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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 /* calculates a = B^n mod b for Montgomery reduction |
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18 * Where B is the base [e.g. 2^DIGIT_BIT]. |
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19 * B^n mod b is computed by first computing |
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20 * A = B^(n-1) which doesn't require a reduction but a simple OR. |
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21 * then C = A * B = B^n is computed by performing upto DIGIT_BIT |
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22 * shifts with subtractions when the result is greater than b. |
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23 * |
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24 * The method is slightly modified to shift B unconditionally upto just under |
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25 * the leading bit of b. This saves alot of multiple precision shifting. |
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26 */ |
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27 int |
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28 mp_montgomery_calc_normalization (mp_int * a, mp_int * b) |
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29 { |
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30 int x, bits, res; |
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31 |
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32 /* how many bits of last digit does b use */ |
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33 bits = mp_count_bits (b) % DIGIT_BIT; |
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34 |
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35 /* compute A = B^(n-1) * 2^(bits-1) */ |
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36 if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { |
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37 return res; |
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38 } |
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39 |
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40 /* now compute C = A * B mod b */ |
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41 for (x = bits - 1; x < (int)DIGIT_BIT; x++) { |
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42 if ((res = mp_mul_2 (a, a)) != MP_OKAY) { |
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43 return res; |
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44 } |
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45 if (mp_cmp_mag (a, b) != MP_LT) { |
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46 if ((res = s_mp_sub (a, b, a)) != MP_OKAY) { |
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47 return res; |
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48 } |
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49 } |
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50 } |
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51 |
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52 return MP_OKAY; |
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53 } |
