fp_x64.c

/********************************************************************************************
* SIDH: an efficient supersingular isogeny cryptography library
*
* Abstract: modular arithmetic optimized for x64 platforms for P434
*********************************************************************************************/

#include "../P434_internal.h"


// Global constants
extern const uint64_t p434[NWORDS_FIELD];
extern const uint64_t p434p1[NWORDS_FIELD]; 
extern const uint64_t p434x2[NWORDS_FIELD]; 


__inline void fpadd434(const digit_t* a, const digit_t* b, digit_t* c)
{ // Modular addition, c = a+b mod p434.
  // Inputs: a, b in [0, 2*p434-1] 
  // Output: c in [0, 2*p434-1] 
    
#if (OS_TARGET == OS_WIN)
    unsigned int i, carry = 0;
    digit_t mask;

    for (i = 0; i < NWORDS_FIELD; i++) {
        ADDC(carry, a[i], b[i], carry, c[i]); 
    }

    carry = 0;
    for (i = 0; i < NWORDS_FIELD; i++) {
        SUBC(carry, c[i], ((digit_t*)p434x2)[i], carry, c[i]); 
    }
    mask = 0 - (digit_t)carry;

    carry = 0;
    for (i = 0; i < NWORDS_FIELD; i++) {
        ADDC(carry, c[i], ((digit_t*)p434x2)[i] & mask, carry, c[i]); 
    } 
    
#elif (OS_TARGET == OS_LINUX)                 
    
    fpadd434_asm(a, b, c);    

#endif
} 


__inline void fpsub434(const digit_t* a, const digit_t* b, digit_t* c)
{ // Modular subtraction, c = a-b mod p434.
  // Inputs: a, b in [0, 2*p434-1] 
  // Output: c in [0, 2*p434-1] 
    
#if (OS_TARGET == OS_WIN)
    unsigned int i, borrow = 0;
    digit_t mask;

    for (i = 0; i < NWORDS_FIELD; i++) {
        SUBC(borrow, a[i], b[i], borrow, c[i]); 
    }
    mask = 0 - (digit_t)borrow;

    borrow = 0;
    for (i = 0; i < NWORDS_FIELD; i++) {
        ADDC(borrow, c[i], ((digit_t*)p434x2)[i] & mask, borrow, c[i]); 
    }
    
#elif (OS_TARGET == OS_LINUX)                 
    
    fpsub434_asm(a, b, c);    

#endif
}


__inline void fpneg434(digit_t* a)
{ // Modular negation, a = -a mod p434.
  // Input/output: a in [0, 2*p434-1] 
    unsigned int i, borrow = 0;
    
    for (i = 0; i < NWORDS_FIELD; i++) {
        SUBC(borrow, ((digit_t*)p434x2)[i], a[i], borrow, a[i]); 
    }
}


void fpdiv2_434(const digit_t* a, digit_t* c)
{ // Modular division by two, c = a/2 mod p434.
  // Input : a in [0, 2*p434-1] 
  // Output: c in [0, 2*p434-1] 
    unsigned int i, carry = 0;
    digit_t mask;
        
    mask = 0 - (digit_t)(a[0] & 1);    // If a is odd compute a+p434
    for (i = 0; i < NWORDS_FIELD; i++) {
        ADDC(carry, a[i], ((digit_t*)p434)[i] & mask, carry, c[i]); 
    }

    mp_shiftr1(c, NWORDS_FIELD);
}  


void fpcorrection434(digit_t* a)
{ // Modular correction to reduce field element a in [0, 2*p434-1] to [0, p434-1].
    unsigned int i, borrow = 0;
    digit_t mask;

    for (i = 0; i < NWORDS_FIELD; i++) {
        SUBC(borrow, a[i], ((digit_t*)p434)[i], borrow, a[i]); 
    }
    mask = 0 - (digit_t)borrow;

    borrow = 0;
    for (i = 0; i < NWORDS_FIELD; i++) {
        ADDC(borrow, a[i], ((digit_t*)p434)[i] & mask, borrow, a[i]); 
    }
}


void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
        
    UNREFERENCED_PARAMETER(nwords);

#if (OS_TARGET == OS_WIN)
    digit_t t = 0;
    uint128_t uv = {0};
    unsigned int carry = 0;
        
    MULADD128(a[0], b[0], uv, carry, uv);
    t += carry;
    c[0] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[0], b[1], uv, carry, uv);
    t += carry;
    MULADD128(a[1], b[0], uv, carry, uv);
    t += carry;
    c[1] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[0], b[2], uv, carry, uv);
    t += carry;
    MULADD128(a[1], b[1], uv, carry, uv);
    t += carry;
    MULADD128(a[2], b[0], uv, carry, uv);
    t += carry;
    c[2] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[0], b[3], uv, carry, uv);
    t += carry;
    MULADD128(a[2], b[1], uv, carry, uv);
    t += carry;
    MULADD128(a[1], b[2], uv, carry, uv);
    t += carry;
    MULADD128(a[3], b[0], uv, carry, uv);
    t += carry;
    c[3] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[0], b[4], uv, carry, uv);
    t += carry;
    MULADD128(a[3], b[1], uv, carry, uv);
    t += carry;
    MULADD128(a[2], b[2], uv, carry, uv);
    t += carry;
    MULADD128(a[1], b[3], uv, carry, uv);
    t += carry;
    MULADD128(a[4], b[0], uv, carry, uv);
    t += carry;
    c[4] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[0], b[5], uv, carry, uv);
    t += carry;
    MULADD128(a[4], b[1], uv, carry, uv);
    t += carry;
    MULADD128(a[3], b[2], uv, carry, uv);
    t += carry;
    MULADD128(a[2], b[3], uv, carry, uv);
    t += carry;
    MULADD128(a[1], b[4], uv, carry, uv);
    t += carry;
    MULADD128(a[5], b[0], uv, carry, uv);
    t += carry;
    c[5] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[0], b[6], uv, carry, uv);
    t += carry;
    MULADD128(a[5], b[1], uv, carry, uv);
    t += carry;
    MULADD128(a[4], b[2], uv, carry, uv);
    t += carry;
    MULADD128(a[3], b[3], uv, carry, uv);
    t += carry;
    MULADD128(a[2], b[4], uv, carry, uv);
    t += carry;
    MULADD128(a[1], b[5], uv, carry, uv);
    t += carry;
    MULADD128(a[6], b[0], uv, carry, uv);
    t += carry;
    c[6] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[6], b[1], uv, carry, uv);
    t += carry;
    MULADD128(a[5], b[2], uv, carry, uv);
    t += carry;
    MULADD128(a[4], b[3], uv, carry, uv);
    t += carry;
    MULADD128(a[3], b[4], uv, carry, uv);
    t += carry;
    MULADD128(a[2], b[5], uv, carry, uv);
    t += carry;
    MULADD128(a[1], b[6], uv, carry, uv);
    t += carry;
    c[7] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[6], b[2], uv, carry, uv);
    t += carry;
    MULADD128(a[5], b[3], uv, carry, uv);
    t += carry;
    MULADD128(a[4], b[4], uv, carry, uv);
    t += carry;
    MULADD128(a[3], b[5], uv, carry, uv);
    t += carry;
    MULADD128(a[2], b[6], uv, carry, uv);
    t += carry;
    c[8] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[6], b[3], uv, carry, uv);
    t += carry;
    MULADD128(a[5], b[4], uv, carry, uv);
    t += carry;
    MULADD128(a[4], b[5], uv, carry, uv);
    t += carry;
    MULADD128(a[3], b[6], uv, carry, uv);
    t += carry;
    c[9] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[6], b[4], uv, carry, uv);
    t += carry;
    MULADD128(a[5], b[5], uv, carry, uv);
    t += carry;
    MULADD128(a[4], b[6], uv, carry, uv);
    t += carry;
    c[10] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;
    
    MULADD128(a[6], b[5], uv, carry, uv);
    t += carry;
    MULADD128(a[5], b[6], uv, carry, uv);
    t += carry;
    c[11] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    
    MULADD128(a[6], b[6], uv, carry, uv);
    c[12] = uv[0];
    c[13] = uv[1];

#elif (OS_TARGET == OS_LINUX)
    
    mul434_asm(a, b, c);

#endif
}


void rdc_mont(digit_t* ma, digit_t* mc)
{ // Montgomery reduction exploiting special form of the prime.
  // mc = ma*R^-1 mod p434x2, where R = 2^448.
  // If ma < 2^448*p434, the output mc is in the range [0, 2*p434-1].
  // ma is assumed to be in Montgomery representation.
        
#if (OS_TARGET == OS_WIN)
    unsigned int carry;
    digit_t t = 0;
    uint128_t uv = {0};
    
    mc[0] = ma[0];
    mc[1] = ma[1];
    mc[2] = ma[2];
    MUL128(mc[0], ((digit_t*)p434p1)[3], uv);
    ADDC(0, uv[0], ma[3], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    mc[3] = uv[0];
    uv[0] = uv[1];
    uv[1] = 0;

    MULADD128(mc[0], ((digit_t*)p434p1)[4], uv, carry, uv);
    MULADD128(mc[1], ((digit_t*)p434p1)[3], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[4], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[4] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[0], ((digit_t*)p434p1)[5], uv, carry, uv);
    t += carry;
    MULADD128(mc[1], ((digit_t*)p434p1)[4], uv, carry, uv);
    t += carry;
    MULADD128(mc[2], ((digit_t*)p434p1)[3], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[5], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[5] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[0], ((digit_t*)p434p1)[6], uv, carry, uv);
    t += carry;
    MULADD128(mc[1], ((digit_t*)p434p1)[5], uv, carry, uv);
    t += carry;
    MULADD128(mc[2], ((digit_t*)p434p1)[4], uv, carry, uv);
    t += carry;
    MULADD128(mc[3], ((digit_t*)p434p1)[3], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[6], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[6] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[1], ((digit_t*)p434p1)[6], uv, carry, uv);
    t += carry;
    MULADD128(mc[2], ((digit_t*)p434p1)[5], uv, carry, uv);
    t += carry;
    MULADD128(mc[3], ((digit_t*)p434p1)[4], uv, carry, uv);
    t += carry;
    MULADD128(mc[4], ((digit_t*)p434p1)[3], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[7], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[0] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[2], ((digit_t*)p434p1)[6], uv, carry, uv);
    t += carry;
    MULADD128(mc[3], ((digit_t*)p434p1)[5], uv, carry, uv);
    t += carry;
    MULADD128(mc[4], ((digit_t*)p434p1)[4], uv, carry, uv);
    t += carry;
    MULADD128(mc[5], ((digit_t*)p434p1)[3], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[8], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[1] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[3], ((digit_t*)p434p1)[6], uv, carry, uv);
    t += carry;
    MULADD128(mc[4], ((digit_t*)p434p1)[5], uv, carry, uv);
    t += carry;
    MULADD128(mc[5], ((digit_t*)p434p1)[4], uv, carry, uv);
    t += carry;
    MULADD128(mc[6], ((digit_t*)p434p1)[3], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[9], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[2] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[4], ((digit_t*)p434p1)[6], uv, carry, uv);
    t += carry;
    MULADD128(mc[5], ((digit_t*)p434p1)[5], uv, carry, uv);
    t += carry;
    MULADD128(mc[6], ((digit_t*)p434p1)[4], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[10], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[3] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[5], ((digit_t*)p434p1)[6], uv, carry, uv);
    t += carry;
    MULADD128(mc[6], ((digit_t*)p434p1)[5], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[11], carry, uv[0]); 
    ADDC(carry, uv[1], 0, carry, uv[1]); 
    t += carry; 
    mc[4] = uv[0];
    uv[0] = uv[1];
    uv[1] = t;
    t = 0;

    MULADD128(mc[6], ((digit_t*)p434p1)[6], uv, carry, uv);
    t += carry;
    ADDC(0, uv[0], ma[12], carry, mc[5]); 
    ADDC(carry, uv[1], ma[13], carry, mc[6]); 
    
#elif (OS_TARGET == OS_LINUX)                 
    
    rdc434_asm(ma, mc);    

#endif
}