_32.obj donna_64.obj dsa.obj eax.obj ec2n.obj eccrypto.obj \
ecp.obj elgamal.obj emsa2.obj eprecomp.obj esign.obj files.obj \
filters.obj fips140.obj fipstest.obj gcm.obj gcm_simd.obj gf256.obj \
gf2_32.obj gf2n.obj gfpcrypt.obj gost.obj gzip.obj hc128.obj hc256.obj \
hex.obj hight.obj hmac.obj hrtimer.obj ida.obj idea.obj iterhash.obj \
kalyna.obj kalynatab.obj keccak.obj keccakc.obj lea.obj lea_simd.obj \
luc.obj mars.obj marss.obj md2.obj md4.obj md5.obj misc.obj modes.obj \
mqueue.obj mqv.obj nbtheory.obj neon_simd.obj oaep.obj osrng.obj \
padlkrng.obj panama.obj pkcspad.obj poly1305.obj polynomi.obj \
ppc_power7.obj ppc_power8.obj ppc_power9.obj ppc_simd.obj pssr.obj \
pubkey.obj queue.obj rabbit.obj rabin.obj randpool.obj rc2.obj rc5.obj \
rc6.obj rdrand.obj rdtables.obj rijndael_simd.obj rijndael.obj ripemd.obj \
rc6.obj rdrand.obj rdtables.obj rijndael.obj rijndael_simd.obj ripemd.obj \
rng.obj rsa.obj rw.obj safer.obj salsa.obj scrypt.obj seal.obj seed.obj \
serpent.obj sha_simd.obj sha.obj sha3.obj shacal2_simd.obj shacal2.obj \
shark.obj sharkbox.obj simeck_simd.obj simeck.obj simon.obj \
simon128_simd.obj simon64_simd.obj skipjack.obj sm3.obj sm4_simd.obj \
sm4.obj sosemanuk.obj speck.obj speck128_simd.obj speck64_simd.obj \
serpent.obj sha.obj sha3.obj sha_simd.obj shacal2.obj shacal2_simd.obj \
shark.obj sharkbox.obj simeck.obj simeck_simd.obj simon.obj \
simon128_simd.obj simon64_simd.obj skipjack.obj sm3.obj sm4.obj \
sm4_simd.obj sosemanuk.obj speck.obj speck128_simd.obj speck64_simd.obj \
square.obj squaretb.obj sse_simd.obj strciphr.obj tea.obj tftables.obj \
threefish.obj tiger.obj tigertab.obj ttmac.obj tweetnacl.obj twofish.obj \
vmac.obj wake.obj whrlpool.obj xtr.obj xtrcrypt.obj zdeflate.obj \
zinflate.obj zlib.obj
vmac.obj wake.obj whrlpool.obj xed25519.obj xtr.obj xtrcrypt.obj \
zdeflate.obj zinflate.obj zlib.obj
TEST_SRCS = \
test.cpp bench1.cpp bench2.cpp bench3.cpp datatest.cpp \

5
cryptlib.vcxproj
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@ -213,6 +213,8 @@
<ClCompile Include="dll.cpp">
<PrecompiledHeader />
</ClCompile>
<ClCompile Include="donna_32.cpp" />
<ClCompile Include="donna_64.cpp" />
<ClCompile Include="dsa.cpp" />
<ClCompile Include="eax.cpp" />
<ClCompile Include="ec2n.cpp" />
@ -335,6 +337,7 @@
<ClCompile Include="vmac.cpp" />
<ClCompile Include="wake.cpp" />
<ClCompile Include="whrlpool.cpp" />
<ClCompile Include="xed25519.cpp" />
<ClCompile Include="xtr.cpp" />
<ClCompile Include="xtrcrypt.cpp" />
<ClCompile Include="zdeflate.cpp" />
@ -413,6 +416,7 @@
<ClInclude Include="dh2.h" />
<ClInclude Include="dmac.h" />
<ClInclude Include="drbg.h" />
<ClInclude Include="donna.h" />
<ClInclude Include="dsa.h" />
<ClInclude Include="eax.h" />
<ClInclude Include="ec2n.h" />
@ -529,6 +533,7 @@
<ClInclude Include="wake.h" />
<ClInclude Include="whrlpool.h" />
<ClInclude Include="words.h" />
<ClInclude Include="xed25519.h" />
<ClInclude Include="xtr.h" />
<ClInclude Include="xtrcrypt.h" />
<ClInclude Include="zdeflate.h" />

21
cryptlib.vcxproj.filters
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@ -119,6 +119,9 @@
<ClCompile Include="cryptlib.cpp">
<Filter>Source Files</Filter>
</ClCompile>
<ClCompile Include="darn.cpp">
<Filter>Source Files</Filter>
</ClCompile>
<ClCompile Include="default.cpp">
<Filter>Source Files</Filter>
</ClCompile>
@ -137,6 +140,12 @@
<ClCompile Include="dll.cpp">
<Filter>Source Files</Filter>
</ClCompile>
<ClCompile Include="donna_32.cpp">
<Filter>Source Files</Filter>
</ClCompile>
<ClCompile Include="donna_64.cpp">
<Filter>Source Files</Filter>
</ClCompile>
<ClCompile Include="dsa.cpp">
<Filter>Source Files</Filter>
</ClCompile>
@ -482,6 +491,9 @@
<ClCompile Include="whrlpool.cpp">
<Filter>Source Files</Filter>
</ClCompile>
<ClCompile Include="xed25519.cpp">
<Filter>Source Files</Filter>
</ClCompile>
<ClCompile Include="xtr.cpp">
<Filter>Source Files</Filter>
</ClCompile>
@ -597,6 +609,9 @@
<ClInclude Include="cryptlib.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="darn.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="default.h">
<Filter>Header Files</Filter>
</ClInclude>
@ -618,6 +633,9 @@
<ClInclude Include="dsa.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="donna.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="eax.h">
<Filter>Header Files</Filter>
</ClInclude>
@ -963,6 +981,9 @@
<ClInclude Include="words.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="xed25519.h">
<Filter>Header Files</Filter>
</ClInclude>
<ClInclude Include="xtr.h">
<Filter>Header Files</Filter>
</ClInclude>

65
donna.h Normal file
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@ -0,0 +1,65 @@
// donna.h - written and placed in public domain by Jeffrey Walton
// This is a port of Adam Langley's curve25519-donna
// located at https://github.com/agl/curve25519-donna
/* Copyright 2008, Google Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following disclaimer
* in the documentation and/or other materials provided with the
* distribution.
* * Neither the name of Google Inc. nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* curve25519-donna: Curve25519 elliptic curve, public key function
*
* http://code.google.com/p/curve25519-donna/
*
* Adam Langley <agl@imperialviolet.org>
*
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
*
* More information about curve25519 can be found here
* http://cr.yp.to/ecdh.html
*
* djb's sample implementation of curve25519 is written in a special assembly
* language called qhasm and uses the floating point registers.
*
* This is, almost, a clean room reimplementation from the curve25519 paper. It
* uses many of the tricks described therein. Only the crecip function is taken
* from the sample implementation. */
#ifndef CRYPTOPP_DONNA_H
#define CRYPTOPP_DONNA_H
#include "cryptlib.h"
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
int curve25519(byte pubkey[32], const byte seckey[32], const byte basepoint[32]);
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_DONNA_H

899
donna_32.cpp Normal file
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@ -0,0 +1,899 @@
// donna_32.cpp - written and placed in public domain by Jeffrey Walton
// This is a port of Adam Langley's curve25519-donna
// located at https://github.com/agl/curve25519-donna
/* Copyright 2008, Google Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following disclaimer
* in the documentation and/or other materials provided with the
* distribution.
* * Neither the name of Google Inc. nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* curve25519-donna: Curve25519 elliptic curve, public key function
*
* http://code.google.com/p/curve25519-donna/
*
* Adam Langley <agl@imperialviolet.org>
*
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
*
* More information about curve25519 can be found here
* http://cr.yp.to/ecdh.html
*
* djb's sample implementation of curve25519 is written in a special assembly
* language called qhasm and uses the floating point registers.
*
* This is, almost, a clean room reimplementation from the curve25519 paper. It
* uses many of the tricks described therein. Only the crecip function is taken
* from the sample implementation. */
#include "pch.h"
#include "config.h"
#include "donna.h"
#include "stdcpp.h"
// This macro is not in a header like config.h because
// we don't want it exposed to user code. We also need
// a standard header like <stdint.h> or <stdef.h>.
// Langley uses uint128_t in the 64-bit code paths so
// we further restrict 64-bit code.
#if (UINTPTR_MAX == 0xffffffff) || !defined(CRYPTOPP_WORD128_AVAILABLE)
# define CRYPTOPP_32BIT 1
#else
# define CRYPTOPP_64BIT 1
#endif
// Squash MS LNK4221 and libtool warnings
extern const char DONNA32_FNAME[] = __FILE__;
#if defined(CRYPTOPP_32BIT)
ANONYMOUS_NAMESPACE_BEGIN
using std::memcpy;
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::word64;
using CryptoPP::sword32;
using CryptoPP::sword64;
typedef sword64 limb;
/* Field element representation:
*
* Field elements are written as an array of signed, 64-bit limbs, least
* significant first. The value of the field element is:
* x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
*
* i.e. the limbs are 26, 25, 26, 25, ... bits wide. */
/* Sum two numbers: output += in */
void fsum(limb *output, const limb *in)
{
for (unsigned int i = 0; i < 10; i += 2) {
output[0+i] = output[0+i] + in[0+i];
output[1+i] = output[1+i] + in[1+i];
}
}
/* Find the difference of two numbers: output = in - output
* (note the order of the arguments!). */
void fdifference(limb *output, const limb *in)
{
for (unsigned int i = 0; i < 10; ++i) {
output[i] = in[i] - output[i];
}
}
/* Multiply a number by a scalar: output = in * scalar */
void fscalar_product(limb *output, const limb *in, const limb scalar)
{
for (unsigned int i = 0; i < 10; ++i) {
output[i] = in[i] * scalar;
}
}
/* Multiply two numbers: output = in2 * in
*
* output must be distinct to both inputs. The inputs are reduced coefficient
* form, the output is not.
*
* output[x] <= 14 * the largest product of the input limbs. */
void fproduct(limb *output, const limb *in2, const limb *in)
{
output[0] = ((limb) ((sword32) in2[0])) * ((sword32) in[0]);
output[1] = ((limb) ((sword32) in2[0])) * ((sword32) in[1]) +
((limb) ((sword32) in2[1])) * ((sword32) in[0]);
output[2] = 2 * ((limb) ((sword32) in2[1])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[2]) +
((limb) ((sword32) in2[2])) * ((sword32) in[0]);
output[3] = ((limb) ((sword32) in2[1])) * ((sword32) in[2]) +
((limb) ((sword32) in2[2])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[3]) +
((limb) ((sword32) in2[3])) * ((sword32) in[0]);
output[4] = ((limb) ((sword32) in2[2])) * ((sword32) in[2]) +
2 * (((limb) ((sword32) in2[1])) * ((sword32) in[3]) +
((limb) ((sword32) in2[3])) * ((sword32) in[1])) +
((limb) ((sword32) in2[0])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[0]);
output[5] = ((limb) ((sword32) in2[2])) * ((sword32) in[3]) +
((limb) ((sword32) in2[3])) * ((sword32) in[2]) +
((limb) ((sword32) in2[1])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[0]);
output[6] = 2 * (((limb) ((sword32) in2[3])) * ((sword32) in[3]) +
((limb) ((sword32) in2[1])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[1])) +
((limb) ((sword32) in2[2])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[2]) +
((limb) ((sword32) in2[0])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[0]);
output[7] = ((limb) ((sword32) in2[3])) * ((sword32) in[4]) +
((limb) ((sword32) in2[4])) * ((sword32) in[3]) +
((limb) ((sword32) in2[2])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[2]) +
((limb) ((sword32) in2[1])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[0]);
output[8] = ((limb) ((sword32) in2[4])) * ((sword32) in[4]) +
2 * (((limb) ((sword32) in2[3])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[3]) +
((limb) ((sword32) in2[1])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[1])) +
((limb) ((sword32) in2[2])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[2]) +
((limb) ((sword32) in2[0])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[0]);
output[9] = ((limb) ((sword32) in2[4])) * ((sword32) in[5]) +
((limb) ((sword32) in2[5])) * ((sword32) in[4]) +
((limb) ((sword32) in2[3])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[3]) +
((limb) ((sword32) in2[2])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[2]) +
((limb) ((sword32) in2[1])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[1]) +
((limb) ((sword32) in2[0])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[0]);
output[10] = 2 * (((limb) ((sword32) in2[5])) * ((sword32) in[5]) +
((limb) ((sword32) in2[3])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[3]) +
((limb) ((sword32) in2[1])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[1])) +
((limb) ((sword32) in2[4])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[4]) +
((limb) ((sword32) in2[2])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[2]);
output[11] = ((limb) ((sword32) in2[5])) * ((sword32) in[6]) +
((limb) ((sword32) in2[6])) * ((sword32) in[5]) +
((limb) ((sword32) in2[4])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[4]) +
((limb) ((sword32) in2[3])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[3]) +
((limb) ((sword32) in2[2])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[2]);
output[12] = ((limb) ((sword32) in2[6])) * ((sword32) in[6]) +
2 * (((limb) ((sword32) in2[5])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[5]) +
((limb) ((sword32) in2[3])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[3])) +
((limb) ((sword32) in2[4])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[4]);
output[13] = ((limb) ((sword32) in2[6])) * ((sword32) in[7]) +
((limb) ((sword32) in2[7])) * ((sword32) in[6]) +
((limb) ((sword32) in2[5])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[5]) +
((limb) ((sword32) in2[4])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[4]);
output[14] = 2 * (((limb) ((sword32) in2[7])) * ((sword32) in[7]) +
((limb) ((sword32) in2[5])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[5])) +
((limb) ((sword32) in2[6])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[6]);
output[15] = ((limb) ((sword32) in2[7])) * ((sword32) in[8]) +
((limb) ((sword32) in2[8])) * ((sword32) in[7]) +
((limb) ((sword32) in2[6])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[6]);
output[16] = ((limb) ((sword32) in2[8])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in2[7])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[7]));
output[17] = ((limb) ((sword32) in2[8])) * ((sword32) in[9]) +
((limb) ((sword32) in2[9])) * ((sword32) in[8]);
output[18] = 2 * ((limb) ((sword32) in2[9])) * ((sword32) in[9]);
}
/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
*
* On entry: |output[i]| < 14*2^54
* On exit: |output[0..8]| < 280*2^54 */
void freduce_degree(limb *output)
{
/* Each of these shifts and adds ends up multiplying the value by 19.
*
* For output[0..8], the absolute entry value is < 14*2^54 and we add, at
* most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */
output[8] += output[18] << 4;
output[8] += output[18] << 1;
output[8] += output[18];
output[7] += output[17] << 4;
output[7] += output[17] << 1;
output[7] += output[17];
output[6] += output[16] << 4;
output[6] += output[16] << 1;
output[6] += output[16];
output[5] += output[15] << 4;
output[5] += output[15] << 1;
output[5] += output[15];
output[4] += output[14] << 4;
output[4] += output[14] << 1;
output[4] += output[14];
output[3] += output[13] << 4;
output[3] += output[13] << 1;
output[3] += output[13];
output[2] += output[12] << 4;
output[2] += output[12] << 1;
output[2] += output[12];
output[1] += output[11] << 4;
output[1] += output[11] << 1;
output[1] += output[11];
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
}
#if (-1 & 3) != 3
#error "This code only works on a two's complement system"
#endif
/* return v / 2^26, using only shifts and adds.
*
* On entry: v can take any value. */
inline limb div_by_2_26(const limb v)
{
/* High word of v; no shift needed. */
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
/* Set to all 1s if v was negative; else set to 0s. */
const int32_t sign = ((int32_t) highword) >> 31;
/* Set to 0x3ffffff if v was negative; else set to 0. */
const int32_t roundoff = ((uint32_t) sign) >> 6;
/* Should return v / (1<<26) */
return (v + roundoff) >> 26;
}
/* return v / (2^25), using only shifts and adds.
*
* On entry: v can take any value. */
inline limb div_by_2_25(const limb v)
{
/* High word of v; no shift needed*/
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
/* Set to all 1s if v was negative; else set to 0s. */
const int32_t sign = ((int32_t) highword) >> 31;
/* Set to 0x1ffffff if v was negative; else set to 0. */
const int32_t roundoff = ((uint32_t) sign) >> 7;
/* Should return v / (1<<25) */
return (v + roundoff) >> 25;
}
/* Reduce all coefficients of the short form input so that |x| < 2^26.
*
* On entry: |output[i]| < 280*2^54 */
void freduce_coefficients(limb *output)
{
output[10] = 0;
for (unsigned int i = 0; i < 10; i += 2) {
limb over = div_by_2_26(output[i]);
/* The entry condition (that |output[i]| < 280*2^54) means that over is, at
* most, 280*2^28 in the first iteration of this loop. This is added to the
* next limb and we can approximate the resulting bound of that limb by
* 281*2^54. */
output[i] -= over << 26;
output[i+1] += over;
/* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
* 281*2^29. When this is added to the next limb, the resulting bound can
* be approximated as 281*2^54.
*
* For subsequent iterations of the loop, 281*2^54 remains a conservative
* bound and no overflow occurs. */
over = div_by_2_25(output[i+1]);
output[i+1] -= over << 25;
output[i+2] += over;
}
/* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
output[10] = 0;
/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
* So |over| will be no more than 2^16. */
{
limb over = div_by_2_26(output[0]);
output[0] -= over << 26;
output[1] += over;
}
/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
* bound on |output[1]| is sufficient to meet our needs. */
}
/* A helpful wrapper around fproduct: output = in * in2.
*
* On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
*
* output must be distinct to both inputs. The output is reduced degree
* (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */
void fmul(limb *output, const limb *in, const limb *in2)
{
limb t[19];
fproduct(t, in, in2);
/* |t[i]| < 14*2^54 */
freduce_degree(t);
freduce_coefficients(t);
/* |t[i]| < 2^26 */
memcpy(output, t, sizeof(limb) * 10);
}
/* Square a number: output = in**2
*
* output must be distinct from the input. The inputs are reduced coefficient
* form, the output is not.
*
* output[x] <= 14 * the largest product of the input limbs. */
void fsquare_inner(limb *output, const limb *in)
{
output[0] = ((limb) ((sword32) in[0])) * ((sword32) in[0]);
output[1] = 2 * ((limb) ((sword32) in[0])) * ((sword32) in[1]);
output[2] = 2 * (((limb) ((sword32) in[1])) * ((sword32) in[1]) +
((limb) ((sword32) in[0])) * ((sword32) in[2]));
output[3] = 2 * (((limb) ((sword32) in[1])) * ((sword32) in[2]) +
((limb) ((sword32) in[0])) * ((sword32) in[3]));
output[4] = ((limb) ((sword32) in[2])) * ((sword32) in[2]) +
4 * ((limb) ((sword32) in[1])) * ((sword32) in[3]) +
2 * ((limb) ((sword32) in[0])) * ((sword32) in[4]);
output[5] = 2 * (((limb) ((sword32) in[2])) * ((sword32) in[3]) +
((limb) ((sword32) in[1])) * ((sword32) in[4]) +
((limb) ((sword32) in[0])) * ((sword32) in[5]));
output[6] = 2 * (((limb) ((sword32) in[3])) * ((sword32) in[3]) +
((limb) ((sword32) in[2])) * ((sword32) in[4]) +
((limb) ((sword32) in[0])) * ((sword32) in[6]) +
2 * ((limb) ((sword32) in[1])) * ((sword32) in[5]));
output[7] = 2 * (((limb) ((sword32) in[3])) * ((sword32) in[4]) +
((limb) ((sword32) in[2])) * ((sword32) in[5]) +
((limb) ((sword32) in[1])) * ((sword32) in[6]) +
((limb) ((sword32) in[0])) * ((sword32) in[7]));
output[8] = ((limb) ((sword32) in[4])) * ((sword32) in[4]) +
2 * (((limb) ((sword32) in[2])) * ((sword32) in[6]) +
((limb) ((sword32) in[0])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in[1])) * ((sword32) in[7]) +
((limb) ((sword32) in[3])) * ((sword32) in[5])));
output[9] = 2 * (((limb) ((sword32) in[4])) * ((sword32) in[5]) +
((limb) ((sword32) in[3])) * ((sword32) in[6]) +
((limb) ((sword32) in[2])) * ((sword32) in[7]) +
((limb) ((sword32) in[1])) * ((sword32) in[8]) +
((limb) ((sword32) in[0])) * ((sword32) in[9]));
output[10] = 2 * (((limb) ((sword32) in[5])) * ((sword32) in[5]) +
((limb) ((sword32) in[4])) * ((sword32) in[6]) +
((limb) ((sword32) in[2])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in[3])) * ((sword32) in[7]) +
((limb) ((sword32) in[1])) * ((sword32) in[9])));
output[11] = 2 * (((limb) ((sword32) in[5])) * ((sword32) in[6]) +
((limb) ((sword32) in[4])) * ((sword32) in[7]) +
((limb) ((sword32) in[3])) * ((sword32) in[8]) +
((limb) ((sword32) in[2])) * ((sword32) in[9]));
output[12] = ((limb) ((sword32) in[6])) * ((sword32) in[6]) +
2 * (((limb) ((sword32) in[4])) * ((sword32) in[8]) +
2 * (((limb) ((sword32) in[5])) * ((sword32) in[7]) +
((limb) ((sword32) in[3])) * ((sword32) in[9])));
output[13] = 2 * (((limb) ((sword32) in[6])) * ((sword32) in[7]) +
((limb) ((sword32) in[5])) * ((sword32) in[8]) +
((limb) ((sword32) in[4])) * ((sword32) in[9]));
output[14] = 2 * (((limb) ((sword32) in[7])) * ((sword32) in[7]) +
((limb) ((sword32) in[6])) * ((sword32) in[8]) +
2 * ((limb) ((sword32) in[5])) * ((sword32) in[9]));
output[15] = 2 * (((limb) ((sword32) in[7])) * ((sword32) in[8]) +
((limb) ((sword32) in[6])) * ((sword32) in[9]));
output[16] = ((limb) ((sword32) in[8])) * ((sword32) in[8]) +
4 * ((limb) ((sword32) in[7])) * ((sword32) in[9]);
output[17] = 2 * ((limb) ((sword32) in[8])) * ((sword32) in[9]);
output[18] = 2 * ((limb) ((sword32) in[9])) * ((sword32) in[9]);
}
/* fsquare sets output = in^2.
*
* On entry: The |in| argument is in reduced coefficients form and |in[i]| <
* 2^27.
*
* On exit: The |output| argument is in reduced coefficients form (indeed, one
* need only provide storage for 10 limbs) and |out[i]| < 2^26. */
void
fsquare(limb *output, const limb *in)
{
limb t[19];
fsquare_inner(t, in);
/* |t[i]| < 14*2^54 because the largest product of two limbs will be <
* 2^(27+27) and fsquare_inner adds together, at most, 14 of those
* products. */
freduce_degree(t);
freduce_coefficients(t);
/* |t[i]| < 2^26 */
memcpy(output, t, sizeof(limb) * 10);
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
void fexpand(limb *output, const byte *input)
{
#define F(n,start,shift,mask) \
output[n] = ((((limb) input[start + 0]) | \
((limb) input[start + 1]) << 8 | \
((limb) input[start + 2]) << 16 | \
((limb) input[start + 3]) << 24) >> shift) & mask;
F(0, 0, 0, 0x3ffffff);
F(1, 3, 2, 0x1ffffff);
F(2, 6, 3, 0x3ffffff);
F(3, 9, 5, 0x1ffffff);
F(4, 12, 6, 0x3ffffff);
F(5, 16, 0, 0x1ffffff);
F(6, 19, 1, 0x3ffffff);
F(7, 22, 3, 0x1ffffff);
F(8, 25, 4, 0x3ffffff);
F(9, 28, 6, 0x1ffffff);
#undef F
}
#if (-32 >> 1) != -16
#error "This code only works when >> does sign-extension on negative numbers"
#endif
/* sword32_eq returns 0xffffffff iff a == b and zero otherwise. */
sword32 sword32_eq(sword32 a, sword32 b)
{
a = ~(a ^ b);
a &= a << 16;
a &= a << 8;
a &= a << 4;
a &= a << 2;
a &= a << 1;
return a >> 31;
}
/* sword32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
* both non-negative. */
sword32 sword32_gte(sword32 a, sword32 b)
{
a -= b;
/* a >= 0 iff a >= b. */
return ~(a >> 31);
}
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array.
*
* On entry: |input_limbs[i]| < 2^26 */
void fcontract(byte *output, limb *input_limbs)
{
int i, j;
sword32 input[10];
sword32 mask;
/* |input_limbs[i]| < 2^26, so it's valid to convert to an sword32. */
for (i = 0; i < 10; i++) {
input[i] = (sword32)input_limbs[i];
}
for (j = 0; j < 2; ++j) {
for (i = 0; i < 9; ++i) {
if ((i & 1) == 1) {
/* This calculation is a time-invariant way to make input[i]
* non-negative by borrowing from the next-larger limb. */
const sword32 mask = input[i] >> 31;
const sword32 carry = -((input[i] & mask) >> 25);
input[i] = input[i] + (carry << 25);
input[i+1] = input[i+1] - carry;
} else {
const sword32 mask = input[i] >> 31;
const sword32 carry = -((input[i] & mask) >> 26);
input[i] = input[i] + (carry << 26);
input[i+1] = input[i+1] - carry;
}
}
/* There's no greater limb for input[9] to borrow from, but we can multiply
* by 19 and borrow from input[0], which is valid mod 2^255-19. */
{
const sword32 mask = input[9] >> 31;
const sword32 carry = -((input[9] & mask) >> 25);
input[9] = input[9] + (carry << 25);
input[0] = input[0] - (carry * 19);
}
/* After the first iteration, input[1..9] are non-negative and fit within
* 25 or 26 bits, depending on position. However, input[0] may be
* negative. */
}
/* The first borrow-propagation pass above ended with every limb
except (possibly) input[0] non-negative.
If input[0] was negative after the first pass, then it was because of a
carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
In the second pass, each limb is decreased by at most one. Thus the second
borrow-propagation pass could only have wrapped around to decrease
input[0] again if the first pass left input[0] negative *and* input[1]
through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
and this last borrow-propagation step will leave input[1] non-negative. */
{
const sword32 mask = input[0] >> 31;
const sword32 carry = -((input[0] & mask) >> 26);
input[0] = input[0] + (carry << 26);
input[1] = input[1] - carry;
}
/* All input[i] are now non-negative. However, there might be values between
* 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */
for (j = 0; j < 2; j++) {
for (i = 0; i < 9; i++) {
if ((i & 1) == 1) {
const sword32 carry = input[i] >> 25;
input[i] &= 0x1ffffff;
input[i+1] += carry;
} else {
const sword32 carry = input[i] >> 26;
input[i] &= 0x3ffffff;
input[i+1] += carry;
}
}
{
const sword32 carry = input[9] >> 25;
input[9] &= 0x1ffffff;
input[0] += 19*carry;
}
}
/* If the first carry-chain pass, just above, ended up with a carry from
* input[9], and that caused input[0] to be out-of-bounds, then input[0] was
* < 2^26 + 2*19, because the carry was, at most, two.
*
* If the second pass carried from input[9] again then input[0] is < 2*19 and
* the input[9] -> input[0] carry didn't push input[0] out of bounds. */
/* It still remains the case that input might be between 2^255-19 and 2^255.
* In this case, input[1..9] must take their maximum value and input[0] must
* be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */
mask = sword32_gte(input[0], 0x3ffffed);
for (i = 1; i < 10; i++) {
if ((i & 1) == 1) {
mask &= sword32_eq(input[i], 0x1ffffff);
} else {
mask &= sword32_eq(input[i], 0x3ffffff);
}
}
/* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
* this conditionally subtracts 2^255-19. */
input[0] -= mask & 0x3ffffed;
for (i = 1; i < 10; i++) {
if ((i & 1) == 1) {
input[i] -= mask & 0x1ffffff;
} else {
input[i] -= mask & 0x3ffffff;
}
}
input[1] <<= 2;
input[2] <<= 3;
input[3] <<= 5;
input[4] <<= 6;
input[6] <<= 1;
input[7] <<= 3;
input[8] <<= 4;
input[9] <<= 6;
#define F(i, s) \
output[s+0] |= input[i] & 0xff; \
output[s+1] = (input[i] >> 8) & 0xff; \
output[s+2] = (input[i] >> 16) & 0xff; \
output[s+3] = (input[i] >> 24) & 0xff;
output[0] = 0;
output[16] = 0;
F(0,0);
F(1,3);
F(2,6);
F(3,9);
F(4,12);
F(5,16);
F(6,19);
F(7,22);
F(8,25);
F(9,28);
#undef F
}
/* Input: Q, Q', Q-Q'
* Output: 2Q, Q+Q'
*
* x2 z3: long form
* x3 z3: long form
* x z: short form, destroyed
* xprime zprime: short form, destroyed
* qmqp: short form, preserved
*
* On entry and exit, the absolute value of the limbs of all inputs and outputs
* are < 2^26. */
void fmonty(limb *x2, limb *z2, /* output 2Q */
limb *x3, limb *z3, /* output Q + Q' */
limb *x, limb *z, /* input Q */
limb *xprime, limb *zprime, /* input Q' */
const limb *qmqp /* input Q - Q' */)
{
limb origx[10], origxprime[10], zzz[19], xx[19], zz[19];
limb xxprime[19], zzprime[19], zzzprime[19], xxxprime[19];
memcpy(origx, x, 10 * sizeof(limb));
fsum(x, z);
/* |x[i]| < 2^27 */
fdifference(z, origx); /* does x - z */
/* |z[i]| < 2^27 */
memcpy(origxprime, xprime, sizeof(limb) * 10);
fsum(xprime, zprime);
/* |xprime[i]| < 2^27 */
fdifference(zprime, origxprime);
/* |zprime[i]| < 2^27 */
fproduct(xxprime, xprime, z);
/* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
* 2^(27+27) and fproduct adds together, at most, 14 of those products.
* (Approximating that to 2^58 doesn't work out.) */
fproduct(zzprime, x, zprime);
/* |zzprime[i]| < 14*2^54 */
freduce_degree(xxprime);
freduce_coefficients(xxprime);
/* |xxprime[i]| < 2^26 */
freduce_degree(zzprime);
freduce_coefficients(zzprime);
/* |zzprime[i]| < 2^26 */
memcpy(origxprime, xxprime, sizeof(limb) * 10);
fsum(xxprime, zzprime);
/* |xxprime[i]| < 2^27 */
fdifference(zzprime, origxprime);
/* |zzprime[i]| < 2^27 */
fsquare(xxxprime, xxprime);
/* |xxxprime[i]| < 2^26 */
fsquare(zzzprime, zzprime);
/* |zzzprime[i]| < 2^26 */
fproduct(zzprime, zzzprime, qmqp);
/* |zzprime[i]| < 14*2^52 */
freduce_degree(zzprime);
freduce_coefficients(zzprime);
/* |zzprime[i]| < 2^26 */
memcpy(x3, xxxprime, sizeof(limb) * 10);
memcpy(z3, zzprime, sizeof(limb) * 10);
fsquare(xx, x);
/* |xx[i]| < 2^26 */
fsquare(zz, z);
/* |zz[i]| < 2^26 */
fproduct(x2, xx, zz);
/* |x2[i]| < 14*2^52 */
freduce_degree(x2);
freduce_coefficients(x2);
/* |x2[i]| < 2^26 */
fdifference(zz, xx); // does zz = xx - zz
/* |zz[i]| < 2^27 */
memset(zzz + 10, 0, sizeof(limb) * 9);
fscalar_product(zzz, zz, 121665);
/* |zzz[i]| < 2^(27+17) */
/* No need to call freduce_degree here:
fscalar_product doesn't increase the degree of its input. */
freduce_coefficients(zzz);
/* |zzz[i]| < 2^26 */
fsum(zzz, xx);
/* |zzz[i]| < 2^27 */
fproduct(z2, zz, zzz);
/* |z2[i]| < 14*2^(26+27) */
freduce_degree(z2);
freduce_coefficients(z2);
/* |z2|i| < 2^26 */
}
/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
* them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
* side-channel attacks.
*
* NOTE that this function requires that 'iswap' be 1 or 0; other values give
* wrong results. Also, the two limb arrays must be in reduced-coefficient,
* reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
* and all all values in a[0..9],b[0..9] must have magnitude less than
* INT32_MAX. */
void swap_conditional(limb a[19], limb b[19], limb iswap)
{
const sword32 swap = (sword32) -iswap;
for (unsigned int i = 0; i < 10; ++i) {
const sword32 x = swap & ( ((sword32)a[i]) ^ ((sword32)b[i]) );
a[i] = ((sword32)a[i]) ^ x;
b[i] = ((sword32)b[i]) ^ x;
}
}
/* Calculates nQ where Q is the x-coordinate of a point on the curve
*
* resultx/resultz: the x coordinate of the resulting curve point (short form)
* n: a little endian, 32-byte number
* q: a point of the curve (short form) */
void
cmult(limb *resultx, limb *resultz, const byte *n, const limb *q)
{
limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
memcpy(nqpqx, q, sizeof(limb) * 10);
for (unsigned int i = 0; i < 32; ++i) {
byte b = n[31 - i];
for (unsigned int j = 0; j < 8; ++j) {
const limb bit = b >> 7;
swap_conditional(nqx, nqpqx, bit);
swap_conditional(nqz, nqpqz, bit);
fmonty(nqx2, nqz2,
nqpqx2, nqpqz2,
nqx, nqz,
nqpqx, nqpqz,
q);
swap_conditional(nqx2, nqpqx2, bit);
swap_conditional(nqz2, nqpqz2, bit);
t = nqx;
nqx = nqx2;
nqx2 = t;
t = nqz;
nqz = nqz2;
nqz2 = t;
t = nqpqx;
nqpqx = nqpqx2;
nqpqx2 = t;
t = nqpqz;
nqpqz = nqpqz2;
nqpqz2 = t;
b <<= 1;
}
}
memcpy(resultx, nqx, sizeof(limb) * 10);
memcpy(resultz, nqz, sizeof(limb) * 10);
}
// -----------------------------------------------------------------------------
// Shamelessly copied from djb's code
// -----------------------------------------------------------------------------
void crecip(limb *out, const limb *z)
{
limb z2[10];
limb z9[10];
limb z11[10];
limb z2_5_0[10];
limb z2_10_0[10];
limb z2_20_0[10];
limb z2_50_0[10];
limb z2_100_0[10];
limb t0[10];
limb t1[10];
int i;
/* 2 */ fsquare(z2,z);
/* 4 */ fsquare(t1,z2);
/* 8 */ fsquare(t0,t1);
/* 9 */ fmul(z9,t0,z);
/* 11 */ fmul(z11,z9,z2);
/* 22 */ fsquare(t0,z11);
/* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
/* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
/* 2^7 - 2^2 */ fsquare(t1,t0);
/* 2^8 - 2^3 */ fsquare(t0,t1);
/* 2^9 - 2^4 */ fsquare(t1,t0);
/* 2^10 - 2^5 */ fsquare(t0,t1);
/* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
/* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
/* 2^12 - 2^2 */ fsquare(t1,t0);
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
/* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
/* 2^22 - 2^2 */ fsquare(t1,t0);
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
/* 2^41 - 2^1 */ fsquare(t1,t0);
/* 2^42 - 2^2 */ fsquare(t0,t1);
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
/* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
/* 2^52 - 2^2 */ fsquare(t1,t0);
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
/* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
/* 2^102 - 2^2 */ fsquare(t0,t1);
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
/* 2^201 - 2^1 */ fsquare(t0,t1);
/* 2^202 - 2^2 */ fsquare(t1,t0);
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
/* 2^251 - 2^1 */ fsquare(t1,t0);
/* 2^252 - 2^2 */ fsquare(t0,t1);
/* 2^253 - 2^3 */ fsquare(t1,t0);
/* 2^254 - 2^4 */ fsquare(t0,t1);
/* 2^255 - 2^5 */ fsquare(t1,t0);
/* 2^255 - 21 */ fmul(out,t1,z11);
}
ANONYMOUS_NAMESPACE_END
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
int curve25519(byte pubkey[32], const byte seckey[32], const byte basepoint[32])
{
limb bp[10], x[10], z[11], zmone[10];
byte e[32]; int i;
for (i = 0; i < 32; ++i)
e[i] = seckey[i];
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
fexpand(bp, basepoint);
cmult(x, z, e, bp);
crecip(zmone, z);
fmul(z, x, zmone);
fcontract(pubkey, z);
return 0;
}
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_32BIT

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// donna_64.cpp - written and placed in public domain by Jeffrey Walton
// This is a port of Adam Langley's curve25519-donna
// located at https://github.com/agl/curve25519-donna
/* Copyright 2008, Google Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following disclaimer
* in the documentation and/or other materials provided with the
* distribution.
* * Neither the name of Google Inc. nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* curve25519-donna: Curve25519 elliptic curve, public key function
*
* http://code.google.com/p/curve25519-donna/
*
* Adam Langley <agl@imperialviolet.org>
*
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
*
* More information about curve25519 can be found here
* http://cr.yp.to/ecdh.html
*
* djb's sample implementation of curve25519 is written in a special assembly
* language called qhasm and uses the floating point registers.
*
* This is, almost, a clean room reimplementation from the curve25519 paper. It
* uses many of the tricks described therein. Only the crecip function is taken
* from the sample implementation. */
#include "pch.h"
#include "config.h"
#include "donna.h"
#include "stdcpp.h"
// This macro is not in a header like config.h because
// we don't want it exposed to user code. We also need
// a standard header like <stdint.h> or <stdef.h>.
// Langley uses uint128_t in the 64-bit code paths so
// we further restrict 64-bit code.
#if (UINTPTR_MAX == 0xffffffff) || !defined(CRYPTOPP_WORD128_AVAILABLE)
# define CRYPTOPP_32BIT 1
#else
# define CRYPTOPP_64BIT 1
#endif
// Squash MS LNK4221 and libtool warnings
extern const char DONNA64_FNAME[] = __FILE__;
#if defined(CRYPTOPP_64BIT)
ANONYMOUS_NAMESPACE_BEGIN
using std::memcpy;
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::word64;
using CryptoPP::sword32;
using CryptoPP::sword64;
using CryptoPP::word128;
typedef word64 limb;
typedef limb felem[5];
// This is a special gcc mode for 128-bit integers. It's implemented on 64-bit
// platforms only as far as I know.
//typedef unsigned uint128_t __attribute__((mode(TI)));
/* Sum two numbers: output += in */
inline void fsum(limb *output, const limb *in)
{
output[0] += in[0];
output[1] += in[1];
output[2] += in[2];
output[3] += in[3];
output[4] += in[4];
}
/* Find the difference of two numbers: output = in - output
* (note the order of the arguments!)
*
* Assumes that out[i] < 2**52
* On return, out[i] < 2**55
*/
inline void fdifference_backwards(felem out, const felem in)
{
/* 152 is 19 << 3 */
const limb two54m152 = (((limb)1) << 54) - 152;
const limb two54m8 = (((limb)1) << 54) - 8;
out[0] = in[0] + two54m152 - out[0];
out[1] = in[1] + two54m8 - out[1];
out[2] = in[2] + two54m8 - out[2];
out[3] = in[3] + two54m8 - out[3];
out[4] = in[4] + two54m8 - out[4];
}
/* Multiply a number by a scalar: output = in * scalar */
inline void fscalar_product(felem output, const felem in, const limb scalar)
{
word128 a;
a = ((word128) in[0]) * scalar;
output[0] = ((limb)a) & 0x7ffffffffffff;
a = ((word128) in[1]) * scalar + ((limb) (a >> 51));
output[1] = ((limb)a) & 0x7ffffffffffff;
a = ((word128) in[2]) * scalar + ((limb) (a >> 51));
output[2] = ((limb)a) & 0x7ffffffffffff;
a = ((word128) in[3]) * scalar + ((limb) (a >> 51));
output[3] = ((limb)a) & 0x7ffffffffffff;
a = ((word128) in[4]) * scalar + ((limb) (a >> 51));
output[4] = ((limb)a) & 0x7ffffffffffff;
output[0] += (a >> 51) * 19;
}
/* Multiply two numbers: output = in2 * in
*
* output must be distinct to both inputs. The inputs are reduced coefficient
* form, the output is not.
*
* Assumes that in[i] < 2**55 and likewise for in2.
* On return, output[i] < 2**52
*/
inline void fmul(felem output, const felem in2, const felem in)
{
word128 t[5];
limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
r0 = in[0];
r1 = in[1];
r2 = in[2];
r3 = in[3];
r4 = in[4];
s0 = in2[0];
s1 = in2[1];
s2 = in2[2];
s3 = in2[3];
s4 = in2[4];
t[0] = ((word128) r0) * s0;
t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
r4 *= 19;
r1 *= 19;
r2 *= 19;
r3 *= 19;
t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
t[3] += ((word128) r4) * s4;
r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
r2 += c;
output[0] = r0;
output[1] = r1;
output[2] = r2;
output[3] = r3;
output[4] = r4;
}
inline void fsquare_times(felem output, const felem in, limb count)
{
word128 t[5];
limb r0,r1,r2,r3,r4,c;
limb d0,d1,d2,d4,d419;
r0 = in[0];
r1 = in[1];
r2 = in[2];
r3 = in[3];
r4 = in[4];
do {
d0 = r0 * 2;
d1 = r1 * 2;
d2 = r2 * 2 * 19;
d419 = r4 * 19;
d4 = d419 * 2;
t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
r2 += c;
} while(--count);
output[0] = r0;
output[1] = r1;
output[2] = r2;
output[3] = r3;
output[4] = r4;
}
/* Load a little-endian 64-bit number */
limb load_limb(const byte *in)
{
return
((limb)in[0]) |
(((limb)in[1]) << 8) |
(((limb)in[2]) << 16) |
(((limb)in[3]) << 24) |
(((limb)in[4]) << 32) |
(((limb)in[5]) << 40) |
(((limb)in[6]) << 48) |
(((limb)in[7]) << 56);
}
void store_limb(byte *out, limb in)
{
out[0] = in & 0xff;
out[1] = (in >> 8) & 0xff;
out[2] = (in >> 16) & 0xff;
out[3] = (in >> 24) & 0xff;
out[4] = (in >> 32) & 0xff;
out[5] = (in >> 40) & 0xff;
out[6] = (in >> 48) & 0xff;
out[7] = (in >> 56) & 0xff;
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
void fexpand(limb *output, const byte *in)
{
output[0] = load_limb(in) & 0x7ffffffffffff;
output[1] = (load_limb(in+6) >> 3) & 0x7ffffffffffff;
output[2] = (load_limb(in+12) >> 6) & 0x7ffffffffffff;
output[3] = (load_limb(in+19) >> 1) & 0x7ffffffffffff;
output[4] = (load_limb(in+24) >> 12) & 0x7ffffffffffff;
}
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array
*/
void fcontract(byte *output, const felem input)
{
word128 t[5];
t[0] = input[0];
t[1] = input[1];
t[2] = input[2];
t[3] = input[3];
t[4] = input[4];
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
/* now t is between 0 and 2^255-1, properly carried. */
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
t[0] += 19;
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
t[0] += 0x8000000000000 - 19;
t[1] += 0x8000000000000 - 1;
t[2] += 0x8000000000000 - 1;
t[3] += 0x8000000000000 - 1;
t[4] += 0x8000000000000 - 1;
/* now between 2^255 and 2^256-20, and offset by 2^255. */
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[4] &= 0x7ffffffffffff;
store_limb(output, t[0] | (t[1] << 51));
store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
}
/* Input: Q, Q', Q-Q'
* Output: 2Q, Q+Q'
*
* x2 z3: long form
* x3 z3: long form
* x z: short form, destroyed
* xprime zprime: short form, destroyed
* qmqp: short form, preserved
*/
void fmonty(limb *x2, limb *z2, /* output 2Q */
limb *x3, limb *z3, /* output Q + Q' */
limb *x, limb *z, /* input Q */
limb *xprime, limb *zprime, /* input Q' */
const limb *qmqp /* input Q - Q' */)
{
limb origx[5], origxprime[5], zzz[5], xx[5], zz[5];
limb xxprime[5], zzprime[5], zzzprime[5];
memcpy(origx, x, 5 * sizeof(limb));
fsum(x, z);
fdifference_backwards(z, origx); // does x - z
memcpy(origxprime, xprime, sizeof(limb) * 5);
fsum(xprime, zprime);
fdifference_backwards(zprime, origxprime);
fmul(xxprime, xprime, z);
fmul(zzprime, x, zprime);
memcpy(origxprime, xxprime, sizeof(limb) * 5);
fsum(xxprime, zzprime);
fdifference_backwards(zzprime, origxprime);
fsquare_times(x3, xxprime, 1);
fsquare_times(zzzprime, zzprime, 1);
fmul(z3, zzzprime, qmqp);
fsquare_times(xx, x, 1);
fsquare_times(zz, z, 1);
fmul(x2, xx, zz);
fdifference_backwards(zz, xx); // does zz = xx - zz
fscalar_product(zzz, zz, 121665);
fsum(zzz, xx);
fmul(z2, zz, zzz);
}
// -----------------------------------------------------------------------------
// Maybe swap the contents of two limb arrays (@a and @b), each @len elements
// long. Perform the swap iff @swap is non-zero.
//
// This function performs the swap without leaking any side-channel
// information.
// -----------------------------------------------------------------------------
void swap_conditional(limb a[5], limb b[5], limb iswap)
{
const limb swap = -iswap;
for (unsigned int i = 0; i < 5; ++i) {
const limb x = swap & (a[i] ^ b[i]);
a[i] ^= x;
b[i] ^= x;
}
}
/* Calculates nQ where Q is the x-coordinate of a point on the curve
*
* resultx/resultz: the x coordinate of the resulting curve point (short form)
* n: a little endian, 32-byte number
* q: a point of the curve (short form)
*/
void cmult(limb *resultx, limb *resultz, const byte *n, const limb *q)
{
limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
memcpy(nqpqx, q, sizeof(limb) * 5);
for (unsigned int i = 0; i < 32; ++i) {
byte b = n[31 - i];
for (unsigned int j = 0; j < 8; ++j) {
const limb bit = b >> 7;
swap_conditional(nqx, nqpqx, bit);
swap_conditional(nqz, nqpqz, bit);
fmonty(nqx2, nqz2,
nqpqx2, nqpqz2,
nqx, nqz,
nqpqx, nqpqz,
q);
swap_conditional(nqx2, nqpqx2, bit);
swap_conditional(nqz2, nqpqz2, bit);
t = nqx;
nqx = nqx2;
nqx2 = t;
t = nqz;
nqz = nqz2;
nqz2 = t;
t = nqpqx;
nqpqx = nqpqx2;
nqpqx2 = t;
t = nqpqz;
nqpqz = nqpqz2;
nqpqz2 = t;
b <<= 1;
}
}
memcpy(resultx, nqx, sizeof(limb) * 5);
memcpy(resultz, nqz, sizeof(limb) * 5);
}
// -----------------------------------------------------------------------------
// Shamelessly copied from djb's code, tightened a little
// -----------------------------------------------------------------------------
void crecip(felem out, const felem z)
{
felem a,t0,b,c;
/* 2 */ fsquare_times(a, z, 1); // a = 2
/* 8 */ fsquare_times(t0, a, 2);
/* 9 */ fmul(b, t0, z); // b = 9
/* 11 */ fmul(a, b, a); // a = 11
/* 22 */ fsquare_times(t0, a, 1);
/* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
/* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
/* 2^10 - 2^0 */ fmul(b, t0, b);
/* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
/* 2^20 - 2^0 */ fmul(c, t0, b);
/* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
/* 2^40 - 2^0 */ fmul(t0, t0, c);
/* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
/* 2^50 - 2^0 */ fmul(b, t0, b);
/* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
/* 2^100 - 2^0 */ fmul(c, t0, b);
/* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
/* 2^200 - 2^0 */ fmul(t0, t0, c);
/* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
/* 2^250 - 2^0 */ fmul(t0, t0, b);
/* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
/* 2^255 - 21 */ fmul(out, t0, a);
}
ANONYMOUS_NAMESPACE_END
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
int curve25519(byte pubkey[32], const byte seckey[32], const byte basepoint[32])
{
limb bp[5], x[5], z[5], zmone[5];
uint8_t e[32];
int i;
for (i = 0;i < 32;++i)
e[i] = seckey[i];
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
fexpand(bp, basepoint);
cmult(x, z, e, bp);
crecip(zmone, z);
fmul(z, x, zmone);
fcontract(pubkey, z);
return 0;
}
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_64BIT

7
test.cpp
View File

@ -829,9 +829,10 @@ bool Validate(int alg, bool thorough, const char *seedInput)
case 12: result = ValidateThreeWay(); break;
case 13: result = ValidateBBS(); break;
case 14: result = ValidateDH(); break;
case 15: result = ValidateRSA(); break;
case 16: result = ValidateElGamal(); break;
case 17: result = ValidateDSA(thorough); break;
case 15: result = ValidateX25519(); break;
case 16: result = ValidateRSA(); break;
case 17: result = ValidateElGamal(); break;
case 18: result = ValidateDSA(thorough); break;
// case 18: result = ValidateHAVAL(); break;
case 19: result = ValidateSAFER(); break;
case 20: result = ValidateLUC(); break;

80
validat0.cpp
View File

@ -21,6 +21,11 @@
#include "gzip.h"
#include "zlib.h"
//curve25519
#include "xed25519.h"
#include "donna.h"
#include "naclite.h"
#include <iostream>
#include <iomanip>
#include <sstream>
@ -41,12 +46,11 @@ NAMESPACE_BEGIN(Test)
// Issue 64: "PolynomialMod2::operator<<=", http://github.com/weidai11/cryptopp/issues/64
bool TestPolynomialMod2()
{
std::cout << "\nTesting PolynomialMod2 bit operations...\n\n";
bool pass1 = true, pass2 = true, pass3 = true;
std::cout << "\nTesting PolynomialMod2 bit operations...\n\n";
static const unsigned int start = 0;
static const unsigned int stop = 4 * WORD_BITS + 1;
const unsigned int start = 0;
const unsigned int stop = 4 * WORD_BITS + 1;
for (unsigned int i = start; i < stop; i++)
{
@ -424,10 +428,54 @@ bool TestCompressors()
return !fail1 && !fail2 && !fail3;
}
bool TestCurve25519()
{
std::cout << "\nTesting curve25519 Key Agreements...\n\n";
const unsigned int AGREE_COUNT = 64;
bool pass = true;
SecByteBlock priv1(32), priv2(32), pub1(32), pub2(32), share1(32), share2(32);
for (unsigned int i=0; i<AGREE_COUNT; ++i)
{
// Langley's curve25519-donna
GlobalRNG().GenerateBlock(priv1, priv1.size());
GlobalRNG().GenerateBlock(priv2, priv2.size());
priv1[0] &= 248; priv1[31] &= 127; priv1[31] |= 64;
priv2[0] &= 248; priv2[31] &= 127; priv2[31] |= 64;
const byte base[32] = {9};
Donna::curve25519(pub1, priv1, base);
Donna::curve25519(pub2, priv2, base);
int ret1 = Donna::curve25519(share1, priv1, pub2);
int ret2 = Donna::curve25519(share2, priv2, pub1);
int ret3 = std::memcmp(share1, share2, 32);
// Bernstein's Tweet NaCl
NaCl::crypto_box_keypair(pub2, priv2);
int ret4 = Donna::curve25519(share1, priv1, pub2);
int ret5 = NaCl::crypto_scalarmult(share2, priv2, pub1);
int ret6 = std::memcmp(share1, share2, 32);
bool fail = ret1 != 0 || ret2 != 0 || ret3 != 0 || ret4 != 0 || ret5 != 0 || ret6 != 0;
pass = pass && !fail;
}
if (pass)
std::cout << "passed:";
else
std::cout << "FAILED:";
std::cout << " " << AGREE_COUNT << " key agreements" << std::endl;
return pass;
}
bool TestEncryptors()
{
std::cout << "\nTesting Default Encryptors and Decryptors...\n\n";
static const unsigned int ENCRYPT_COUNT = 64, ENCRYPT_MAC_COUNT = 64;
const unsigned int ENCRYPT_COUNT = 64, ENCRYPT_MAC_COUNT = 64;
bool fail0 = false, fail1 = false, fail2 = false, fail3 = false, fail4 = false;
// **************************************************************
@ -440,7 +488,7 @@ bool TestEncryptors()
// This data was generated with Crypto++ 5.6.2
//StringSource(message, true, new LegacyEncryptorWithMAC(password.c_str(), new FileSink("TestData/defdmac1.bin")));
FileSource("TestData/defdmac1.bin", true, new LegacyDecryptorWithMAC(password.c_str(), new StringSink(recovered)));
FileSource(DataDir("TestData/defdmac1.bin").c_str(), true, new LegacyDecryptorWithMAC(password.c_str(), new StringSink(recovered)));
if (message != recovered)
throw Exception(Exception::OTHER_ERROR, "LegacyDecryptorWithMAC failed a self test");
@ -449,7 +497,7 @@ bool TestEncryptors()
// This data was generated with Crypto++ 6.0
//StringSource(message, true, new DefaultEncryptorWithMAC(password.c_str(), new FileSink("TestData/defdmac2.bin")));
FileSource("TestData/defdmac2.bin", true, new DefaultDecryptorWithMAC(password.c_str(), new StringSink(recovered)));
FileSource(DataDir("TestData/defdmac2.bin").c_str(), true, new DefaultDecryptorWithMAC(password.c_str(), new StringSink(recovered)));
if (message != recovered)
throw Exception(Exception::OTHER_ERROR, "DefaultDecryptorWithMAC failed a self test");
}
@ -658,9 +706,9 @@ bool TestEncryptors()
bool TestSharing()
{
std::cout << "\nInformation Dispersal and Secret Sharing...\n\n";
static const unsigned int INFORMATION_SHARES = 64;
static const unsigned int SECRET_SHARES = 64;
static const unsigned int CHID_LENGTH = 4;
const unsigned int INFORMATION_SHARES = 64;
const unsigned int SECRET_SHARES = 64;
const unsigned int CHID_LENGTH = 4;
bool pass=true, fail=false;
// ********** Infrmation Dispersal **********//
@ -1337,7 +1385,7 @@ bool TestASN1Parse()
// All the types Crypto++ recognizes.
// "C" is one content octet with value 0x43.
static const ASN1_TestTuple bitStrings[] =
const ASN1_TestTuple bitStrings[] =
{
// The first "\x00" content octet is the "initial octet" representing unused bits. In the
// primitive encoding form, there may be zero, one or more contents after the initial octet.
@ -1364,7 +1412,7 @@ bool TestASN1Parse()
pass = RunASN1TestSet(bitStrings, COUNTOF(bitStrings)) && pass;
static const ASN1_TestTuple octetStrings[] =
const ASN1_TestTuple octetStrings[] =
{
// In the primitive encoding form, there may be zero, one or more contents.
{ACCEPT, OCTET_STRING, "OCTET_STRING", "\x04\x00", 2}, // definite length, short form, zero content octets
@ -1391,7 +1439,7 @@ bool TestASN1Parse()
pass = RunASN1TestSet(octetStrings, COUNTOF(octetStrings)) && pass;
static const ASN1_TestTuple utf8Strings[] =
const ASN1_TestTuple utf8Strings[] =
{
{ACCEPT, UTF8_STRING, "UTF8_STRING", "\x0c\x00", 2}, // definite length, short form, zero content octets
{ACCEPT, UTF8_STRING, "UTF8_STRING", "\x0c\x01" "C", 3}, // definite length, short form, expected content octets
@ -1417,7 +1465,7 @@ bool TestASN1Parse()
pass = RunASN1TestSet(utf8Strings, COUNTOF(utf8Strings)) && pass;
static const ASN1_TestTuple printableStrings[] =
const ASN1_TestTuple printableStrings[] =
{
{ACCEPT, PRINTABLE_STRING, "PRINTABLE_STRING", "\x13\x00", 2}, // definite length, short form, zero content octets
{ACCEPT, PRINTABLE_STRING, "PRINTABLE_STRING", "\x13\x01" "C", 3}, // definite length, short form, expected content octets
@ -1443,7 +1491,7 @@ bool TestASN1Parse()
pass = RunASN1TestSet(printableStrings, COUNTOF(printableStrings)) && pass;
static const ASN1_TestTuple ia5Strings[] =
const ASN1_TestTuple ia5Strings[] =
{
{ACCEPT, IA5_STRING, "IA5_STRING", "\x16\x00", 2}, // definite length, short form, zero content octets
{ACCEPT, IA5_STRING, "IA5_STRING", "\x16\x01" "C", 3}, // definite length, short form, expected content octets
@ -1469,7 +1517,7 @@ bool TestASN1Parse()
pass = RunASN1TestSet(ia5Strings, COUNTOF(ia5Strings)) && pass;
static const ASN1_TestTuple integerValues[] =
const ASN1_TestTuple integerValues[] =
{
// 8.3.1 The encoding of an integer value shall be primitive. The contents octets shall consist of one or more octets.
{REJECT, INTEGER, "INTEGER", "\x02\x00", 2}, // definite length, short form, zero content octets

2
validat3.cpp
View File

@ -87,6 +87,7 @@ bool ValidateAll(bool thorough)
pass=TestCompressors() && pass;
pass=TestSharing() && pass;
pass=TestEncryptors() && pass;
pass=TestCurve25519() && pass;
#endif
pass=ValidateCRC32() && pass;
@ -170,6 +171,7 @@ bool ValidateAll(bool thorough)
pass=ValidateBBS() && pass;
pass=ValidateDH() && pass;
pass=ValidateX25519() && pass;
pass=ValidateMQV() && pass;
pass=ValidateHMQV() && pass;
pass=ValidateFHMQV() && pass;

10
validat7.cpp
View File

@ -22,6 +22,7 @@
#include "xtr.h"
#include "hmqv.h"
#include "pubkey.h"
#include "xed25519.h"
#include "xtrcrypt.h"
#include "eccrypto.h"
@ -50,6 +51,15 @@ bool ValidateDH()
return SimpleKeyAgreementValidate(dh);
}
bool ValidateX25519()
{
std::cout << "\nx25519 validation suite running...\n\n";
FileSource f(DataDir("TestData/x25519.dat").c_str(), true, new HexDecoder);
x25519 dh(f);
return SimpleKeyAgreementValidate(dh);
}
bool ValidateMQV()
{
std::cout << "\nMQV validation suite running...\n\n";

2
validate.h
View File

@ -109,6 +109,7 @@ bool ValidateCMAC();
bool ValidateBBS();
bool ValidateDH();
bool ValidateX25519();
bool ValidateMQV();
bool ValidateHMQV();
bool ValidateFHMQV();
@ -160,6 +161,7 @@ bool TestStringSink();
// Additional tests due to no coverage
bool TestCompressors();
bool TestEncryptors();
bool TestCurve25519();
bool TestMersenne();
bool TestSharing();
# if defined(CRYPTOPP_ALTIVEC_AVAILABLE)

143
xed25519.cpp Normal file
View File

@ -0,0 +1,143 @@
// xed25519_32.cpp - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Adam
// Langley's curve25519-donna.
#include "pch.h"
#include "cryptlib.h"
#include "asn.h"
#include "integer.h"
#include "filters.h"
#include "xed25519.h"
#include "donna.h"
NAMESPACE_BEGIN(CryptoPP)
x25519::x25519(const byte y[32], const byte x[32])
{
std::memcpy(m_pk, y, 32);
std::memcpy(m_sk, x, 32);
}
x25519::x25519(const Integer &y, const Integer &x)
{
ArraySink ys(m_pk, 32);
y.Encode(ys, 32);
ArraySink xs(m_sk, 32);
x.Encode(xs, 32);
}
x25519::x25519(RandomNumberGenerator &rng)
{
GeneratePrivateKey(rng, m_sk);
GeneratePublicKey(NullRNG(), m_sk, m_pk);
}
x25519::x25519(BufferedTransformation &params)
{
// TODO: Fix the on-disk format once we know what it is.
BERSequenceDecoder seq(params);
BERGeneralDecoder x(seq, BIT_STRING);
if (!x.IsDefiniteLength() || x.MaxRetrievable() < 32)
BERDecodeError();
x.Get(m_sk, 32);
x.MessageEnd();
BERGeneralDecoder y(seq, OCTET_STRING);
if (!y.IsDefiniteLength() || y.MaxRetrievable() < 32)
BERDecodeError();
y.Get(m_pk, 32);
y.MessageEnd();
seq.MessageEnd();
}
void x25519::DEREncode(BufferedTransformation &params) const
{
// TODO: Fix the on-disk format once we know what it is.
DERSequenceEncoder seq(params);
DERSequenceEncoder x(seq, BIT_STRING);
x.Put(m_sk, 32);
x.MessageEnd();
DERSequenceEncoder y(seq, OCTET_STRING);
y.Put(m_pk, 32);
y.MessageEnd();
seq.MessageEnd();
}
bool x25519::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
CRYPTOPP_UNUSED(rng);
CRYPTOPP_UNUSED(level);
// TODO: add weak keys test
return true;
}
bool x25519::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
if (valueType == typeid(ConstByteArrayParameter))
{
if (std::strcmp(name, "SecretKey") == 0)
{
std::memcpy(pValue, m_sk, 32);
return true;
}
else if (std::strcmp(name, "PublicKey") == 0)
{
std::memcpy(pValue, m_pk, 32);
return true;
}
}
return false;
}
void x25519::AssignFrom(const NameValuePairs &source)
{
ConstByteArrayParameter val;
if (source.GetValue("SecretKey", val))
{
std::memcpy(m_sk, val.begin(), 32);
}
else if (source.GetValue("PublicKey", val))
{
std::memcpy(m_pk, val.begin(), 32);
}
}
void x25519::GeneratePrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
{
rng.GenerateBlock(privateKey, 32);
privateKey[0] &= 248;
privateKey[31] &= 127;
privateKey[31] |= 64;
}
void x25519::GeneratePublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
{
CRYPTOPP_UNUSED(rng);
const byte base[32] = {9};
(void)Donna::curve25519(publicKey, privateKey, base);
}
bool x25519::Agree(byte *agreedValue, const byte *privateKey, const byte *otherPublicKey, bool validateOtherPublicKey) const
{
CRYPTOPP_ASSERT(agreedValue != NULLPTR);
CRYPTOPP_ASSERT(otherPublicKey != NULLPTR);
if (validateOtherPublicKey && Validate(NullRNG(), 3) == false)
return false;
return Donna::curve25519(agreedValue, privateKey, otherPublicKey) == 0;
}
NAMESPACE_END // CryptoPP

44
xed25519.h Normal file
View File

@ -0,0 +1,44 @@
// xed25519.h - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Adam
// Langley's curve25519-donna.
#ifndef CRYPTOPP_XED25519_H
#define CRYPTOPP_XED25519_H
#include "cryptlib.h"
#include "algparam.h"
NAMESPACE_BEGIN(CryptoPP)
class Integer;
/// \brief x25519 with key validation
class x25519 : public SimpleKeyAgreementDomain, public CryptoParameters
{
public:
x25519(const byte y[32], const byte x[32]);
x25519(const Integer &y, const Integer &x);
x25519(RandomNumberGenerator &rng);
x25519(BufferedTransformation &params);
void DEREncode(BufferedTransformation &params) const;
bool Validate(RandomNumberGenerator &rng, unsigned int level) const;
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const;
void AssignFrom(const NameValuePairs &source);
CryptoParameters & AccessCryptoParameters() {return *this;}
unsigned int AgreedValueLength() const {return 32;}
unsigned int PrivateKeyLength() const {return 32;}
unsigned int PublicKeyLength() const {return 32;}
void GeneratePrivateKey(RandomNumberGenerator &rng, byte *privateKey) const;
void GeneratePublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const;
bool Agree(byte *agreedValue, const byte *privateKey, const byte *otherPublicKey, bool validateOtherPublicKey=true) const;
private:
FixedSizeSecBlock<byte, 32> m_sk, m_pk;
};
NAMESPACE_END // CryptoPP
#endif // CRYPTOPP_XED25519_H