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1 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
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2 * |
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3 * LibTomMath is a library that provides multiple-precision |
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4 * integer arithmetic as well as number theoretic functionality. |
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5 * |
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6 * The library was designed directly after the MPI library by |
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7 * Michael Fromberger but has been written from scratch with |
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8 * additional optimizations in place. |
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9 * |
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10 * The library is free for all purposes without any express |
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11 * guarantee it works. |
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12 * |
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13 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
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14 */ |
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15 #include <tommath.h> |
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16 |
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17 /* setups the montgomery reduction stuff */ |
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18 int |
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19 mp_montgomery_setup (mp_int * n, mp_digit * rho) |
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20 { |
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21 mp_digit x, b; |
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22 |
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23 /* fast inversion mod 2**k |
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24 * |
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25 * Based on the fact that |
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26 * |
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27 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) |
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28 * => 2*X*A - X*X*A*A = 1 |
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29 * => 2*(1) - (1) = 1 |
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30 */ |
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31 b = n->dp[0]; |
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32 |
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33 if ((b & 1) == 0) { |
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34 return MP_VAL; |
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35 } |
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36 |
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37 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */ |
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38 x *= 2 - b * x; /* here x*a==1 mod 2**8 */ |
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39 #if !defined(MP_8BIT) |
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40 x *= 2 - b * x; /* here x*a==1 mod 2**16 */ |
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41 #endif |
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42 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) |
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43 x *= 2 - b * x; /* here x*a==1 mod 2**32 */ |
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44 #endif |
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45 #ifdef MP_64BIT |
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46 x *= 2 - b * x; /* here x*a==1 mod 2**64 */ |
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47 #endif |
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48 |
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49 /* rho = -1/m mod b */ |
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50 *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK; |
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51 |
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52 return MP_OKAY; |
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53 } |
