BigNumberUtil.cpp

/*
 * Copyright (C) 2015 Southern Storm Software, Pty Ltd.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included
 * in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 * DEALINGS IN THE SOFTWARE.
 */

#include "BigNumberUtil.h"
#include "utility/EndianUtil.h"
#include "utility/LimbUtil.h"
#include <string.h>

void BigNumberUtil::unpackLE(limb_t *limbs, size_t count,
                             const uint8_t *bytes, size_t len)
{
#if BIGNUMBER_LIMB_8BIT
    if (len < count) {
        memcpy(limbs, bytes, len);
        memset(limbs + len, 0, count - len);
    } else {
        memcpy(limbs, bytes, count);
    }
#elif CRYPTO_LITTLE_ENDIAN
    count *= sizeof(limb_t);
    if (len < count) {
        memcpy(limbs, bytes, len);
        memset(((uint8_t *)limbs) + len, 0, count - len);
    } else {
        memcpy(limbs, bytes, count);
    }
#elif BIGNUMBER_LIMB_16BIT
    while (count > 0 && len >= 2) {
        *limbs++ = ((limb_t)(bytes[0])) |
                  (((limb_t)(bytes[1])) << 8);
        bytes += 2;
        --count;
        len -= 2;
    }
    if (count > 0 && len == 1) {
        *limbs++ = ((limb_t)(bytes[0]));
        --count;
    }
    while (count > 0) {
        *limbs++ = 0;
        --count;
    }
#elif BIGNUMBER_LIMB_32BIT
    while (count > 0 && len >= 4) {
        *limbs++ = ((limb_t)(bytes[0])) |
                  (((limb_t)(bytes[1])) <<  8) |
                  (((limb_t)(bytes[2])) << 16) |
                  (((limb_t)(bytes[3])) << 24);
        bytes += 4;
        --count;
        len -= 4;
    }
    if (count > 0) {
        if (len == 3) {
            *limbs++ = ((limb_t)(bytes[0])) |
                      (((limb_t)(bytes[1])) <<  8) |
                      (((limb_t)(bytes[2])) << 16);
        } else if (len == 2) {
            *limbs++ = ((limb_t)(bytes[0])) |
                      (((limb_t)(bytes[1])) <<  8);
        } else if (len == 1) {
            *limbs++ = ((limb_t)(bytes[0]));
        }
        --count;
    }
    while (count > 0) {
        *limbs++ = 0;
        --count;
    }
#endif
}

void BigNumberUtil::unpackBE(limb_t *limbs, size_t count,
                             const uint8_t *bytes, size_t len)
{
#if BIGNUMBER_LIMB_8BIT
    while (count > 0 && len > 0) {
        --count;
        --len;
        *limbs++ = bytes[len];
    }
    memset(limbs, 0, count);
#elif BIGNUMBER_LIMB_16BIT
    bytes += len;
    while (count > 0 && len >= 2) {
        --count;
        bytes -= 2;
        len -= 2;
        *limbs++ = ((limb_t)(bytes[1])) |
                  (((limb_t)(bytes[0])) << 8);
    }
    if (count > 0 && len == 1) {
        --count;
        --bytes;
        *limbs++ = (limb_t)(bytes[0]);
    }
    memset(limbs, 0, count * sizeof(limb_t));
#elif BIGNUMBER_LIMB_32BIT
    bytes += len;
    while (count > 0 && len >= 4) {
        --count;
        bytes -= 4;
        len -= 4;
        *limbs++ = ((limb_t)(bytes[3])) |
                  (((limb_t)(bytes[2])) << 8) |
                  (((limb_t)(bytes[1])) << 16) |
                  (((limb_t)(bytes[0])) << 24);
    }
    if (count > 0) {
        if (len == 3) {
            --count;
            bytes -= 3;
            *limbs++ = ((limb_t)(bytes[2])) |
                      (((limb_t)(bytes[1])) << 8) |
                      (((limb_t)(bytes[0])) << 16);
        } else if (len == 2) {
            --count;
            bytes -= 2;
            *limbs++ = ((limb_t)(bytes[1])) |
                      (((limb_t)(bytes[0])) << 8);
        } else if (len == 1) {
            --count;
            --bytes;
            *limbs++ = (limb_t)(bytes[0]);
        }
    }
    memset(limbs, 0, count * sizeof(limb_t));
#endif
}

void BigNumberUtil::packLE(uint8_t *bytes, size_t len,
                           const limb_t *limbs, size_t count)
{
#if BIGNUMBER_LIMB_8BIT
    if (len <= count) {
        memcpy(bytes, limbs, len);
    } else {
        memcpy(bytes, limbs, count);
        memset(bytes + count, 0, len - count);
    }
#elif CRYPTO_LITTLE_ENDIAN
    count *= sizeof(limb_t);
    if (len <= count) {
        memcpy(bytes, limbs, len);
    } else {
        memcpy(bytes, limbs, count);
        memset(bytes + count, 0, len - count);
    }
#elif BIGNUMBER_LIMB_16BIT
    limb_t word;
    while (count > 0 && len >= 2) {
        word = *limbs++;
        bytes[0] = (uint8_t)word;
        bytes[1] = (uint8_t)(word >> 8);
        --count;
        len -= 2;
        bytes += 2;
    }
    if (count > 0 && len == 1) {
        bytes[0] = (uint8_t)(*limbs);
        --len;
        ++bytes;
    }
    memset(bytes, 0, len);
#elif BIGNUMBER_LIMB_32BIT
    limb_t word;
    while (count > 0 && len >= 4) {
        word = *limbs++;
        bytes[0] = (uint8_t)word;
        bytes[1] = (uint8_t)(word >> 8);
        bytes[2] = (uint8_t)(word >> 16);
        bytes[3] = (uint8_t)(word >> 24);
        --count;
        len -= 4;
        bytes += 4;
    }
    if (count > 0) {
        if (len == 3) {
            word = *limbs;
            bytes[0] = (uint8_t)word;
            bytes[1] = (uint8_t)(word >> 8);
            bytes[2] = (uint8_t)(word >> 16);
            len -= 3;
            bytes += 3;
        } else if (len == 2) {
            word = *limbs;
            bytes[0] = (uint8_t)word;
            bytes[1] = (uint8_t)(word >> 8);
            len -= 2;
            bytes += 2;
        } else if (len == 1) {
            bytes[0] = (uint8_t)(*limbs);
            --len;
            ++bytes;
        }
    }
    memset(bytes, 0, len);
#endif
}

void BigNumberUtil::packBE(uint8_t *bytes, size_t len,
                           const limb_t *limbs, size_t count)
{
#if BIGNUMBER_LIMB_8BIT
    if (len > count) {
        size_t size = len - count;
        memset(bytes, 0, size);
        len -= size;
        bytes += size;
    } else if (len < count) {
        count = len;
    }
    limbs += count;
    while (count > 0) {
        --count;
        *bytes++ = *(--limbs);
    }
#elif BIGNUMBER_LIMB_16BIT
    size_t countBytes = count * sizeof(limb_t);
    limb_t word;
    if (len >= countBytes) {
        size_t size = len - countBytes;
        memset(bytes, 0, size);
        len -= size;
        bytes += size;
        limbs += count;
    } else {
        count = len / sizeof(limb_t);
        limbs += count;
        if ((len & 1) != 0)
            *bytes++ = (uint8_t)(*limbs);
    }
    while (count > 0) {
        --count;
        word = *(--limbs);
        *bytes++ = (uint8_t)(word >> 8);
        *bytes++ = (uint8_t)word;
    }
#elif BIGNUMBER_LIMB_32BIT
    size_t countBytes = count * sizeof(limb_t);
    limb_t word;
    if (len >= countBytes) {
        size_t size = len - countBytes;
        memset(bytes, 0, size);
        len -= size;
        bytes += size;
        limbs += count;
    } else {
        count = len / sizeof(limb_t);
        limbs += count;
        if ((len & 3) == 3) {
            word = *limbs;
            *bytes++ = (uint8_t)(word >> 16);
            *bytes++ = (uint8_t)(word >> 8);
            *bytes++ = (uint8_t)word;
        } else if ((len & 3) == 2) {
            word = *limbs;
            *bytes++ = (uint8_t)(word >> 8);
            *bytes++ = (uint8_t)word;
        } else if ((len & 3) == 1) {
            *bytes++ = (uint8_t)(*limbs);
        }
    }
    while (count > 0) {
        --count;
        word = *(--limbs);
        *bytes++ = (uint8_t)(word >> 24);
        *bytes++ = (uint8_t)(word >> 16);
        *bytes++ = (uint8_t)(word >> 8);
        *bytes++ = (uint8_t)word;
    }
#endif
}

limb_t BigNumberUtil::add(limb_t *result, const limb_t *x,
                          const limb_t *y, size_t size)
{
    dlimb_t carry = 0;
    while (size > 0) {
        carry += *x++;
        carry += *y++;
        *result++ = (limb_t)carry;
        carry >>= LIMB_BITS;
        --size;
    }
    return (limb_t)carry;
}

limb_t BigNumberUtil::sub(limb_t *result, const limb_t *x,
                          const limb_t *y, size_t size)
{
    dlimb_t borrow = 0;
    while (size > 0) {
        borrow = ((dlimb_t)(*x++)) - (*y++) - ((borrow >> LIMB_BITS) & 0x01);
        *result++ = (limb_t)borrow;
        --size;
    }
    return ((limb_t)(borrow >> LIMB_BITS)) & 0x01;
}

void BigNumberUtil::mul(limb_t *result, const limb_t *x, size_t xcount,
                        const limb_t *y, size_t ycount)
{
    size_t i, j;
    dlimb_t carry;
    limb_t word;
    const limb_t *xx;
    limb_t *rr;

    // Multiply the lowest limb of y by x.
    carry = 0;
    word = y[0];
    xx = x;
    rr = result;
    for (i = 0; i < xcount; ++i) {
        carry += ((dlimb_t)(*xx++)) * word;
        *rr++ = (limb_t)carry;
        carry >>= LIMB_BITS;
    }
    *rr = (limb_t)carry;

    // Multiply and add the remaining limbs of y by x.
    for (i = 1; i < ycount; ++i) {
        word = y[i];
        carry = 0;
        xx = x;
        rr = result + i;
        for (j = 0; j < xcount; ++j) {
            carry += ((dlimb_t)(*xx++)) * word;
            carry += *rr;
            *rr++ = (limb_t)carry;
            carry >>= LIMB_BITS;
        }
        *rr = (limb_t)carry;
    }
}

void BigNumberUtil::reduceQuick(limb_t *result, const limb_t *x,
                                const limb_t *y, size_t size)
{
    // Subtract "y" from "x" and turn the borrow into an AND mask.
    limb_t mask = sub(result, x, y, size);
    mask = (~mask) + 1;

    // Add "y" back to the result if the mask is non-zero.
    dlimb_t carry = 0;
    while (size > 0) {
        carry += *result;
        carry += (*y++ & mask);
        *result++ = (limb_t)carry;
        carry >>= LIMB_BITS;
        --size;
    }
}

limb_t BigNumberUtil::add_P(limb_t *result, const limb_t *x,
                            const limb_t *y, size_t size)
{
    dlimb_t carry = 0;
    while (size > 0) {
        carry += *x++;
        carry += pgm_read_limb(y++);
        *result++ = (limb_t)carry;
        carry >>= LIMB_BITS;
        --size;
    }
    return (limb_t)carry;
}

limb_t BigNumberUtil::sub_P(limb_t *result, const limb_t *x,
                            const limb_t *y, size_t size)
{
    dlimb_t borrow = 0;
    while (size > 0) {
        borrow = ((dlimb_t)(*x++)) - pgm_read_limb(y++) - ((borrow >> LIMB_BITS) & 0x01);
        *result++ = (limb_t)borrow;
        --size;
    }
    return ((limb_t)(borrow >> LIMB_BITS)) & 0x01;
}

void BigNumberUtil::mul_P(limb_t *result, const limb_t *x, size_t xcount,
                          const limb_t *y, size_t ycount)
{
    size_t i, j;
    dlimb_t carry;
    limb_t word;
    const limb_t *xx;
    limb_t *rr;

    // Multiply the lowest limb of y by x.
    carry = 0;
    word = pgm_read_limb(&(y[0]));
    xx = x;
    rr = result;
    for (i = 0; i < xcount; ++i) {
        carry += ((dlimb_t)(*xx++)) * word;
        *rr++ = (limb_t)carry;
        carry >>= LIMB_BITS;
    }
    *rr = (limb_t)carry;

    // Multiply and add the remaining limb of y by x.
    for (i = 1; i < ycount; ++i) {
        word = pgm_read_limb(&(y[i]));
        carry = 0;
        xx = x;
        rr = result + i;
        for (j = 0; j < xcount; ++j) {
            carry += ((dlimb_t)(*xx++)) * word;
            carry += *rr;
            *rr++ = (limb_t)carry;
            carry >>= LIMB_BITS;
        }
        *rr = (limb_t)carry;
    }
}

void BigNumberUtil::reduceQuick_P(limb_t *result, const limb_t *x,
                                  const limb_t *y, size_t size)
{
    // Subtract "y" from "x" and turn the borrow into an AND mask.
    limb_t mask = sub_P(result, x, y, size);
    mask = (~mask) + 1;

    // Add "y" back to the result if the mask is non-zero.
    dlimb_t carry = 0;
    while (size > 0) {
        carry += *result;
        carry += (pgm_read_limb(y++) & mask);
        *result++ = (limb_t)carry;
        carry >>= LIMB_BITS;
        --size;
    }
}