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/*
* Rabin-Williams
* (C) 1999-2008 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/rw.h>
#include <botan/numthry.h>
#include <botan/keypair.h>
#include <botan/look_pk.h>
#include <botan/parsing.h>
#include <algorithm>
namespace Botan {
/*
* Rabin-Williams Public Operation
*/
BigInt RW_PublicKey::public_op(const BigInt& i) const
{
if((i > (n >> 1)) || i.is_negative())
throw Invalid_Argument(algo_name() + "::public_op: i > n / 2 || i < 0");
BigInt r = core.public_op(i);
if(r % 16 == 12) return r;
if(r % 8 == 6) return 2*r;
r = n - r;
if(r % 16 == 12) return r;
if(r % 8 == 6) return 2*r;
throw Invalid_Argument(algo_name() + "::public_op: Invalid input");
}
/*
* Rabin-Williams Verification Function
*/
SecureVector<byte> RW_PublicKey::verify(const byte in[], u32bit len) const
{
BigInt i(in, len);
return BigInt::encode(public_op(i));
}
/*
* Create a Rabin-Williams private key
*/
RW_PrivateKey::RW_PrivateKey(RandomNumberGenerator& rng,
u32bit bits, u32bit exp)
{
if(bits < 512)
throw Invalid_Argument(algo_name() + ": Can't make a key that is only " +
to_string(bits) + " bits long");
if(exp < 2 || exp % 2 == 1)
throw Invalid_Argument(algo_name() + ": Invalid encryption exponent");
e = exp;
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;
if(n.bits() != bits)
throw Self_Test_Failure(algo_name() + " private key generation failed");
d = inverse_mod(e, lcm(p - 1, q - 1) >> 1);
d1 = d % (p - 1);
d2 = d % (q - 1);
c = inverse_mod(q, p);
core = IF_Core(rng, e, n, d, p, q, d1, d2, c);
gen_check(rng);
}
/*
* Rabin-Williams Signature Operation
*/
SecureVector<byte> RW_PrivateKey::sign(const byte in[], u32bit len,
RandomNumberGenerator&) const
{
BigInt i(in, len);
if(i >= n || i % 16 != 12)
throw Invalid_Argument(algo_name() + "::sign: Invalid input");
BigInt r;
if(jacobi(i, n) == 1) r = core.private_op(i);
else r = core.private_op(i >> 1);
r = std::min(r, n - r);
if(i != public_op(r))
throw Self_Test_Failure(algo_name() + " private operation check failed");
return BigInt::encode_1363(r, n.bytes());
}
/*
* 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;
try
{
KeyPair::check_key(rng,
get_pk_signer(*this, "EMSA2(SHA-1)"),
get_pk_verifier(*this, "EMSA2(SHA-1)")
);
}
catch(Self_Test_Failure)
{
return false;
}
return true;
}
RW_Signature_Operation::RW_Signature_Operation(const RW_PrivateKey& rw) :
q(rw.get_q()),
c(rw.get_c()),
n(rw.get_n()),
powermod_d1_p(rw.get_d1(), rw.get_p()),
powermod_d2_q(rw.get_d2(), rw.get_q()),
mod_p(rw.get_p())
{
}
SecureVector<byte> RW_Signature_Operation::sign(const byte msg[],
u32bit 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;
BigInt j1 = powermod_d1_p(i);
BigInt j2 = powermod_d2_q(i);
j1 = mod_p.reduce(sub_mul(j1, j2, c));
BigInt r = mul_add(j1, q, j2);
r = std::min(r, n - r);
return BigInt::encode_1363(r, n.bytes());
}
SecureVector<byte>
RW_Verification_Operation::verify_mr(const byte msg[], u32bit 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(r);
if(r % 8 == 6)
return BigInt::encode(2*r);
r = n - r;
if(r % 16 == 12)
return BigInt::encode(r);
if(r % 8 == 6)
return BigInt::encode(2*r);
throw Invalid_Argument("RW signature verification: Invalid signature");
}
}
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