47 lines
1.2 KiB
C
47 lines
1.2 KiB
C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is library that provides for multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library is designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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*/
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#include <tommath.h>
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/* setups the montgomery reduction stuff */
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int
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mp_montgomery_setup (mp_int * a, mp_digit * mp)
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{
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unsigned long x, b;
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/* fast inversion mod 2^32
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*
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* Based on the fact that
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*
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* XA = 1 (mod 2^n) => (X(2-XA)) A = 1 (mod 2^2n)
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* => 2*X*A - X*X*A*A = 1
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* => 2*(1) - (1) = 1
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*/
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b = a->dp[0];
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if ((b & 1) == 0) {
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return MP_VAL;
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}
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x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2^4 */
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x *= 2 - b * x; /* here x*a==1 mod 2^8 */
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x *= 2 - b * x; /* here x*a==1 mod 2^16; each step doubles the nb of bits */
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x *= 2 - b * x; /* here x*a==1 mod 2^32 */
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/* t = -1/m mod b */
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*mp = ((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - (x & MP_MASK);
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return MP_OKAY;
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}
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