projects/hoofbaby: deps/Platinum/ThirdParty/Neptune/ThirdParty/axTLS/crypto/bigint.c comparison

comparison deps/Platinum/ThirdParty/Neptune/ThirdParty/axTLS/crypto/bigint.c @ 0:3425707ddbf6

Initial import (hopefully this mercurial stuff works...)

author	fraserofthenight
date	Mon, 06 Jul 2009 08:06:28 -0700
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--1:000000000000
+:3425707ddbf6
+/*
+* Copyright (c) 2007, Cameron Rich
+*
+* All rights reserved.
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions are met:
+*
+* * Redistributions of source code must retain the above copyright notice,
+*   this list of conditions and the following disclaimer.
+* * Redistributions in binary form must reproduce the above copyright notice,
+*   this list of conditions and the following disclaimer in the documentation
+*   and/or other materials provided with the distribution.
+* * Neither the name of the axTLS project nor the names of its contributors
+*   may be used to endorse or promote products derived from this software
+*   without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+/**
+* @defgroup bigint_api Big Integer API
+* @brief The bigint implementation as used by the axTLS project.
+*
+* The bigint library is for RSA encryption/decryption as well as signing.
+* This code tries to minimise use of malloc/free by maintaining a small
+* cache. A bigint context may maintain state by being made "permanent".
+* It be be later released with a bi_depermanent() and bi_free() call.
+*
+* It supports the following reduction techniques:
+* - Classical
+* - Barrett
+* - Montgomery
+*
+* It also implements the following:
+* - Karatsuba multiplication
+* - Squaring
+* - Sliding window exponentiation
+* - Chinese Remainder Theorem (implemented in rsa.c).
+*
+* All the algorithms used are pretty standard, and designed for different
+* data bus sizes. Negative numbers are not dealt with at all, so a subtraction
+* may need to be tested for negativity.
+*
+* This library steals some ideas from Jef Poskanzer
+* <http://cs.marlboro.edu/term/cs-fall02/algorithms/crypto/RSA/bigint>
+* and GMP <http://www.swox.com/gmp>. It gets most of its implementation
+* detail from "The Handbook of Applied Cryptography"
+* <http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf>
+* @{
+*/
+#include <stdlib.h>
+#include <limits.h>
+#include <string.h>
+#include <stdio.h>
+#include <time.h>
+#include "bigint.h"
+#define V1      v->comps[v->size-1]                 /**< v1 for division */
+#define V2      v->comps[v->size-2]                 /**< v2 for division */
+#define U(j)    tmp_u->comps[tmp_u->size-j-1]       /**< uj for division */
+#define Q(j)    quotient->comps[quotient->size-j-1] /**< qj for division */
+static bigint *bi_int_multiply(BI_CTX *ctx, bigint *bi, comp i);
+static bigint *bi_int_divide(BI_CTX *ctx, bigint *biR, comp denom);
+static bigint *alloc(BI_CTX *ctx, int size);
+static bigint *trim(bigint *bi);
+static void more_comps(bigint *bi, int n);
+#if defined(CONFIG_BIGINT_KARATSUBA) || defined(CONFIG_BIGINT_BARRETT) || \
+defined(CONFIG_BIGINT_MONTGOMERY)
+static bigint *comp_right_shift(bigint *biR, int num_shifts);
+static bigint *comp_left_shift(bigint *biR, int num_shifts);
+#endif
+#ifdef CONFIG_BIGINT_CHECK_ON
+static void check(const bigint *bi);
+#else
+#define check(A)                /**< disappears in normal production mode */
+#endif
+/**
+* @brief Start a new bigint context.
+* @return A bigint context.
+*/
+BI_CTX *bi_initialize(void)
+{
+/* calloc() sets everything to zero */
+BI_CTX *ctx = (BI_CTX *)calloc(1, sizeof(BI_CTX));
+/* the radix */
+ctx->bi_radix = alloc(ctx, 2);
+ctx->bi_radix->comps[0] = 0;
+ctx->bi_radix->comps[1] = 1;
+bi_permanent(ctx->bi_radix);
+return ctx;
+}
+/**
+* @brief Close the bigint context and free any resources.
+*
+* Free up any used memory - a check is done if all objects were not
+* properly freed.
+* @param ctx [in]   The bigint session context.
+*/
+void bi_terminate(BI_CTX *ctx)
+{
+bi_depermanent(ctx->bi_radix);
+bi_free(ctx, ctx->bi_radix);
+if (ctx->active_count != 0)
+{
+#ifdef CONFIG_SSL_FULL_MODE
+printf("bi_terminate: there were %d un-freed bigints\n",
+ctx->active_count);
+#endif
+abort();
+}
+bi_clear_cache(ctx);
+free(ctx);
+}
+/**
+*@brief Clear the memory cache.
+*/
+void bi_clear_cache(BI_CTX *ctx)
+{
+bigint *p, *pn;
+if (ctx->free_list == NULL)
+return;
+for (p = ctx->free_list; p != NULL; p = pn)
+{
+pn = p->next;
+free(p->comps);
+free(p);
+}
+ctx->free_count = 0;
+ctx->free_list = NULL;
+}
+/**
+* @brief Increment the number of references to this object.
+* It does not do a full copy.
+* @param bi [in]   The bigint to copy.
+* @return A reference to the same bigint.
+*/
+bigint *bi_copy(bigint *bi)
+{
+check(bi);
+if (bi->refs != PERMANENT)
+bi->refs++;
+return bi;
+}
+/**
+* @brief Simply make a bigint object "unfreeable" if bi_free() is called on it.
+*
+* For this object to be freed, bi_depermanent() must be called.
+* @param bi [in]   The bigint to be made permanent.
+*/
+void bi_permanent(bigint *bi)
+{
+check(bi);
+if (bi->refs != 1)
+{
+#ifdef CONFIG_SSL_FULL_MODE
+printf("bi_permanent: refs was not 1\n");
+#endif
+abort();
+}
+bi->refs = PERMANENT;
+}
+/**
+* @brief Take a permanent object and make it eligible for freedom.
+* @param bi [in]   The bigint to be made back to temporary.
+*/
+void bi_depermanent(bigint *bi)
+{
+check(bi);
+if (bi->refs != PERMANENT)
+{
+#ifdef CONFIG_SSL_FULL_MODE
+printf("bi_depermanent: bigint was not permanent\n");
+#endif
+abort();
+}
+bi->refs = 1;
+}
+/**
+* @brief Free a bigint object so it can be used again.
+*
+* The memory itself it not actually freed, just tagged as being available
+* @param ctx [in]   The bigint session context.
+* @param bi [in]    The bigint to be freed.
+*/
+void bi_free(BI_CTX *ctx, bigint *bi)
+{
+check(bi);
+if (bi->refs == PERMANENT)
+{
+return;
+}
+if (--bi->refs > 0)
+{
+return;
+}
+bi->next = ctx->free_list;
+ctx->free_list = bi;
+ctx->free_count++;
+if (--ctx->active_count < 0)
+{
+#ifdef CONFIG_SSL_FULL_MODE
+printf("bi_free: active_count went negative "
+"- double-freed bigint?\n");
+#endif
+abort();
+}
+}
+/**
+* @brief Convert an (unsigned) integer into a bigint.
+* @param ctx [in]   The bigint session context.
+* @param i [in]     The (unsigned) integer to be converted.
+*
+*/
+bigint *int_to_bi(BI_CTX *ctx, comp i)
+{
+bigint *biR = alloc(ctx, 1);
+biR->comps[0] = i;
+return biR;
+}
+/**
+* @brief Do a full copy of the bigint object.
+* @param ctx [in]   The bigint session context.
+* @param bi  [in]   The bigint object to be copied.
+*/
+bigint *bi_clone(BI_CTX *ctx, const bigint *bi)
+{
+bigint *biR = alloc(ctx, bi->size);
+check(bi);
+memcpy(biR->comps, bi->comps, bi->size*COMP_BYTE_SIZE);
+return biR;
+}
+/**
+* @brief Perform an addition operation between two bigints.
+* @param ctx [in]  The bigint session context.
+* @param bia [in]  A bigint.
+* @param bib [in]  Another bigint.
+* @return The result of the addition.
+*/
+bigint *bi_add(BI_CTX *ctx, bigint *bia, bigint *bib)
+{
+int n;
+comp carry = 0;
+comp *pa, *pb;
+check(bia);
+check(bib);
+n = max(bia->size, bib->size);
+more_comps(bia, n+1);
+more_comps(bib, n);
+pa = bia->comps;
+pb = bib->comps;
+do
+{
+comp  sl, rl, cy1;
+sl = *pa + *pb++;
+rl = sl + carry;
+cy1 = sl < *pa;
+carry = cy1 | (rl < sl);
+*pa++ = rl;
+} while (--n != 0);
+*pa = carry;                  /* do overflow */
+bi_free(ctx, bib);
+return trim(bia);
+}
+/**
+* @brief Perform a subtraction operation between two bigints.
+* @param ctx [in]  The bigint session context.
+* @param bia [in]  A bigint.
+* @param bib [in]  Another bigint.
+* @param is_negative [out] If defined, indicates that the result was negative.
+* is_negative may be null.
+* @return The result of the subtraction. The result is always positive.
+*/
+bigint *bi_subtract(BI_CTX *ctx,
+bigint *bia, bigint *bib, int *is_negative)
+{
+int n = bia->size;
+comp *pa, *pb, carry = 0;
+check(bia);
+check(bib);
+more_comps(bib, n);
+pa = bia->comps;
+pb = bib->comps;
+do
+{
+comp sl, rl, cy1;
+sl = *pa - *pb++;
+rl = sl - carry;
+cy1 = sl > *pa;
+carry = cy1 | (rl > sl);
+*pa++ = rl;
+} while (--n != 0);
+if (is_negative)    /* indicate a negative result */
+{
+*is_negative = carry;
+}
+bi_free(ctx, trim(bib));    /* put bib back to the way it was */
+return trim(bia);
+}
+/**
+* Perform a multiply between a bigint an an (unsigned) integer
+*/
+static bigint *bi_int_multiply(BI_CTX *ctx, bigint *bia, comp b)
+{
+int j = 0, n = bia->size;
+bigint *biR = alloc(ctx, n + 1);
+comp carry = 0;
+comp *r = biR->comps;
+comp *a = bia->comps;
+check(bia);
+/* clear things to start with */
+memset(r, 0, ((n+1)*COMP_BYTE_SIZE));
+do
+{
+long_comp tmp = *r + (long_comp)a[j]*b + carry;
+*r++ = (comp)tmp;              /* downsize */
+carry = (comp)(tmp >> COMP_BIT_SIZE);
+} while (++j < n);
+*r = carry;
+bi_free(ctx, bia);
+return trim(biR);
+}
+/**
+* @brief Does both division and modulo calculations.
+*
+* Used extensively when doing classical reduction.
+* @param ctx [in]  The bigint session context.
+* @param u [in]    A bigint which is the numerator.
+* @param v [in]    Either the denominator or the modulus depending on the mode.
+* @param is_mod [n] Determines if this is a normal division (0) or a reduction
+* (1).
+* @return  The result of the division/reduction.
+*/
+bigint *bi_divide(BI_CTX *ctx, bigint *u, bigint *v, int is_mod)
+{
+int n = v->size, m = u->size-n;
+int j = 0, orig_u_size = u->size;
+uint8_t mod_offset = ctx->mod_offset;
+comp d;
+bigint *quotient, *tmp_u;
+comp q_dash;
+check(u);
+check(v);
+/* if doing reduction and we are < mod, then return mod */
+if (is_mod && bi_compare(v, u) > 0)
+{
+bi_free(ctx, v);
+return u;
+}
+quotient = alloc(ctx, m+1);
+tmp_u = alloc(ctx, n+1);
+v = trim(v);        /* make sure we have no leading 0's */
+d = (comp)((long_comp)COMP_RADIX/(V1+1));
+/* clear things to start with */
+memset(quotient->comps, 0, ((quotient->size)*COMP_BYTE_SIZE));
+/* normalise */
+if (d > 1)
+{
+u = bi_int_multiply(ctx, u, d);
+if (is_mod)
+{
+v = ctx->bi_normalised_mod[mod_offset];
+}
+else
+{
+v = bi_int_multiply(ctx, v, d);
+}
+}
+if (orig_u_size == u->size)  /* new digit position u0 */
+{
+more_comps(u, orig_u_size + 1);
+}
+do
+{
+/* get a temporary short version of u */
+memcpy(tmp_u->comps, &u->comps[u->size-n-1-j], (n+1)*COMP_BYTE_SIZE);
+/* calculate q' */
+if (U(0) == V1)
+{
+q_dash = COMP_RADIX-1;
+}
+else
+{
+q_dash = (comp)(((long_comp)U(0)*COMP_RADIX + U(1))/V1);
+}
+if (v->size > 1 && V2)
+{
+/* we are implementing the following:
+if (V2*q_dash > (((U(0)*COMP_RADIX + U(1) -
+q_dash*V1)*COMP_RADIX) + U(2))) ... */
+comp inner = (comp)((long_comp)COMP_RADIX*U(0) + U(1) -
+(long_comp)q_dash*V1);
+if ((long_comp)V2*q_dash > (long_comp)inner*COMP_RADIX + U(2))
+{
+q_dash--;
+}
+}
+/* multiply and subtract */
+if (q_dash)
+{
+int is_negative;
+tmp_u = bi_subtract(ctx, tmp_u,
+bi_int_multiply(ctx, bi_copy(v), q_dash), &is_negative);
+more_comps(tmp_u, n+1);
+Q(j) = q_dash;
+/* add back */
+if (is_negative)
+{
+Q(j)--;
+tmp_u = bi_add(ctx, tmp_u, bi_copy(v));
+/* lop off the carry */
+tmp_u->size--;
+v->size--;
+}
+}
+else
+{
+Q(j) = 0;
+}
+/* copy back to u */
+memcpy(&u->comps[u->size-n-1-j], tmp_u->comps, (n+1)*COMP_BYTE_SIZE);
+} while (++j <= m);
+bi_free(ctx, tmp_u);
+bi_free(ctx, v);
+if (is_mod)     /* get the remainder */
+{
+bi_free(ctx, quotient);
+return bi_int_divide(ctx, trim(u), d);
+}
+else            /* get the quotient */
+{
+bi_free(ctx, u);
+return trim(quotient);
+}
+}
+/*
+* Perform an integer divide on a bigint.
+*/
+static bigint *bi_int_divide(BI_CTX *ctx, bigint *biR, comp denom)
+{
+int i = biR->size - 1;
+(void)ctx; /* unused */
+long_comp r = 0;
+check(biR);
+do
+{
+r = (r<<COMP_BIT_SIZE) + biR->comps[i];
+biR->comps[i] = (comp)(r / denom);
+r %= denom;
+} while (--i >= 0);
+return trim(biR);
+}
+#ifdef CONFIG_BIGINT_MONTGOMERY
+/**
+* There is a need for the value of integer N' such that B^-1(B-1)-N^-1N'=1,
+* where B^-1(B-1) mod N=1. Actually, only the least significant part of
+* N' is needed, hence the definition N0'=N' mod b. We reproduce below the
+* simple algorithm from an article by Dusse and Kaliski to efficiently
+* find N0' from N0 and b */
+static comp modular_inverse(bigint *bim)
+{
+int i;
+comp t = 1;
+comp two_2_i_minus_1 = 2;   /* 2^(i-1) */
+long_comp two_2_i = 4;      /* 2^i */
+comp N = bim->comps[0];
+for (i = 2; i <= COMP_BIT_SIZE; i++)
+{
+if ((long_comp)N*t%two_2_i >= two_2_i_minus_1)
+{
+t += two_2_i_minus_1;
+}
+two_2_i_minus_1 <<= 1;
+two_2_i <<= 1;
+}
+return (comp)(COMP_RADIX-t);
+}
+#endif
+#if defined(CONFIG_BIGINT_KARATSUBA) || defined(CONFIG_BIGINT_BARRETT) || \
+defined(CONFIG_BIGINT_MONTGOMERY)
+/**
+* Take each component and shift down (in terms of components)
+*/
+static bigint *comp_right_shift(bigint *biR, int num_shifts)
+{
+int i = biR->size-num_shifts;
+comp *x = biR->comps;
+comp *y = &biR->comps[num_shifts];
+check(biR);
+if (i <= 0)     /* have we completely right shifted? */
+{
+biR->comps[0] = 0;  /* return 0 */
+biR->size = 1;
+return biR;
+}
+do
+{
+*x++ = *y++;
+} while (--i > 0);
+biR->size -= num_shifts;
+return biR;
+}
+/**
+* Take each component and shift it up (in terms of components)
+*/
+static bigint *comp_left_shift(bigint *biR, int num_shifts)
+{
+int i = biR->size-1;
+comp *x, *y;
+check(biR);
+if (num_shifts <= 0)
+{
+return biR;
+}
+more_comps(biR, biR->size + num_shifts);
+x = &biR->comps[i+num_shifts];
+y = &biR->comps[i];
+do
+{
+*x-- = *y--;
+} while (i--);
+memset(biR->comps, 0, num_shifts*COMP_BYTE_SIZE); /* zero LS comps */
+return biR;
+}
+#endif
+/**
+* @brief Allow a binary sequence to be imported as a bigint.
+* @param ctx [in]  The bigint session context.
+* @param data [in] The data to be converted.
+* @param size [in] The number of bytes of data.
+* @return A bigint representing this data.
+*/
+bigint *bi_import(BI_CTX *ctx, const uint8_t *data, int size)
+{
+bigint *biR = alloc(ctx, (size+COMP_BYTE_SIZE-1)/COMP_BYTE_SIZE);
+int i, j = 0, offset = 0;
+memset(biR->comps, 0, biR->size*COMP_BYTE_SIZE);
+for (i = size-1; i >= 0; i--)
+{
+biR->comps[offset] += data[i] << (j*8);
+if (++j == COMP_BYTE_SIZE)
+{
+j = 0;
+offset ++;
+}
+}
+return trim(biR);
+}
+#ifdef CONFIG_SSL_FULL_MODE
+/**
+* @brief The testharness uses this code to import text hex-streams and
+* convert them into bigints.
+* @param ctx [in]  The bigint session context.
+* @param data [in] A string consisting of hex characters. The characters must
+* be in upper case.
+* @return A bigint representing this data.
+*/
+bigint *bi_str_import(BI_CTX *ctx, const char *data)
+{
+int size = strlen(data);
+bigint *biR = alloc(ctx, (size+COMP_NUM_NIBBLES-1)/COMP_NUM_NIBBLES);
+int i, j = 0, offset = 0;
+memset(biR->comps, 0, biR->size*COMP_BYTE_SIZE);
+for (i = size-1; i >= 0; i--)
+{
+int num = (data[i] <= '9') ? (data[i] - '0') : (data[i] - 'A' + 10);
+biR->comps[offset] += num << (j*4);
+if (++j == COMP_NUM_NIBBLES)
+{
+j = 0;
+offset ++;
+}
+}
+return biR;
+}
+void bi_print(const char *label, bigint *x)
+{
+int i, j;
+if (x == NULL)
+{
+printf("%s: (null)\n", label);
+return;
+}
+printf("%s: (size %d)\n", label, x->size);
+for (i = x->size-1; i >= 0; i--)
+{
+for (j = COMP_NUM_NIBBLES-1; j >= 0; j--)
+{
+comp mask = 0x0f << (j*4);
+comp num = (x->comps[i] & mask) >> (j*4);
+putc((num <= 9) ? (num + '0') : (num + 'A' - 10), stdout);
+}
+}
+printf("\n");
+}
+#endif
+/**
+* @brief Take a bigint and convert it into a byte sequence.
+*
+* This is useful after a decrypt operation.
+* @param ctx [in]  The bigint session context.
+* @param x [in]  The bigint to be converted.
+* @param data [out] The converted data as a byte stream.
+* @param size [in] The maximum size of the byte stream. Unused bytes will be
+* zeroed.
+*/
+void bi_export(BI_CTX *ctx, bigint *x, uint8_t *data, int size)
+{
+int i, j, k = size-1;
+check(x);
+memset(data, 0, size);  /* ensure all leading 0's are cleared */
+for (i = 0; i < x->size; i++)
+{
+for (j = 0; j < COMP_BYTE_SIZE; j++)
+{
+comp mask = 0xff << (j*8);
+int num = (x->comps[i] & mask) >> (j*8);
+data[k--] = num;
+if (k < 0)
+{
+break;
+}
+}
+}
+bi_free(ctx, x);
+}
+/**
+* @brief Pre-calculate some of the expensive steps in reduction.
+*
+* This function should only be called once (normally when a session starts).
+* When the session is over, bi_free_mod() should be called. bi_mod_power()
+* relies on this function being called.
+* @param ctx [in]  The bigint session context.
+* @param bim [in]  The bigint modulus that will be used.
+* @param mod_offset [in] There are three moduluii that can be stored - the
+* standard modulus, and its two primes p and q. This offset refers to which
+* modulus we are referring to.
+* @see bi_free_mod(), bi_mod_power().
+*/
+void bi_set_mod(BI_CTX *ctx, bigint *bim, int mod_offset)
+{
+int k = bim->size;
+comp d = (comp)((long_comp)COMP_RADIX/(bim->comps[k-1]+1));
+#ifdef CONFIG_BIGINT_MONTGOMERY
+bigint *R, *R2;
+#endif
+ctx->bi_mod[mod_offset] = bim;
+bi_permanent(ctx->bi_mod[mod_offset]);
+ctx->bi_normalised_mod[mod_offset] = bi_int_multiply(ctx, bim, d);
+bi_permanent(ctx->bi_normalised_mod[mod_offset]);
+#if defined(CONFIG_BIGINT_MONTGOMERY)
+/* set montgomery variables */
+R = comp_left_shift(bi_clone(ctx, ctx->bi_radix), k-1);     /* R */
+R2 = comp_left_shift(bi_clone(ctx, ctx->bi_radix), k*2-1);  /* R^2 */
+ctx->bi_RR_mod_m[mod_offset] = bi_mod(ctx, R2);             /* R^2 mod m */
+ctx->bi_R_mod_m[mod_offset] = bi_mod(ctx, R);               /* R mod m */
+bi_permanent(ctx->bi_RR_mod_m[mod_offset]);
+bi_permanent(ctx->bi_R_mod_m[mod_offset]);
+ctx->N0_dash[mod_offset] = modular_inverse(ctx->bi_mod[mod_offset]);
+#elif defined (CONFIG_BIGINT_BARRETT)
+ctx->bi_mu[mod_offset] =
+bi_divide(ctx, comp_left_shift(
+bi_clone(ctx, ctx->bi_radix), k*2-1), ctx->bi_mod[mod_offset], 0);
+bi_permanent(ctx->bi_mu[mod_offset]);
+#endif
+}
+/**
+* @brief Used when cleaning various bigints at the end of a session.
+* @param ctx [in]  The bigint session context.
+* @param mod_offset [in] The offset to use.
+* @see bi_set_mod().
+*/
+void bi_free_mod(BI_CTX *ctx, int mod_offset)
+{
+bi_depermanent(ctx->bi_mod[mod_offset]);
+bi_free(ctx, ctx->bi_mod[mod_offset]);
+#if defined (CONFIG_BIGINT_MONTGOMERY)
+bi_depermanent(ctx->bi_RR_mod_m[mod_offset]);
+bi_depermanent(ctx->bi_R_mod_m[mod_offset]);
+bi_free(ctx, ctx->bi_RR_mod_m[mod_offset]);
+bi_free(ctx, ctx->bi_R_mod_m[mod_offset]);
+#elif defined(CONFIG_BIGINT_BARRETT)
+bi_depermanent(ctx->bi_mu[mod_offset]);
+bi_free(ctx, ctx->bi_mu[mod_offset]);
+#endif
+bi_depermanent(ctx->bi_normalised_mod[mod_offset]);
+bi_free(ctx, ctx->bi_normalised_mod[mod_offset]);
+}
+/**
+* Perform a standard multiplication between two bigints.
+*/
+static bigint *regular_multiply(BI_CTX *ctx, bigint *bia, bigint *bib)
+{
+int i, j, i_plus_j;
+int n = bia->size;
+int t = bib->size;
+bigint *biR = alloc(ctx, n + t);
+comp *sr = biR->comps;
+comp *sa = bia->comps;
+comp *sb = bib->comps;
+check(bia);
+check(bib);
+/* clear things to start with */
+memset(biR->comps, 0, ((n+t)*COMP_BYTE_SIZE));
+i = 0;
+do
+{
+comp carry = 0;
+comp b = *sb++;
+i_plus_j = i;
+j = 0;
+do
+{
+long_comp tmp = sr[i_plus_j] + (long_comp)sa[j]*b + carry;
+sr[i_plus_j++] = (comp)tmp;              /* downsize */
+carry = (comp)(tmp >> COMP_BIT_SIZE);
+} while (++j < n);
+sr[i_plus_j] = carry;
+} while (++i < t);
+bi_free(ctx, bia);
+bi_free(ctx, bib);
+return trim(biR);
+}
+#ifdef CONFIG_BIGINT_KARATSUBA
+/*
+* Karatsuba improves on regular multiplication due to only 3 multiplications
+* being done instead of 4. The additional additions/subtractions are O(N)
+* rather than O(N^2) and so for big numbers it saves on a few operations
+*/
+static bigint *karatsuba(BI_CTX *ctx, bigint *bia, bigint *bib, int is_square)
+{
+bigint *x0, *x1;
+bigint *p0, *p1, *p2;
+int m;
+if (is_square)
+{
+m = (bia->size + 1)/2;
+}
+else
+{
+m = (max(bia->size, bib->size) + 1)/2;
+}
+x0 = bi_clone(ctx, bia);
+x0->size = m;
+x1 = bi_clone(ctx, bia);
+comp_right_shift(x1, m);
+bi_free(ctx, bia);
+/* work out the 3 partial products */
+if (is_square)
+{
+p0 = bi_square(ctx, bi_copy(x0));
+p2 = bi_square(ctx, bi_copy(x1));
+p1 = bi_square(ctx, bi_add(ctx, x0, x1));
+}
+else /* normal multiply */
+{
+bigint *y0, *y1;
+y0 = bi_clone(ctx, bib);
+y0->size = m;
+y1 = bi_clone(ctx, bib);
+comp_right_shift(y1, m);
+bi_free(ctx, bib);
+p0 = bi_multiply(ctx, bi_copy(x0), bi_copy(y0));
+p2 = bi_multiply(ctx, bi_copy(x1), bi_copy(y1));
+p1 = bi_multiply(ctx, bi_add(ctx, x0, x1), bi_add(ctx, y0, y1));
+}
+p1 = bi_subtract(ctx,
+bi_subtract(ctx, p1, bi_copy(p2), NULL), bi_copy(p0), NULL);
+comp_left_shift(p1, m);
+comp_left_shift(p2, 2*m);
+return bi_add(ctx, p1, bi_add(ctx, p0, p2));
+}
+#endif
+/**
+* @brief Perform a multiplication operation between two bigints.
+* @param ctx [in]  The bigint session context.
+* @param bia [in]  A bigint.
+* @param bib [in]  Another bigint.
+* @return The result of the multiplication.
+*/
+bigint *bi_multiply(BI_CTX *ctx, bigint *bia, bigint *bib)
+{
+check(bia);
+check(bib);
+#ifdef CONFIG_BIGINT_KARATSUBA
+if (min(bia->size, bib->size) < MUL_KARATSUBA_THRESH)
+{
+return regular_multiply(ctx, bia, bib);
+}
+return karatsuba(ctx, bia, bib, 0);
+#else
+return regular_multiply(ctx, bia, bib);
+#endif
+}
+#ifdef CONFIG_BIGINT_SQUARE
+/*
+* Perform the actual square operion. It takes into account overflow.
+*/
+static bigint *regular_square(BI_CTX *ctx, bigint *bi)
+{
+int t = bi->size;
+int i = 0, j;
+bigint *biR = alloc(ctx, t*2);
+comp *w = biR->comps;
+comp *x = bi->comps;
+comp carry;
+memset(w, 0, biR->size*COMP_BYTE_SIZE);
+do
+{
+long_comp tmp = w[2*i] + (long_comp)x[i]*x[i];
+comp u = 0;
+w[2*i] = (comp)tmp;
+carry = (comp)(tmp >> COMP_BIT_SIZE);
+for (j = i+1; j < t; j++)
+{
+long_comp xx = (long_comp)x[i]*x[j];
+long_comp xx2 = 2*xx;
+long_comp blob = (long_comp)w[i+j]+carry;
+if (u)                  /* previous overflow */
+{
+blob += COMP_RADIX;
+}
+u = 0;
+tmp = xx2 + blob;
+/* check for overflow */
+if ((COMP_MAX-xx) < xx  || (COMP_MAX-xx2) < blob)
+{
+u = 1;
+}
+w[i+j] = (comp)tmp;
+carry = (comp)(tmp >> COMP_BIT_SIZE);
+}
+w[i+t] += carry;
+if (u)
+{
+w[i+t+1] = 1;   /* add carry */
+}
+} while (++i < t);
+bi_free(ctx, bi);
+return trim(biR);
+}
+/**
+* @brief Perform a square operation on a bigint.
+* @param ctx [in]  The bigint session context.
+* @param bia [in]  A bigint.
+* @return The result of the multiplication.
+*/
+bigint *bi_square(BI_CTX *ctx, bigint *bia)
+{
+check(bia);
+#ifdef CONFIG_BIGINT_KARATSUBA
+if (bia->size < SQU_KARATSUBA_THRESH)
+{
+return regular_square(ctx, bia);
+}
+return karatsuba(ctx, bia, NULL, 1);
+#else
+return regular_square(ctx, bia);
+#endif
+}
+#endif
+/**
+* @brief Compare two bigints.
+* @param bia [in]  A bigint.
+* @param bib [in]  Another bigint.
+* @return -1 if smaller, 1 if larger and 0 if equal.
+*/
+int bi_compare(bigint *bia, bigint *bib)
+{
+int r, i;
+check(bia);
+check(bib);
+if (bia->size > bib->size)
+r = 1;
+else if (bia->size < bib->size)
+r = -1;
+else
+{
+comp *a = bia->comps;
+comp *b = bib->comps;
+/* Same number of components.  Compare starting from the high end
+* and working down. */
+r = 0;
+i = bia->size - 1;
+do
+{
+if (a[i] > b[i])
+{
+r = 1;
+break;
+}
+else if (a[i] < b[i])
+{
+r = -1;
+break;
+}
+} while (--i >= 0);
+}
+return r;
+}
+/*
+* Allocate and zero more components.  Does not consume bi.
+*/
+static void more_comps(bigint *bi, int n)
+{
+if (n > bi->max_comps)
+{
+bi->max_comps = max(bi->max_comps * 2, n);
+bi->comps = (comp*)realloc(bi->comps, bi->max_comps * COMP_BYTE_SIZE);
+}
+if (n > bi->size)
+{
+memset(&bi->comps[bi->size], 0, (n-bi->size)*COMP_BYTE_SIZE);
+}
+bi->size = n;
+}
+/*
+* Make a new empty bigint. It may just use an old one if one is available.
+* Otherwise get one off the heap.
+*/
+static bigint *alloc(BI_CTX *ctx, int size)
+{
+bigint *biR;
+/* Can we recycle an old bigint? */
+if (ctx->free_list != NULL)
+{
+biR = ctx->free_list;
+ctx->free_list = biR->next;
+ctx->free_count--;
+if (biR->refs != 0)
+{
+#ifdef CONFIG_SSL_FULL_MODE
+printf("alloc: refs was not 0\n");
+#endif
+abort();    /* create a stack trace from a core dump */
+}
+more_comps(biR, size);
+}
+else
+{
+/* No free bigints available - create a new one. */
+biR = (bigint *)malloc(sizeof(bigint));
+biR->comps = (comp*)malloc(size * COMP_BYTE_SIZE);
+biR->max_comps = size;  /* give some space to spare */
+}
+biR->size = size;
+biR->refs = 1;
+biR->next = NULL;
+ctx->active_count++;
+return biR;
+}
+/*
+* Work out the highest '1' bit in an exponent. Used when doing sliding-window
+* exponentiation.
+*/
+static int find_max_exp_index(bigint *biexp)
+{
+int i = COMP_BIT_SIZE-1;
+comp shift = COMP_RADIX/2;
+comp test = biexp->comps[biexp->size-1];    /* assume no leading zeroes */
+check(biexp);
+do
+{
+if (test & shift)
+{
+return i+(biexp->size-1)*COMP_BIT_SIZE;
+}
+shift >>= 1;
+} while (--i != 0);
+return -1;      /* error - must have been a leading 0 */
+}
+/*
+* Is a particular bit is an exponent 1 or 0? Used when doing sliding-window
+* exponentiation.
+*/
+static int exp_bit_is_one(bigint *biexp, int offset)
+{
+comp test = biexp->comps[offset / COMP_BIT_SIZE];
+int num_shifts = offset % COMP_BIT_SIZE;
+comp shift = 1;
+int i;
+check(biexp);
+for (i = 0; i < num_shifts; i++)
+{
+shift <<= 1;
+}
+return test & shift;
+}
+#ifdef CONFIG_BIGINT_CHECK_ON
+/*
+* Perform a sanity check on bi.
+*/
+static void check(const bigint *bi)
+{
+if (bi->refs <= 0)
+{
+printf("check: zero or negative refs in bigint\n");
+abort();
+}
+if (bi->next != NULL)
+{
+printf("check: attempt to use a bigint from "
+"the free list\n");
+abort();
+}
+}
+#endif
+/*
+* Delete any leading 0's (and allow for 0).
+*/
+static bigint *trim(bigint *bi)
+{
+check(bi);
+while (bi->comps[bi->size-1] == 0 && bi->size > 1)
+{
+bi->size--;
+}
+return bi;
+}
+#if defined(CONFIG_BIGINT_MONTGOMERY)
+/**
+* @brief Perform a single montgomery reduction.
+* @param ctx [in]  The bigint session context.
+* @param bixy [in]  A bigint.
+* @return The result of the montgomery reduction.
+*/
+bigint *bi_mont(BI_CTX *ctx, bigint *bixy)
+{
+int i = 0, n;
+uint8_t mod_offset = ctx->mod_offset;
+bigint *bim = ctx->bi_mod[mod_offset];
+comp mod_inv = ctx->N0_dash[mod_offset];
+check(bixy);
+if (ctx->use_classical)     /* just use classical instead */
+{
+return bi_mod(ctx, bixy);
+}
+n = bim->size;
+do
+{
+bixy = bi_add(ctx, bixy, comp_left_shift(
+bi_int_multiply(ctx, bim, bixy->comps[i]*mod_inv), i));
+} while (++i < n);
+comp_right_shift(bixy, n);
+if (bi_compare(bixy, bim) >= 0)
+{
+bixy = bi_subtract(ctx, bixy, bim, NULL);
+}
+return bixy;
+}
+#elif defined(CONFIG_BIGINT_BARRETT)
+/*
+* Stomp on the most significant components to give the illusion of a "mod base
+* radix" operation
+*/
+static bigint *comp_mod(bigint *bi, int mod)
+{
+check(bi);
+if (bi->size > mod)
+{
+bi->size = mod;
+}
+return bi;
+}
+/*
+* Barrett reduction has no need for some parts of the product, so ignore bits
+* of the multiply. This routine gives Barrett its big performance
+* improvements over Classical/Montgomery reduction methods.
+*/
+static bigint *partial_multiply(BI_CTX *ctx, bigint *bia, bigint *bib,
+int inner_partial, int outer_partial)
+{
+int i = 0, j, n = bia->size, t = bib->size;
+bigint *biR;
+comp carry;
+comp *sr, *sa, *sb;
+check(bia);
+check(bib);
+biR = alloc(ctx, n + t);
+sa = bia->comps;
+sb = bib->comps;
+sr = biR->comps;
+if (inner_partial)
+{
+memset(sr, 0, inner_partial*COMP_BYTE_SIZE);
+}
+else    /* outer partial */
+{
+if (n < outer_partial || t < outer_partial) /* should we bother? */
+{
+bi_free(ctx, bia);
+bi_free(ctx, bib);
+biR->comps[0] = 0;      /* return 0 */
+biR->size = 1;
+return biR;
+}
+memset(&sr[outer_partial], 0, (n+t-outer_partial)*COMP_BYTE_SIZE);
+}
+do
+{
+comp *a = sa;
+comp b = *sb++;
+long_comp tmp;
+int i_plus_j = i;
+carry = 0;
+j = n;
+if (outer_partial && i_plus_j < outer_partial)
+{
+i_plus_j = outer_partial;
+a = &sa[outer_partial-i];
+j = n-(outer_partial-i);
+}
+do
+{
+if (inner_partial && i_plus_j >= inner_partial)
+{
+break;
+}
+tmp = sr[i_plus_j] + ((long_comp)*a++)*b + carry;
+sr[i_plus_j++] = (comp)tmp;              /* downsize */
+carry = (comp)(tmp >> COMP_BIT_SIZE);
+} while (--j != 0);
+sr[i_plus_j] = carry;
+} while (++i < t);
+bi_free(ctx, bia);
+bi_free(ctx, bib);
+return trim(biR);
+}
+/**
+* @brief Perform a single Barrett reduction.
+* @param ctx [in]  The bigint session context.
+* @param bi [in]  A bigint.
+* @return The result of the Barrett reduction.
+*/
+bigint *bi_barrett(BI_CTX *ctx, bigint *bi)
+{
+bigint *q1, *q2, *q3, *r1, *r2, *r;
+uint8_t mod_offset = ctx->mod_offset;
+bigint *bim = ctx->bi_mod[mod_offset];
+int k = bim->size;
+check(bi);
+check(bim);
+/* use Classical method instead  - Barrett cannot help here */
+if (bi->size > k*2)
+{
+return bi_mod(ctx, bi);
+}
+q1 = comp_right_shift(bi_clone(ctx, bi), k-1);
+/* do outer partial multiply */
+q2 = partial_multiply(ctx, q1, ctx->bi_mu[mod_offset], 0, k-1);
+q3 = comp_right_shift(q2, k+1);
+r1 = comp_mod(bi, k+1);
+/* do inner partial multiply */
+r2 = comp_mod(partial_multiply(ctx, q3, bim, k+1, 0), k+1);
+r = bi_subtract(ctx, r1, r2, NULL);
+/* if (r >= m) r = r - m; */
+if (bi_compare(r, bim) >= 0)
+{
+r = bi_subtract(ctx, r, bim, NULL);
+}
+return r;
+}
+#endif /* CONFIG_BIGINT_BARRETT */
+#ifdef CONFIG_BIGINT_SLIDING_WINDOW
+/*
+* Work out g1, g3, g5, g7... etc for the sliding-window algorithm
+*/
+static void precompute_slide_window(BI_CTX *ctx, int window, bigint *g1)
+{
+int k = 1, i;
+bigint *g2;
+for (i = 0; i < window-1; i++)   /* compute 2^(window-1) */
+{
+k <<= 1;
+}
+ctx->g = (bigint **)malloc(k*sizeof(bigint *));
+ctx->g[0] = bi_clone(ctx, g1);
+bi_permanent(ctx->g[0]);
+g2 = bi_residue(ctx, bi_square(ctx, ctx->g[0]));   /* g^2 */
+for (i = 1; i < k; i++)
+{
+ctx->g[i] = bi_residue(ctx, bi_multiply(ctx, ctx->g[i-1], bi_copy(g2)));
+bi_permanent(ctx->g[i]);
+}
+bi_free(ctx, g2);
+ctx->window = k;
+}
+#endif
+/**
+* @brief Perform a modular exponentiation.
+*
+* This function requires bi_set_mod() to have been called previously. This is
+* one of the optimisations used for performance.
+* @param ctx [in]  The bigint session context.
+* @param bi  [in]  The bigint on which to perform the mod power operation.
+* @param biexp [in] The bigint exponent.
+* @return The result of the mod exponentiation operation
+* @see bi_set_mod().
+*/
+bigint *bi_mod_power(BI_CTX *ctx, bigint *bi, bigint *biexp)
+{
+int i = find_max_exp_index(biexp), j, window_size = 1;
+bigint *biR = int_to_bi(ctx, 1);
+#if defined(CONFIG_BIGINT_MONTGOMERY)
+uint8_t mod_offset = ctx->mod_offset;
+if (!ctx->use_classical)
+{
+/* preconvert */
+bi = bi_mont(ctx,
+bi_multiply(ctx, bi, ctx->bi_RR_mod_m[mod_offset]));    /* x' */
+bi_free(ctx, biR);
+biR = ctx->bi_R_mod_m[mod_offset];                              /* A */
+}
+#endif
+check(bi);
+check(biexp);
+#ifdef CONFIG_BIGINT_SLIDING_WINDOW
+for (j = i; j > 32; j /= 5) /* work out an optimum size */
+window_size++;
+/* work out the slide constants */
+precompute_slide_window(ctx, window_size, bi);
+#else   /* just one constant */
+ctx->g = (bigint **)malloc(sizeof(bigint *));
+ctx->g[0] = bi_clone(ctx, bi);
+ctx->window = 1;
+bi_permanent(ctx->g[0]);
+#endif
+/* if sliding-window is off, then only one bit will be done at a time and
+* will reduce to standard left-to-right exponentiation */
+do
+{
+if (exp_bit_is_one(biexp, i))
+{
+int l = i-window_size+1;
+int part_exp = 0;
+if (l < 0)  /* LSB of exponent will always be 1 */
+l = 0;
+else
+{
+while (exp_bit_is_one(biexp, l) == 0)
+l++;    /* go back up */
+}
+/* build up the section of the exponent */
+for (j = i; j >= l; j--)
+{
+biR = bi_residue(ctx, bi_square(ctx, biR));
+if (exp_bit_is_one(biexp, j))
+part_exp++;
+if (j != l)
+part_exp <<= 1;
+}
+part_exp = (part_exp-1)/2;  /* adjust for array */
+biR = bi_residue(ctx, bi_multiply(ctx, biR, ctx->g[part_exp]));
+i = l-1;
+}
+else    /* square it */
+{
+biR = bi_residue(ctx, bi_square(ctx, biR));
+i--;
+}
+} while (i >= 0);
+/* cleanup */
+for (i = 0; i < ctx->window; i++)
+{
+bi_depermanent(ctx->g[i]);
+bi_free(ctx, ctx->g[i]);
+}
+free(ctx->g);
+bi_free(ctx, bi);
+bi_free(ctx, biexp);
+#if defined CONFIG_BIGINT_MONTGOMERY
+return ctx->use_classical ? biR : bi_mont(ctx, biR); /* convert back */
+#else /* CONFIG_BIGINT_CLASSICAL or CONFIG_BIGINT_BARRETT */
+return biR;
+#endif
+}
+#ifdef CONFIG_SSL_CERT_VERIFICATION
+/**
+* @brief Perform a modular exponentiation using a temporary modulus.
+*
+* We need this function to check the signatures of certificates. The modulus
+* of this function is temporary as it's just used for authentication.
+* @param ctx [in]  The bigint session context.
+* @param bi  [in]  The bigint to perform the exp/mod.
+* @param bim [in]  The temporary modulus.
+* @param biexp [in] The bigint exponent.
+* @return The result of the mod exponentiation operation
+* @see bi_set_mod().
+*/
+bigint *bi_mod_power2(BI_CTX *ctx, bigint *bi, bigint *bim, bigint *biexp)
+{
+bigint *biR, *tmp_biR;
+/* Set up a temporary bigint context and transfer what we need between
+* them. We need to do this since we want to keep the original modulus
+* which is already in this context. This operation is only called when
+* doing peer verification, and so is not expensive :-) */
+BI_CTX *tmp_ctx = bi_initialize();
+bi_set_mod(tmp_ctx, bi_clone(tmp_ctx, bim), BIGINT_M_OFFSET);
+tmp_biR = bi_mod_power(tmp_ctx,
+bi_clone(tmp_ctx, bi),
+bi_clone(tmp_ctx, biexp));
+biR = bi_clone(ctx, tmp_biR);
+bi_free(tmp_ctx, tmp_biR);
+bi_free_mod(tmp_ctx, BIGINT_M_OFFSET);
+bi_terminate(tmp_ctx);
+bi_free(ctx, bi);
+bi_free(ctx, bim);
+bi_free(ctx, biexp);
+return biR;
+}
+#endif
+#ifdef CONFIG_BIGINT_CRT
+/**
+* @brief Use the Chinese Remainder Theorem to quickly perform RSA decrypts.
+*
+* @param ctx [in]  The bigint session context.
+* @param bi  [in]  The bigint to perform the exp/mod.
+* @param dP [in] CRT's dP bigint
+* @param dQ [in] CRT's dQ bigint
+* @param p [in] CRT's p bigint
+* @param q [in] CRT's q bigint
+* @param qInv [in] CRT's qInv bigint
+* @return The result of the CRT operation
+*/
+bigint *bi_crt(BI_CTX *ctx, bigint *bi,
+bigint *dP, bigint *dQ,
+bigint *p, bigint *q, bigint *qInv)
+{
+bigint *m1, *m2, *h;
+/* Montgomery has a condition the 0 < x, y < m and these products violate
+* that condition. So disable Montgomery when using CRT */
+#if defined(CONFIG_BIGINT_MONTGOMERY)
+ctx->use_classical = 1;
+#endif
+ctx->mod_offset = BIGINT_P_OFFSET;
+m1 = bi_mod_power(ctx, bi_copy(bi), dP);
+ctx->mod_offset = BIGINT_Q_OFFSET;
+m2 = bi_mod_power(ctx, bi, dQ);
+h = bi_subtract(ctx, bi_add(ctx, m1, p), bi_copy(m2), NULL);
+h = bi_multiply(ctx, h, qInv);
+ctx->mod_offset = BIGINT_P_OFFSET;
+h = bi_residue(ctx, h);
+#if defined(CONFIG_BIGINT_MONTGOMERY)
+ctx->use_classical = 0;         /* reset for any further operation */
+#endif
+return bi_add(ctx, m2, bi_multiply(ctx, q, h));
+}
+#endif
+/** @} */

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comparison deps/Platinum/ThirdParty/Neptune/ThirdParty/axTLS/crypto/bigint.c @ 0:3425707ddbf6