rw.cpp

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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/parsing.h>
#include <algorithm>
 
namespace Botan {
 
/*
* Create a Rabin-Williams private key
*/
RW_PrivateKey::RW_PrivateKey(RandomNumberGenerator& rng,
                             size_t bits, size_t 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;
 
   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)");
   }
 
RW_Signature_Operation::RW_Signature_Operation(const RW_PrivateKey& rw) :
   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())
   {
   }
 
SecureVector<byte>
RW_Signature_Operation::sign(const byte msg[], size_t msg_len,
                             RandomNumberGenerator& rng)
   {
   if(!blinder.initialized())
      {
      BigInt k(rng, n.bits() / 2);
      blinder = Blinder(power_mod(k, e, n), inverse_mod(k, n), n);
      }
 
   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);
 
   BigInt j1 = powermod_d1_p(i);
   BigInt j2 = powermod_d2_q(i);
   j1 = mod_p.reduce(sub_mul(j1, j2, c));
 
   BigInt r = blinder.unblind(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[], 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(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");
   }
 
}