arne
/
cryptopp
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Implmented Bernstein\'s Tweaked Roots for Rabin-Williams signatures. Thanks to Evgeny Sidorov for suggesting it

reviewable/pr7/r1
Jeffrey Walton 2015-07-02 17:41:19 -04:00
parent 70bddb83ef
commit 260810ce63
2 changed files with 122 additions and 25 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

129
rw.cpp
View File

@ -5,8 +5,14 @@
#include "nbtheory.h"
#include "asn.h"
#ifndef NDEBUG
# include <cassert>
#endif
#ifndef CRYPTOPP_IMPORTS
static const bool CRYPTOPP_RW_USE_OMP = false;
NAMESPACE_BEGIN(CryptoPP)
void RWFunction::BERDecode(BufferedTransformation &bt)
@ -99,6 +105,55 @@ void InvertibleRWFunction::GenerateRandom(RandomNumberGenerator &rng, const Name
m_n = m_p * m_q;
m_u = m_q.InverseMod(m_p);
Precompute();
}
void InvertibleRWFunction::Initialize(const Integer &n, const Integer &p, const Integer &q, const Integer &u)
{
m_n = n; m_p = p; m_q = q; m_u = u;
Precompute();
}
void InvertibleRWFunction::PrecomputeTweakedRoots() const
{
ModularArithmetic modp(m_p), modq(m_q);
#pragma omp parallel sections if(CRYPTOPP_RW_USE_OMP)
{
#pragma omp section
m_pre_2_9p = modp.Exponentiate(2, (9 * m_p - 11)/8);
#pragma omp section
m_pre_2_3q = modq.Exponentiate(2, (3 * m_q - 5)/8);
#pragma omp section
m_pre_q_p = modp.Exponentiate(m_q, m_p - 2);
}
m_precompute = true;
}
void InvertibleRWFunction::LoadPrecomputation(BufferedTransformation &bt)
{
BERSequenceDecoder seq(bt);
m_pre_2_9p.BERDecode(seq);
m_pre_2_3q.BERDecode(seq);
m_pre_q_p.BERDecode(seq);
seq.MessageEnd();
m_precompute = true;
}
void InvertibleRWFunction::SavePrecomputation(BufferedTransformation &bt) const
{
if(!m_precompute)
Precompute();
DERSequenceEncoder seq(bt);
m_pre_2_9p.DEREncode(seq);
m_pre_2_3q.DEREncode(seq);
m_pre_q_p.DEREncode(seq);
seq.MessageEnd();
}
void InvertibleRWFunction::BERDecode(BufferedTransformation &bt)
@ -109,6 +164,8 @@ void InvertibleRWFunction::BERDecode(BufferedTransformation &bt)
m_q.BERDecode(seq);
m_u.BERDecode(seq);
seq.MessageEnd();
m_precompute = false;
}
void InvertibleRWFunction::DEREncode(BufferedTransformation &bt) const
@ -121,46 +178,70 @@ void InvertibleRWFunction::DEREncode(BufferedTransformation &bt) const
seq.MessageEnd();
}
// DJB's "RSA signatures and Rabin-Williams signatures..." (http://cr.yp.to/sigs/rwsota-20080131.pdf).
Integer InvertibleRWFunction::CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
{
DoQuickSanityCheck();
ModularArithmetic modn(m_n);
if(!m_precompute)
Precompute();
ModularArithmetic modn(m_n), modp(m_p), modq(m_q);
Integer r, rInv;
// do this in a loop for people using small numbers for testing
do {
do
{
// Do this in a loop for people using small numbers for testing
r.Randomize(rng, Integer::One(), m_n - Integer::One());
// Fix for CVE-2015-2141. Thanks to Evgeny Sidorov for reporting.
// Squaring to satisfy Jacobi requirements suggested by Jean-Pierre Muench.
// Squaring to satisfy Jacobi requirements suggested by Jean-Pierre Munch.
r = modn.Square(r);
rInv = modn.MultiplicativeInverse(r);
} while (rInv.IsZero());
} while(rInv.IsZero());
Integer re = modn.Square(r);
re = modn.Multiply(re, x); // blind
re = modn.Multiply(re, x); // blind
Integer cp=re%m_p, cq=re%m_q;
if (Jacobi(cp, m_p) * Jacobi(cq, m_q) != 1)
const Integer &h = re, &p = m_p, &q = m_q, &n = m_n;
Integer e, f;
const Integer U = modq.Exponentiate(h, (q+1)/8);
if(((modq.Exponentiate(U, 4) - h) % q).IsZero())
e = Integer::One();
else
e = -1;
const Integer eh = e*h, V = modp.Exponentiate(eh, (p-3)/8);
if(((modp.Multiply(modp.Exponentiate(V, 4), modp.Exponentiate(eh, 2)) - eh) % p).IsZero())
f = Integer::One();
else
f = 2;
Integer W, X;
#pragma omp parallel sections if(CRYPTOPP_RW_USE_OMP)
{
cp = cp.IsOdd() ? (cp+m_p) >> 1 : cp >> 1;
cq = cq.IsOdd() ? (cq+m_q) >> 1 : cq >> 1;
}
#pragma omp parallel
#pragma omp sections
#pragma omp section
{
#pragma omp section
cp = ModularSquareRoot(cp, m_p);
#pragma omp section
cq = ModularSquareRoot(cq, m_q);
W = (f.IsUnit() ? U : modq.Multiply(m_pre_2_3q, U));
}
#pragma omp section
{
const Integer t = modp.Multiply(modp.Exponentiate(V, 3), eh);
X = (f.IsUnit() ? t : modp.Multiply(m_pre_2_9p, t));
}
}
const Integer Y = W + q * modp.Multiply(m_pre_q_p, (X - W));
Integer y = CRT(cq, m_q, cp, m_p, m_u);
y = modn.Multiply(y, rInv); // unblind
y = STDMIN(y, m_n-y);
if (ApplyFunction(y) != x) // check
// Signature
Integer s = modn.Multiply(modn.Square(Y), rInv);
assert((e * f * s.Squared()) % m_n == x);
// IEEE P1363, Section 8.2.8 IFSP-RW, p.44
s = STDMIN(s, m_n - s);
if (ApplyFunction(s) != x) // check
throw Exception(Exception::OTHER_ERROR, "InvertibleRWFunction: computational error during private key operation");
return y;
return s;
}
bool InvertibleRWFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
@ -195,6 +276,8 @@ void InvertibleRWFunction::AssignFrom(const NameValuePairs &source)
CRYPTOPP_SET_FUNCTION_ENTRY(Prime2)
CRYPTOPP_SET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
;
m_precompute = false;
}
NAMESPACE_END

18
rw.h
View File

@ -48,8 +48,9 @@ class CRYPTOPP_DLL InvertibleRWFunction : public RWFunction, public TrapdoorFunc
typedef InvertibleRWFunction ThisClass;
public:
void Initialize(const Integer &n, const Integer &p, const Integer &q, const Integer &u)
{m_n = n; m_p = p; m_q = q; m_u = u;}
InvertibleRWFunction() : m_precompute(false) {}
void Initialize(const Integer &n, const Integer &p, const Integer &q, const Integer &u);
// generate a random private key
void Initialize(RandomNumberGenerator &rng, unsigned int modulusBits)
{GenerateRandomWithKeySize(rng, modulusBits);}
@ -79,8 +80,21 @@ public:
void SetPrime2(const Integer &q) {m_q = q;}
void SetMultiplicativeInverseOfPrime2ModPrime1(const Integer &u) {m_u = u;}
virtual bool SupportsPrecomputation() const {return true;}
virtual void Precompute(unsigned int unused = 0) {PrecomputeTweakedRoots();}
virtual void Precompute(unsigned int unused = 0) const {PrecomputeTweakedRoots();}
virtual void LoadPrecomputation(BufferedTransformation &storedPrecomputation);
virtual void SavePrecomputation(BufferedTransformation &storedPrecomputation) const;
protected:
void PrecomputeTweakedRoots() const;
protected:
Integer m_p, m_q, m_u;
mutable Integer m_pre_2_9p, m_pre_2_3q, m_pre_q_p;
mutable bool m_precompute;
};
//! RW