r_keygen.c

RSA加密实现

/* R_KEYGEN.C - key-pair generation for RSAREF
 */

/* Copyright (C) RSA Laboratories, a division of RSA Data Security,
     Inc., created 1991. All rights reserved.
 */

#include "global.h"
#include "rsaref.h"
#include "r_random.h"
#include "nn.h"
#include "prime.h"

static int RSAFilter PROTO_LIST
  ((NN_DIGIT *, unsigned int, NN_DIGIT *, unsigned int));
static int RelativelyPrime PROTO_LIST
  ((NN_DIGIT *, unsigned int, NN_DIGIT *, unsigned int));

/* Generates an RSA key pair with a given length and public exponent.
 */
int R_GeneratePEMKeys (publicKey, privateKey, protoKey, randomStruct)
R_RSA_PUBLIC_KEY *publicKey;                          /* new RSA public key */
R_RSA_PRIVATE_KEY *privateKey;                       /* new RSA private key */
R_RSA_PROTO_KEY *protoKey;                             /* RSA prototype key */
R_RANDOM_STRUCT *randomStruct;                          /* random structure */
{
  NN_DIGIT d[MAX_NN_DIGITS], dP[MAX_NN_DIGITS], dQ[MAX_NN_DIGITS],
    e[MAX_NN_DIGITS], n[MAX_NN_DIGITS], p[MAX_NN_DIGITS], phiN[MAX_NN_DIGITS],
    pMinus1[MAX_NN_DIGITS], q[MAX_NN_DIGITS], qInv[MAX_NN_DIGITS],
    qMinus1[MAX_NN_DIGITS], t[MAX_NN_DIGITS], u[MAX_NN_DIGITS],
    v[MAX_NN_DIGITS];
  int status;
  unsigned int nDigits, pBits, pDigits, qBits;
  
  if ((protoKey->bits < MIN_RSA_MODULUS_BITS) || 
      (protoKey->bits > MAX_RSA_MODULUS_BITS))
    return (RE_MODULUS_LEN);
  nDigits = (protoKey->bits + NN_DIGIT_BITS - 1) / NN_DIGIT_BITS;
  pDigits = (nDigits + 1) / 2;
  pBits = (protoKey->bits + 1) / 2;
  qBits = protoKey->bits - pBits;

  /* NOTE: for 65537, this assumes NN_DIGIT is at least 17 bits. */
  NN_ASSIGN_DIGIT
    (e, protoKey->useFermat4 ? (NN_DIGIT)65537 : (NN_DIGIT)3, nDigits);

  /* Generate prime p between 3*2^(pBits-2) and 2^pBits-1, searching
       in steps of 2, until one satisfies gcd (p-1, e) = 1.
   */
  NN_Assign2Exp (t, pBits-1, pDigits);
  NN_Assign2Exp (u, pBits-2, pDigits);
  NN_Add (t, t, u, pDigits);
  NN_ASSIGN_DIGIT (v, 1, pDigits);
  NN_Sub (v, t, v, pDigits);
  NN_Add (u, u, v, pDigits);
  NN_ASSIGN_DIGIT (v, 2, pDigits);
  do {
    if (status = GeneratePrime (p, t, u, v, pDigits, randomStruct))
      return (status);
  }
  while (! RSAFilter (p, pDigits, e, 1));
  
  /* Generate prime q between 3*2^(qBits-2) and 2^qBits-1, searching
       in steps of 2, until one satisfies gcd (q-1, e) = 1.
   */
  NN_Assign2Exp (t, qBits-1, pDigits);
  NN_Assign2Exp (u, qBits-2, pDigits);
  NN_Add (t, t, u, pDigits);
  NN_ASSIGN_DIGIT (v, 1, pDigits);
  NN_Sub (v, t, v, pDigits);
  NN_Add (u, u, v, pDigits);
  NN_ASSIGN_DIGIT (v, 2, pDigits);
  do {
    if (status = GeneratePrime (q, t, u, v, pDigits, randomStruct))
      return (status);
  }
  while (! RSAFilter (q, pDigits, e, 1));
  
  /* Sort so that p > q. (p = q case is extremely unlikely.)
   */
  if (NN_Cmp (p, q, pDigits) < 0) {
    NN_Assign (t, p, pDigits);
    NN_Assign (p, q, pDigits);
    NN_Assign (q, t, pDigits);
  }

  /* Compute n = pq, qInv = q^{-1} mod p, d = e^{-1} mod (p-1)(q-1),
     dP = d mod p-1, dQ = d mod q-1.
   */
  NN_Mult (n, p, q, pDigits);
  NN_ModInv (qInv, q, p, pDigits);
  
  NN_ASSIGN_DIGIT (t, 1, pDigits);
  NN_Sub (pMinus1, p, t, pDigits);
  NN_Sub (qMinus1, q, t, pDigits);
  NN_Mult (phiN, pMinus1, qMinus1, pDigits);

  NN_ModInv (d, e, phiN, nDigits);
  NN_Mod (dP, d, nDigits, pMinus1, pDigits);
  NN_Mod (dQ, d, nDigits, qMinus1, pDigits);
  
  publicKey->bits = privateKey->bits = protoKey->bits;
  NN_Encode (publicKey->modulus, MAX_RSA_MODULUS_LEN, n, nDigits);
  NN_Encode (publicKey->exponent, MAX_RSA_MODULUS_LEN, e, 1);
  R_memcpy 
    ((POINTER)privateKey->modulus, (POINTER)publicKey->modulus,
     MAX_RSA_MODULUS_LEN);
  R_memcpy
    ((POINTER)privateKey->publicExponent, (POINTER)publicKey->exponent,
     MAX_RSA_MODULUS_LEN);
  NN_Encode (privateKey->exponent, MAX_RSA_MODULUS_LEN, d, nDigits);
  NN_Encode (privateKey->prime[0], MAX_RSA_PRIME_LEN, p, pDigits);
  NN_Encode (privateKey->prime[1], MAX_RSA_PRIME_LEN, q, pDigits);
  NN_Encode (privateKey->primeExponent[0], MAX_RSA_PRIME_LEN, dP, pDigits);
  NN_Encode (privateKey->primeExponent[1], MAX_RSA_PRIME_LEN, dQ, pDigits);
  NN_Encode (privateKey->coefficient, MAX_RSA_PRIME_LEN, qInv, pDigits);
   
  /* Zeroize sensitive information.
   */
  R_memset ((POINTER)d, 0, sizeof (d));
  R_memset ((POINTER)dP, 0, sizeof (dP));
  R_memset ((POINTER)dQ, 0, sizeof (dQ));
  R_memset ((POINTER)p, 0, sizeof (p));
  R_memset ((POINTER)phiN, 0, sizeof (phiN));
  R_memset ((POINTER)pMinus1, 0, sizeof (pMinus1));
  R_memset ((POINTER)q, 0, sizeof (q));
  R_memset ((POINTER)qInv, 0, sizeof (qInv));
  R_memset ((POINTER)qMinus1, 0, sizeof (qMinus1));
  R_memset ((POINTER)t, 0, sizeof (t));
  
  return (0);
}

/* Returns nonzero iff GCD (a-1, b) = 1.

   Lengths: a[aDigits], b[bDigits].
   Assumes aDigits < MAX_NN_DIGITS, bDigits < MAX_NN_DIGITS.
 */
static int RSAFilter (a, aDigits, b, bDigits)
NN_DIGIT *a, *b;
unsigned int aDigits, bDigits;
{
  int status;
  NN_DIGIT aMinus1[MAX_NN_DIGITS], t[MAX_NN_DIGITS];
  
  NN_ASSIGN_DIGIT (t, 1, aDigits);
  NN_Sub (aMinus1, a, t, aDigits);
  
  status = RelativelyPrime (aMinus1, aDigits, b, bDigits);

  /* Zeroize sensitive information.
   */
  R_memset ((POINTER)aMinus1, 0, sizeof (aMinus1));
  
  return (status);
}

/* Returns nonzero iff a and b are relatively prime.

   Lengths: a[aDigits], b[bDigits].
   Assumes aDigits >= bDigits, aDigits < MAX_NN_DIGITS.
 */
static int RelativelyPrime (a, aDigits, b, bDigits)
NN_DIGIT *a, *b;
unsigned int aDigits, bDigits;
{
  int status;
  NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS];
  
  NN_AssignZero (t, aDigits);
  NN_Assign (t, b, bDigits);
  NN_Gcd (t, a, t, aDigits);
  NN_ASSIGN_DIGIT (u, 1, aDigits);

  status = NN_EQUAL (t, u, aDigits);
  
  /* Zeroize sensitive information.
   */
  R_memset ((POINTER)t, 0, sizeof (t));
  
  return (status);
}