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/*
* Rabin-Williams
* (C) 1999-2008 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/internal/pk_utils.h>
#include <botan/rw.h>
#include <botan/keypair.h>
#include <botan/parsing.h>
#include <botan/reducer.h>
#include <botan/blinding.h>
#include <algorithm>
#include <future>
namespace Botan {
/*
* Create a Rabin-Williams private key
*/
RW_PrivateKey::RW_PrivateKey(RandomNumberGenerator& rng,
size_t bits, size_t exp)
{
if(bits < 1024)
throw Invalid_Argument(algo_name() + ": Can't make a key that is only " +
std::to_string(bits) + " bits long");
if(exp < 2 || exp % 2 == 1)
throw Invalid_Argument(algo_name() + ": Invalid encryption exponent");
e = exp;
do
{
p = random_prime(rng, (bits + 1) / 2, e / 2, 3, 4);
q = random_prime(rng, bits - p.bits(), e / 2, ((p % 8 == 3) ? 7 : 3), 8);
n = p * q;
} while(n.bits() != bits);
d = inverse_mod(e, lcm(p - 1, q - 1) >> 1);
d1 = d % (p - 1);
d2 = d % (q - 1);
c = inverse_mod(q, p);
gen_check(rng);
}
/*
* Check Private Rabin-Williams Parameters
*/
bool RW_PrivateKey::check_key(RandomNumberGenerator& rng, bool strong) const
{
if(!IF_Scheme_PrivateKey::check_key(rng, strong))
return false;
if(!strong)
return true;
if((e * d) % (lcm(p - 1, q - 1) / 2) != 1)
return false;
return KeyPair::signature_consistency_check(rng, *this, "EMSA2(SHA-1)");
}
namespace {
/**
* Rabin-Williams Signature Operation
*/
class RW_Signature_Operation : public PK_Ops::Signature_with_EMSA
{
public:
typedef RW_PrivateKey Key_Type;
RW_Signature_Operation(const RW_PrivateKey& rw,
const std::string& emsa) :
PK_Ops::Signature_with_EMSA(emsa),
n(rw.get_n()),
e(rw.get_e()),
q(rw.get_q()),
c(rw.get_c()),
powermod_d1_p(rw.get_d1(), rw.get_p()),
powermod_d2_q(rw.get_d2(), rw.get_q()),
mod_p(rw.get_p()),
blinder(n,
[this](const BigInt& k) { return power_mod(k, e, n); },
[this](const BigInt& k) { return inverse_mod(k, n); })
{
}
size_t max_input_bits() const override { return (n.bits() - 1); }
secure_vector<byte> raw_sign(const byte msg[], size_t msg_len,
RandomNumberGenerator& rng) override;
private:
const BigInt& n;
const BigInt& e;
const BigInt& q;
const BigInt& c;
Fixed_Exponent_Power_Mod powermod_d1_p, powermod_d2_q;
Modular_Reducer mod_p;
Blinder blinder;
};
secure_vector<byte>
RW_Signature_Operation::raw_sign(const byte msg[], size_t msg_len,
RandomNumberGenerator&)
{
BigInt i(msg, msg_len);
if(i >= n || i % 16 != 12)
throw Invalid_Argument("Rabin-Williams: invalid input");
if(jacobi(i, n) != 1)
i >>= 1;
i = blinder.blind(i);
auto future_j1 = std::async(std::launch::async, powermod_d1_p, i);
const BigInt j2 = powermod_d2_q(i);
BigInt j1 = future_j1.get();
j1 = mod_p.reduce(sub_mul(j1, j2, c));
const BigInt r = blinder.unblind(mul_add(j1, q, j2));
return BigInt::encode_1363(std::min(r, n - r), n.bytes());
}
/**
* Rabin-Williams Verification Operation
*/
class RW_Verification_Operation : public PK_Ops::Verification_with_EMSA
{
public:
typedef RW_PublicKey Key_Type;
RW_Verification_Operation(const RW_PublicKey& rw, const std::string& emsa) :
PK_Ops::Verification_with_EMSA(emsa),
n(rw.get_n()), powermod_e_n(rw.get_e(), rw.get_n())
{}
size_t max_input_bits() const override { return (n.bits() - 1); }
bool with_recovery() const override { return true; }
secure_vector<byte> verify_mr(const byte msg[], size_t msg_len) override;
private:
const BigInt& n;
Fixed_Exponent_Power_Mod powermod_e_n;
};
secure_vector<byte>
RW_Verification_Operation::verify_mr(const byte msg[], size_t msg_len)
{
BigInt m(msg, msg_len);
if((m > (n >> 1)) || m.is_negative())
throw Invalid_Argument("RW signature verification: m > n / 2 || m < 0");
BigInt r = powermod_e_n(m);
if(r % 16 == 12)
return BigInt::encode_locked(r);
if(r % 8 == 6)
return BigInt::encode_locked(2*r);
r = n - r;
if(r % 16 == 12)
return BigInt::encode_locked(r);
if(r % 8 == 6)
return BigInt::encode_locked(2*r);
throw Invalid_Argument("RW signature verification: Invalid signature");
}
BOTAN_REGISTER_PK_SIGNATURE_OP("RW", RW_Signature_Operation);
BOTAN_REGISTER_PK_VERIFY_OP("RW", RW_Verification_Operation);
}
}
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