path: root/src/lib/libcrypto/bn/s2n_bignum.h

// $OpenBSD: s2n_bignum.h,v 1.4 2025/08/12 10:01:37 jsing Exp $
//
// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
//
// Permission to use, copy, modify, and/or distribute this software for any
// purpose with or without fee is hereby granted, provided that the above
// copyright notice and this permission notice appear in all copies.
//
// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
// ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
// ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
// OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

// ----------------------------------------------------------------------------
// C prototypes for s2n-bignum functions, so you can use them in C programs via
//
//  #include "s2n-bignum.h"
//
// The functions are listed in alphabetical order with a brief description
// in comments for each one. For more detailed documentation see the comment
// banner at the top of the corresponding assembly (.S) file, and
// for the last word in what properties it satisfies see the spec in the
// formal proof (the .ml file in the architecture-specific directory).
//
// For some functions there are additional variants with names ending in
// "_alt". These have the same core mathematical functionality as their
// non-"alt" versions, but can be better suited to some microarchitectures:
//
//      - On x86, the "_alt" forms avoid BMI and ADX instruction set
//        extensions, so will run on any x86_64 machine, even older ones
//
//      - On ARM, the "_alt" forms target machines with higher multiplier
//        throughput, generally offering higher performance there.
// ----------------------------------------------------------------------------


#if defined(_MSC_VER) || !defined(__STDC_VERSION__) || __STDC_VERSION__ < 199901L || defined(__STDC_NO_VLA__)
#define S2N_BIGNUM_STATIC
#else
#define S2N_BIGNUM_STATIC static
#endif

// Add, z := x + y
// Inputs x[m], y[n]; outputs function return (carry-out) and z[p]
extern uint64_t bignum_add (uint64_t p, uint64_t *z, uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Add modulo p_25519, z := (x + y) mod p_25519, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_add_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Add modulo p_256, z := (x + y) mod p_256, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_add_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Add modulo p_256k1, z := (x + y) mod p_256k1, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_add_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Add modulo p_384, z := (x + y) mod p_384, assuming x and y reduced
// Inputs x[6], y[6]; output z[6]
extern void bignum_add_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);

// Add modulo p_521, z := (x + y) mod p_521, assuming x and y reduced
// Inputs x[9], y[9]; output z[9]
extern void bignum_add_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9], const uint64_t y[S2N_BIGNUM_STATIC 9]);

// Add modulo p_sm2, z := (x + y) mod p_sm2, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_add_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Compute "amontification" constant z :== 2^{128k} (congruent mod m)
// Input m[k]; output z[k]; temporary buffer t[>=k]
extern void bignum_amontifier (uint64_t k, uint64_t *z, const uint64_t *m, uint64_t *t);

// Almost-Montgomery multiply, z :== (x * y / 2^{64k}) (congruent mod m)
// Inputs x[k], y[k], m[k]; output z[k]
extern void bignum_amontmul (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *y, const uint64_t *m);

// Almost-Montgomery reduce, z :== (x' / 2^{64p}) (congruent mod m)
// Inputs x[n], m[k], p; output z[k]
extern void bignum_amontredc (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x, const uint64_t *m, uint64_t p);

// Almost-Montgomery square, z :== (x^2 / 2^{64k}) (congruent mod m)
// Inputs x[k], m[k]; output z[k]
extern void bignum_amontsqr (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *m);

// Convert 4-digit (256-bit) bignum to/from big-endian form
// Input x[4]; output z[4]
extern void bignum_bigendian_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert 6-digit (384-bit) bignum to/from big-endian form
// Input x[6]; output z[6]
extern void bignum_bigendian_6 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Select bitfield starting at bit n with length l <= 64
// Inputs x[k], n, l; output function return
extern uint64_t bignum_bitfield (uint64_t k, const uint64_t *x, uint64_t n, uint64_t l);

// Return size of bignum in bits
// Input x[k]; output function return
extern uint64_t bignum_bitsize (uint64_t k, const uint64_t *x);

// Divide by a single (nonzero) word, z := x / m and return x mod m
// Inputs x[n], m; outputs function return (remainder) and z[k]
extern uint64_t bignum_cdiv (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x, uint64_t m);

// Divide by a single word, z := x / m when known to be exact
// Inputs x[n], m; output z[k]
extern void bignum_cdiv_exact (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x, uint64_t m);

// Count leading zero digits (64-bit words)
// Input x[k]; output function return
extern uint64_t bignum_cld (uint64_t k, const uint64_t *x);

// Count leading zero bits
// Input x[k]; output function return
extern uint64_t bignum_clz (uint64_t k, const uint64_t *x);

// Multiply-add with single-word multiplier, z := z + c * y
// Inputs c, y[n]; outputs function return (carry-out) and z[k]
extern uint64_t bignum_cmadd (uint64_t k, uint64_t *z, uint64_t c, uint64_t n, const uint64_t *y);

// Negated multiply-add with single-word multiplier, z := z - c * y
// Inputs c, y[n]; outputs function return (negative carry-out) and z[k]
extern uint64_t bignum_cmnegadd (uint64_t k, uint64_t *z, uint64_t c, uint64_t n, const uint64_t *y);

// Find modulus of bignum w.r.t. single nonzero word m, returning x mod m
// Input x[k], m; output function return
extern uint64_t bignum_cmod (uint64_t k, const uint64_t *x, uint64_t m);

// Multiply by a single word, z := c * y
// Inputs c, y[n]; outputs function return (carry-out) and z[k]
extern uint64_t bignum_cmul (uint64_t k, uint64_t *z, uint64_t c, uint64_t n, const uint64_t *y);

// Multiply by a single word modulo p_25519, z := (c * x) mod p_25519, assuming x reduced
// Inputs c, x[4]; output z[4]
extern void bignum_cmul_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_cmul_p25519_alt (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Multiply by a single word modulo p_256, z := (c * x) mod p_256, assuming x reduced
// Inputs c, x[4]; output z[4]
extern void bignum_cmul_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_cmul_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Multiply by a single word modulo p_256k1, z := (c * x) mod p_256k1, assuming x reduced
// Inputs c, x[4]; output z[4]
extern void bignum_cmul_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_cmul_p256k1_alt (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Multiply by a single word modulo p_384, z := (c * x) mod p_384, assuming x reduced
// Inputs c, x[6]; output z[6]
extern void bignum_cmul_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 6]);
extern void bignum_cmul_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Multiply by a single word modulo p_521, z := (c * x) mod p_521, assuming x reduced
// Inputs c, x[9]; output z[9]
extern void bignum_cmul_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 9]);
extern void bignum_cmul_p521_alt (uint64_t z[S2N_BIGNUM_STATIC 9], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Multiply by a single word modulo p_sm2, z := (c * x) mod p_sm2, assuming x reduced
// Inputs c, x[4]; output z[4]
extern void bignum_cmul_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_cmul_sm2_alt (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t c, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Test bignums for coprimality, gcd(x,y) = 1
// Inputs x[m], y[n]; output function return; temporary buffer t[>=2*max(m,n)]
extern uint64_t bignum_coprime (uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y, uint64_t *t);

// Copy bignum with zero-extension or truncation, z := x
// Input x[n]; output z[k]
extern void bignum_copy (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x);

// Given table: uint64_t[height*width], copy table[idx*width...(idx+1)*width-1]
// into z[0..width-1].
// This function is constant-time with respect to the value of `idx`. This is
// achieved by reading the whole table and using the bit-masking to get the
// `idx`-th row.
// Input table[height*width]; output z[width]
extern void bignum_copy_row_from_table (uint64_t *z, const uint64_t *table, uint64_t height,
        uint64_t width, uint64_t idx);

// Given table: uint64_t[height*width], copy table[idx*width...(idx+1)*width-1]
// into z[0..width-1]. width must be a multiple of 8.
// This function is constant-time with respect to the value of `idx`. This is
// achieved by reading the whole table and using the bit-masking to get the
// `idx`-th row.
// Input table[height*width]; output z[width]
extern void bignum_copy_row_from_table_8n (uint64_t *z, const uint64_t *table,
        uint64_t height, uint64_t width, uint64_t idx);

// Given table: uint64_t[height*16], copy table[idx*16...(idx+1)*16-1] into z[0..row-1].
// This function is constant-time with respect to the value of `idx`. This is
// achieved by reading the whole table and using the bit-masking to get the
// `idx`-th row.
// Input table[height*16]; output z[16]
extern void bignum_copy_row_from_table_16 (uint64_t *z, const uint64_t *table,
        uint64_t height, uint64_t idx);

// Given table: uint64_t[height*32], copy table[idx*32...(idx+1)*32-1] into z[0..row-1].
// This function is constant-time with respect to the value of `idx`. This is
// achieved by reading the whole table and using the bit-masking to get the
// `idx`-th row.
// Input table[height*32]; output z[32]
extern void bignum_copy_row_from_table_32 (uint64_t *z, const uint64_t *table,
        uint64_t height, uint64_t idx);

// Count trailing zero digits (64-bit words)
// Input x[k]; output function return
extern uint64_t bignum_ctd (uint64_t k, const uint64_t *x);

// Count trailing zero bits
// Input x[k]; output function return
extern uint64_t bignum_ctz (uint64_t k, const uint64_t *x);

// Convert from almost-Montgomery form, z := (x / 2^256) mod p_256
// Input x[4]; output z[4]
extern void bignum_deamont_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_deamont_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert from almost-Montgomery form, z := (x / 2^256) mod p_256k1
// Input x[4]; output z[4]
extern void bignum_deamont_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert from almost-Montgomery form, z := (x / 2^384) mod p_384
// Input x[6]; output z[6]
extern void bignum_deamont_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);
extern void bignum_deamont_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Convert from almost-Montgomery form z := (x / 2^576) mod p_521
// Input x[9]; output z[9]
extern void bignum_deamont_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Convert from almost-Montgomery form z := (x / 2^256) mod p_sm2
// Input x[4]; output z[4]
extern void bignum_deamont_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert from (almost-)Montgomery form z := (x / 2^{64k}) mod m
// Inputs x[k], m[k]; output z[k]
extern void bignum_demont (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *m);

// Convert from Montgomery form z := (x / 2^256) mod p_256, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_demont_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_demont_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert from Montgomery form z := (x / 2^256) mod p_256k1, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_demont_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert from Montgomery form z := (x / 2^384) mod p_384, assuming x reduced
// Input x[6]; output z[6]
extern void bignum_demont_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);
extern void bignum_demont_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Convert from Montgomery form z := (x / 2^576) mod p_521, assuming x reduced
// Input x[9]; output z[9]
extern void bignum_demont_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Convert from Montgomery form z := (x / 2^256) mod p_sm2, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_demont_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Select digit x[n]
// Inputs x[k], n; output function return
extern uint64_t bignum_digit (uint64_t k, const uint64_t *x, uint64_t n);

// Return size of bignum in digits (64-bit word)
// Input x[k]; output function return
extern uint64_t bignum_digitsize (uint64_t k, const uint64_t *x);

// Divide bignum by 10: z' := z div 10, returning remainder z mod 10
// Inputs z[k]; outputs function return (remainder) and z[k]
extern uint64_t bignum_divmod10 (uint64_t k, uint64_t *z);

// Double modulo p_25519, z := (2 * x) mod p_25519, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_double_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Double modulo p_256, z := (2 * x) mod p_256, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_double_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Double modulo p_256k1, z := (2 * x) mod p_256k1, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_double_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Double modulo p_384, z := (2 * x) mod p_384, assuming x reduced
// Input x[6]; output z[6]
extern void bignum_double_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Double modulo p_521, z := (2 * x) mod p_521, assuming x reduced
// Input x[9]; output z[9]
extern void bignum_double_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Double modulo p_sm2, z := (2 * x) mod p_sm2, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_double_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Extended Montgomery reduce, returning results in input-output buffer
// Inputs z[2*k], m[k], w; outputs function return (extra result bit) and z[2*k]
extern uint64_t bignum_emontredc (uint64_t k, uint64_t *z, const uint64_t *m, uint64_t w);

// Extended Montgomery reduce in 8-digit blocks, results in input-output buffer
// Inputs z[2*k], m[k], w; outputs function return (extra result bit) and z[2*k]
extern uint64_t bignum_emontredc_8n (uint64_t k, uint64_t *z, const uint64_t *m, uint64_t w);
// Inputs z[2*k], m[k], w; outputs function return (extra result bit) and z[2*k]
// Temporary buffer m_precalc[12*(k/4-1)]
extern uint64_t bignum_emontredc_8n_cdiff (uint64_t k, uint64_t *z, const uint64_t *m,
                                          uint64_t w, uint64_t *m_precalc);

// Test bignums for equality, x = y
// Inputs x[m], y[n]; output function return
extern uint64_t bignum_eq (uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Test bignum for even-ness
// Input x[k]; output function return
extern uint64_t bignum_even (uint64_t k, const uint64_t *x);

// Convert 4-digit (256-bit) bignum from big-endian bytes
// Input x[32] (bytes); output z[4]
extern void bignum_frombebytes_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint8_t x[S2N_BIGNUM_STATIC 32]);

// Convert 6-digit (384-bit) bignum from big-endian bytes
// Input x[48] (bytes); output z[6]
extern void bignum_frombebytes_6 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint8_t x[S2N_BIGNUM_STATIC 48]);

// Convert 4-digit (256-bit) bignum from little-endian bytes
// Input x[32] (bytes); output z[4]
extern void bignum_fromlebytes_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint8_t x[S2N_BIGNUM_STATIC 32]);

// Convert 6-digit (384-bit) bignum from little-endian bytes
// Input x[48] (bytes); output z[6]
extern void bignum_fromlebytes_6 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint8_t x[S2N_BIGNUM_STATIC 48]);

// Convert little-endian bytes to 9-digit 528-bit bignum
// Input x[66] (bytes); output z[9]
extern void bignum_fromlebytes_p521 (uint64_t z[S2N_BIGNUM_STATIC 9],const uint8_t x[S2N_BIGNUM_STATIC 66]);

// Compare bignums, x >= y
// Inputs x[m], y[n]; output function return
extern uint64_t bignum_ge (uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Compare bignums, x > y
// Inputs x[m], y[n]; output function return
extern uint64_t bignum_gt (uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Halve modulo p_256, z := (x / 2) mod p_256, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_half_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Halve modulo p_256k1, z := (x / 2) mod p_256k1, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_half_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Halve modulo p_384, z := (x / 2) mod p_384, assuming x reduced
// Input x[6]; output z[6]
extern void bignum_half_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Halve modulo p_521, z := (x / 2) mod p_521, assuming x reduced
// Input x[9]; output z[9]
extern void bignum_half_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Halve modulo p_sm2, z := (x / 2) mod p_sm2, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_half_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Modular inverse modulo p_25519 = 2^255 - 19
// Input x[4]; output z[4]
extern void bignum_inv_p25519(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Modular inverse modulo p_256 = 2^256 - 2^224 + 2^192 + 2^96 - 1
// Input x[4]; output z[4]
extern void bignum_inv_p256(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Modular inverse modulo p_384 = 2^384 - 2^128 - 2^96 + 2^32 - 1
// Input x[6]; output z[6]
extern void bignum_inv_p384(uint64_t z[S2N_BIGNUM_STATIC 6],const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Modular inverse modulo p_521 = 2^521 - 1
// Input x[9]; output z[9]
extern void bignum_inv_p521(uint64_t z[S2N_BIGNUM_STATIC 9],const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Modular inverse modulo p_sm2 = 2^256 - 2^224 - 2^96 + 2^64 - 1
// Input x[4]; output z[4]
extern void bignum_inv_sm2(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Inverse square root modulo p_25519
// Input x[4]; output function return (Legendre symbol) and z[4]
extern int64_t bignum_invsqrt_p25519(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern int64_t bignum_invsqrt_p25519_alt(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Test bignum for zero-ness, x = 0
// Input x[k]; output function return
extern uint64_t bignum_iszero (uint64_t k, const uint64_t *x);

// Multiply z := x * y
// Inputs x[16], y[16]; output z[32]; temporary buffer t[>=32]
extern void bignum_kmul_16_32 (uint64_t z[S2N_BIGNUM_STATIC 32], const uint64_t x[S2N_BIGNUM_STATIC 16], const uint64_t y[S2N_BIGNUM_STATIC 16], uint64_t t[S2N_BIGNUM_STATIC 32]);

// Multiply z := x * y
// Inputs x[32], y[32]; output z[64]; temporary buffer t[>=96]
extern void bignum_kmul_32_64 (uint64_t z[S2N_BIGNUM_STATIC 64], const uint64_t x[S2N_BIGNUM_STATIC 32], const uint64_t y[S2N_BIGNUM_STATIC 32], uint64_t t[S2N_BIGNUM_STATIC 96]);

// Square, z := x^2
// Input x[16]; output z[32]; temporary buffer t[>=24]
extern void bignum_ksqr_16_32 (uint64_t z[S2N_BIGNUM_STATIC 32], const uint64_t x[S2N_BIGNUM_STATIC 16], uint64_t t[S2N_BIGNUM_STATIC 24]);

// Square, z := x^2
// Input x[32]; output z[64]; temporary buffer t[>=72]
extern void bignum_ksqr_32_64 (uint64_t z[S2N_BIGNUM_STATIC 64], const uint64_t x[S2N_BIGNUM_STATIC 32], uint64_t t[S2N_BIGNUM_STATIC 72]);

// Compare bignums, x <= y
// Inputs x[m], y[n]; output function return
extern uint64_t bignum_le (uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Convert 4-digit (256-bit) bignum to/from little-endian form
// Input x[4]; output z[4]
extern void bignum_littleendian_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert 6-digit (384-bit) bignum to/from little-endian form
// Input x[6]; output z[6]
extern void bignum_littleendian_6 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Compare bignums, x < y
// Inputs x[m], y[n]; output function return
extern uint64_t bignum_lt (uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Multiply-add, z := z + x * y
// Inputs x[m], y[n]; outputs function return (carry-out) and z[k]
extern uint64_t bignum_madd (uint64_t k, uint64_t *z, uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Multiply-add modulo the order of the curve25519/edwards25519 basepoint
// Inputs x[4], y[4], c[4]; output z[4]
extern void bignum_madd_n25519 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4], const uint64_t c[S2N_BIGNUM_STATIC 4]);
extern void bignum_madd_n25519_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4], const uint64_t c[S2N_BIGNUM_STATIC 4]);

// Reduce modulo group order, z := x mod m_25519
// Input x[4]; output z[4]
extern void bignum_mod_m25519_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo basepoint order, z := x mod n_25519
// Input x[k]; output z[4]
extern void bignum_mod_n25519 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);

// Reduce modulo basepoint order, z := x mod n_25519
// Input x[4]; output z[4]
extern void bignum_mod_n25519_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo group order, z := x mod n_256
// Input x[k]; output z[4]
extern void bignum_mod_n256 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);
extern void bignum_mod_n256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);

// Reduce modulo group order, z := x mod n_256
// Input x[4]; output z[4]
extern void bignum_mod_n256_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo group order, z := x mod n_256k1
// Input x[4]; output z[4]
extern void bignum_mod_n256k1_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo group order, z := x mod n_384
// Input x[k]; output z[6]
extern void bignum_mod_n384 (uint64_t z[S2N_BIGNUM_STATIC 6], uint64_t k, const uint64_t *x);
extern void bignum_mod_n384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], uint64_t k, const uint64_t *x);

// Reduce modulo group order, z := x mod n_384
// Input x[6]; output z[6]
extern void bignum_mod_n384_6 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Reduce modulo group order, z := x mod n_521
// Input x[9]; output z[9]
extern void bignum_mod_n521_9 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);
extern void bignum_mod_n521_9_alt (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Reduce modulo group order, z := x mod n_sm2
// Input x[k]; output z[4]
extern void bignum_mod_nsm2 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);
extern void bignum_mod_nsm2_alt (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);

// Reduce modulo group order, z := x mod n_sm2
// Input x[4]; output z[4]
extern void bignum_mod_nsm2_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo field characteristic, z := x mod p_25519
// Input x[4]; output z[4]
extern void bignum_mod_p25519_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo field characteristic, z := x mod p_256
// Input x[k]; output z[4]
extern void bignum_mod_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);
extern void bignum_mod_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);

// Reduce modulo field characteristic, z := x mod p_256
// Input x[4]; output z[4]
extern void bignum_mod_p256_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo field characteristic, z := x mod p_256k1
// Input x[4]; output z[4]
extern void bignum_mod_p256k1_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Reduce modulo field characteristic, z := x mod p_384
// Input x[k]; output z[6]
extern void bignum_mod_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], uint64_t k, const uint64_t *x);
extern void bignum_mod_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], uint64_t k, const uint64_t *x);

// Reduce modulo field characteristic, z := x mod p_384
// Input x[6]; output z[6]
extern void bignum_mod_p384_6 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Reduce modulo field characteristic, z := x mod p_521
// Input x[9]; output z[9]
extern void bignum_mod_p521_9 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Reduce modulo field characteristic, z := x mod p_sm2
// Input x[k]; output z[4]
extern void bignum_mod_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t k, const uint64_t *x);

// Reduce modulo field characteristic, z := x mod p_sm2
// Input x[4]; output z[4]
extern void bignum_mod_sm2_4 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Add modulo m, z := (x + y) mod m, assuming x and y reduced
// Inputs x[k], y[k], m[k]; output z[k]
extern void bignum_modadd (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *y, const uint64_t *m);

// Double modulo m, z := (2 * x) mod m, assuming x reduced
// Inputs x[k], m[k]; output z[k]
extern void bignum_moddouble (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *m);

// Modular exponentiation for arbitrary odd modulus, z := (a^p) mod m
// Inputs a[k], p[k], m[k]; output z[k], temporary buffer t[>=3*k]
extern void bignum_modexp(uint64_t k,uint64_t *z, const uint64_t *a,const uint64_t *p,const uint64_t *m,uint64_t *t);

// Compute "modification" constant z := 2^{64k} mod m
// Input m[k]; output z[k]; temporary buffer t[>=k]
extern void bignum_modifier (uint64_t k, uint64_t *z, const uint64_t *m, uint64_t *t);

// Invert modulo m, z = (1/a) mod b, assuming b is an odd number > 1, a coprime to b
// Inputs a[k], b[k]; output z[k]; temporary buffer t[>=3*k]
extern void bignum_modinv (uint64_t k, uint64_t *z, const uint64_t *a, const uint64_t *b, uint64_t *t);

// Optionally negate modulo m, z := (-x) mod m (if p nonzero) or z := x (if p zero), assuming x reduced
// Inputs p, x[k], m[k]; output z[k]
extern void bignum_modoptneg (uint64_t k, uint64_t *z, uint64_t p, const uint64_t *x, const uint64_t *m);

// Subtract modulo m, z := (x - y) mod m, assuming x and y reduced
// Inputs x[k], y[k], m[k]; output z[k]
extern void bignum_modsub (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *y, const uint64_t *m);

// Compute "montification" constant z := 2^{128k} mod m
// Input m[k]; output z[k]; temporary buffer t[>=k]
extern void bignum_montifier (uint64_t k, uint64_t *z, const uint64_t *m, uint64_t *t);

// Montgomery inverse modulo p_256 = 2^256 - 2^224 + 2^192 + 2^96 - 1
// Input x[4]; output z[4]
extern void bignum_montinv_p256(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Montgomery inverse modulo p_384 = 2^384 - 2^128 - 2^96 + 2^32 - 1
// Input x[6]; output z[6]
extern void bignum_montinv_p384(uint64_t z[S2N_BIGNUM_STATIC 6],const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Montgomery inverse modulo p_sm2 = 2^256 - 2^224 - 2^96 + 2^64 - 1
// Input x[4]; output z[4]
extern void bignum_montinv_sm2(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Montgomery multiply, z := (x * y / 2^{64k}) mod m
// Inputs x[k], y[k], m[k]; output z[k]
extern void bignum_montmul (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *y, const uint64_t *m);

// Montgomery multiply, z := (x * y / 2^256) mod p_256
// Inputs x[4], y[4]; output z[4]
extern void bignum_montmul_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);
extern void bignum_montmul_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Montgomery multiply, z := (x * y / 2^256) mod p_256k1
// Inputs x[4], y[4]; output z[4]
extern void bignum_montmul_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);
extern void bignum_montmul_p256k1_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Montgomery multiply, z := (x * y / 2^384) mod p_384
// Inputs x[6], y[6]; output z[6]
extern void bignum_montmul_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);
extern void bignum_montmul_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);

// Montgomery multiply, z := (x * y / 2^576) mod p_521
// Inputs x[9], y[9]; output z[9]
extern void bignum_montmul_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9], const uint64_t y[S2N_BIGNUM_STATIC 9]);
extern void bignum_montmul_p521_alt (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9], const uint64_t y[S2N_BIGNUM_STATIC 9]);

// Montgomery multiply, z := (x * y / 2^256) mod p_sm2
// Inputs x[4], y[4]; output z[4]
extern void bignum_montmul_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);
extern void bignum_montmul_sm2_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Montgomery reduce, z := (x' / 2^{64p}) MOD m
// Inputs x[n], m[k], p; output z[k]
extern void bignum_montredc (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x, const uint64_t *m, uint64_t p);

// Montgomery square, z := (x^2 / 2^{64k}) mod m
// Inputs x[k], m[k]; output z[k]
extern void bignum_montsqr (uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *m);

// Montgomery square, z := (x^2 / 2^256) mod p_256
// Input x[4]; output z[4]
extern void bignum_montsqr_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_montsqr_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Montgomery square, z := (x^2 / 2^256) mod p_256k1
// Input x[4]; output z[4]
extern void bignum_montsqr_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_montsqr_p256k1_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Montgomery square, z := (x^2 / 2^384) mod p_384
// Input x[6]; output z[6]
extern void bignum_montsqr_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);
extern void bignum_montsqr_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Montgomery square, z := (x^2 / 2^576) mod p_521
// Input x[9]; output z[9]
extern void bignum_montsqr_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);
extern void bignum_montsqr_p521_alt (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Montgomery square, z := (x^2 / 2^256) mod p_sm2
// Input x[4]; output z[4]
extern void bignum_montsqr_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_montsqr_sm2_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Multiply z := x * y
// Inputs x[m], y[n]; output z[k]
extern void bignum_mul (uint64_t k, uint64_t *z, uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Multiply z := x * y
// Inputs x[4], y[4]; output z[8]
extern void bignum_mul_4_8 (uint64_t z[S2N_BIGNUM_STATIC 8], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);
extern void bignum_mul_4_8_alt (uint64_t z[S2N_BIGNUM_STATIC 8], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Multiply z := x * y
// Inputs x[6], y[6]; output z[12]
extern void bignum_mul_6_12 (uint64_t z[S2N_BIGNUM_STATIC 12], const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);
extern void bignum_mul_6_12_alt (uint64_t z[S2N_BIGNUM_STATIC 12], const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);

// Multiply z := x * y
// Inputs x[8], y[8]; output z[16]
extern void bignum_mul_8_16 (uint64_t z[S2N_BIGNUM_STATIC 16], const uint64_t x[S2N_BIGNUM_STATIC 8], const uint64_t y[S2N_BIGNUM_STATIC 8]);
extern void bignum_mul_8_16_alt (uint64_t z[S2N_BIGNUM_STATIC 16], const uint64_t x[S2N_BIGNUM_STATIC 8], const uint64_t y[S2N_BIGNUM_STATIC 8]);

// Multiply modulo p_25519, z := (x * y) mod p_25519
// Inputs x[4], y[4]; output z[4]
extern void bignum_mul_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);
extern void bignum_mul_p25519_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Multiply modulo p_256k1, z := (x * y) mod p_256k1
// Inputs x[4], y[4]; output z[4]
extern void bignum_mul_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);
extern void bignum_mul_p256k1_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Multiply modulo p_521, z := (x * y) mod p_521, assuming x and y reduced
// Inputs x[9], y[9]; output z[9]
extern void bignum_mul_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9], const uint64_t y[S2N_BIGNUM_STATIC 9]);
extern void bignum_mul_p521_alt (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9], const uint64_t y[S2N_BIGNUM_STATIC 9]);

// Multiply bignum by 10 and add word: z := 10 * z + d
// Inputs z[k], d; outputs function return (carry) and z[k]
extern uint64_t bignum_muladd10 (uint64_t k, uint64_t *z, uint64_t d);

// Multiplex/select z := x (if p nonzero) or z := y (if p zero)
// Inputs p, x[k], y[k]; output z[k]
extern void bignum_mux (uint64_t p, uint64_t k, uint64_t *z, const uint64_t *x, const uint64_t *y);

// 256-bit multiplex/select z := x (if p nonzero) or z := y (if p zero)
// Inputs p, x[4], y[4]; output z[4]
extern void bignum_mux_4 (uint64_t p, uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// 384-bit multiplex/select z := x (if p nonzero) or z := y (if p zero)
// Inputs p, x[6], y[6]; output z[6]
extern void bignum_mux_6 (uint64_t p, uint64_t z[S2N_BIGNUM_STATIC 6],const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);

// Select element from 16-element table, z := xs[k*i]
// Inputs xs[16*k], i; output z[k]
extern void bignum_mux16 (uint64_t k, uint64_t *z, const uint64_t *xs, uint64_t i);

// Negate modulo p_25519, z := (-x) mod p_25519, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_neg_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Negate modulo p_256, z := (-x) mod p_256, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_neg_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Negate modulo p_256k1, z := (-x) mod p_256k1, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_neg_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Negate modulo p_384, z := (-x) mod p_384, assuming x reduced
// Input x[6]; output z[6]
extern void bignum_neg_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Negate modulo p_521, z := (-x) mod p_521, assuming x reduced
// Input x[9]; output z[9]
extern void bignum_neg_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Negate modulo p_sm2, z := (-x) mod p_sm2, assuming x reduced
// Input x[4]; output z[4]
extern void bignum_neg_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Negated modular inverse, z := (-1/x) mod 2^{64k}
// Input x[k]; output z[k]
extern void bignum_negmodinv (uint64_t k, uint64_t *z, const uint64_t *x);

// Test bignum for nonzero-ness x =/= 0
// Input x[k]; output function return
extern uint64_t bignum_nonzero (uint64_t k, const uint64_t *x);

// Test 256-bit bignum for nonzero-ness x =/= 0
// Input x[4]; output function return
extern uint64_t bignum_nonzero_4(const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Test 384-bit bignum for nonzero-ness x =/= 0
// Input x[6]; output function return
extern uint64_t bignum_nonzero_6(const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Normalize bignum in-place by shifting left till top bit is 1
// Input z[k]; outputs function return (bits shifted left) and z[k]
extern uint64_t bignum_normalize (uint64_t k, uint64_t *z);

// Test bignum for odd-ness
// Input x[k]; output function return
extern uint64_t bignum_odd (uint64_t k, const uint64_t *x);

// Convert single digit to bignum, z := n
// Input n; output z[k]
extern void bignum_of_word (uint64_t k, uint64_t *z, uint64_t n);

// Optionally add, z := x + y (if p nonzero) or z := x (if p zero)
// Inputs x[k], p, y[k]; outputs function return (carry-out) and z[k]
extern uint64_t bignum_optadd (uint64_t k, uint64_t *z, const uint64_t *x, uint64_t p, const uint64_t *y);

// Optionally negate, z := -x (if p nonzero) or z := x (if p zero)
// Inputs p, x[k]; outputs function return (nonzero input) and z[k]
extern uint64_t bignum_optneg (uint64_t k, uint64_t *z, uint64_t p, const uint64_t *x);

// Optionally negate modulo p_25519, z := (-x) mod p_25519 (if p nonzero) or z := x (if p zero), assuming x reduced
// Inputs p, x[4]; output z[4]
extern void bignum_optneg_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t p, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Optionally negate modulo p_256, z := (-x) mod p_256 (if p nonzero) or z := x (if p zero), assuming x reduced
// Inputs p, x[4]; output z[4]
extern void bignum_optneg_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t p, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Optionally negate modulo p_256k1, z := (-x) mod p_256k1 (if p nonzero) or z := x (if p zero), assuming x reduced
// Inputs p, x[4]; output z[4]
extern void bignum_optneg_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t p, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Optionally negate modulo p_384, z := (-x) mod p_384 (if p nonzero) or z := x (if p zero), assuming x reduced
// Inputs p, x[6]; output z[6]
extern void bignum_optneg_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], uint64_t p, const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Optionally negate modulo p_521, z := (-x) mod p_521 (if p nonzero) or z := x (if p zero), assuming x reduced
// Inputs p, x[9]; output z[9]
extern void bignum_optneg_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], uint64_t p, const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Optionally negate modulo p_sm2, z := (-x) mod p_sm2 (if p nonzero) or z := x (if p zero), assuming x reduced
// Inputs p, x[4]; output z[4]
extern void bignum_optneg_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], uint64_t p, const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Optionally subtract, z := x - y (if p nonzero) or z := x (if p zero)
// Inputs x[k], p, y[k]; outputs function return (carry-out) and z[k]
extern uint64_t bignum_optsub (uint64_t k, uint64_t *z, const uint64_t *x, uint64_t p, const uint64_t *y);

// Optionally subtract or add, z := x + sgn(p) * y interpreting p as signed
// Inputs x[k], p, y[k]; outputs function return (carry-out) and z[k]
extern uint64_t bignum_optsubadd (uint64_t k, uint64_t *z, const uint64_t *x, uint64_t p, const uint64_t *y);

// Return bignum of power of 2, z := 2^n
// Input n; output z[k]
extern void bignum_pow2 (uint64_t k, uint64_t *z, uint64_t n);

// Shift bignum left by c < 64 bits z := x * 2^c
// Inputs x[n], c; outputs function return (carry-out) and z[k]
extern uint64_t bignum_shl_small (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x, uint64_t c);

// Shift bignum right by c < 64 bits z := floor(x / 2^c)
// Inputs x[n], c; outputs function return (bits shifted out) and z[k]
extern uint64_t bignum_shr_small (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x, uint64_t c);

// Square, z := x^2
// Input x[n]; output z[k]
extern void bignum_sqr (uint64_t k, uint64_t *z, uint64_t n, const uint64_t *x);

// Square, z := x^2
// Input x[4]; output z[8]
extern void bignum_sqr_4_8 (uint64_t z[S2N_BIGNUM_STATIC 8], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_sqr_4_8_alt (uint64_t z[S2N_BIGNUM_STATIC 8], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Square, z := x^2
// Input x[6]; output z[12]
extern void bignum_sqr_6_12 (uint64_t z[S2N_BIGNUM_STATIC 12], const uint64_t x[S2N_BIGNUM_STATIC 6]);
extern void bignum_sqr_6_12_alt (uint64_t z[S2N_BIGNUM_STATIC 12], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Square, z := x^2
// Input x[8]; output z[16]
extern void bignum_sqr_8_16 (uint64_t z[S2N_BIGNUM_STATIC 16], const uint64_t x[S2N_BIGNUM_STATIC 8]);
extern void bignum_sqr_8_16_alt (uint64_t z[S2N_BIGNUM_STATIC 16], const uint64_t x[S2N_BIGNUM_STATIC 8]);

// Square modulo p_25519, z := (x^2) mod p_25519
// Input x[4]; output z[4]
extern void bignum_sqr_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_sqr_p25519_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Square modulo p_256k1, z := (x^2) mod p_256k1
// Input x[4]; output z[4]
extern void bignum_sqr_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_sqr_p256k1_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Square modulo p_521, z := (x^2) mod p_521, assuming x reduced
// Input x[9]; output z[9]
extern void bignum_sqr_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);
extern void bignum_sqr_p521_alt (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Square root modulo p_25519
// Input x[4]; output function return (Legendre symbol) and z[4]
extern int64_t bignum_sqrt_p25519(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern int64_t bignum_sqrt_p25519_alt(uint64_t z[S2N_BIGNUM_STATIC 4],const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Subtract, z := x - y
// Inputs x[m], y[n]; outputs function return (carry-out) and z[p]
extern uint64_t bignum_sub (uint64_t p, uint64_t *z, uint64_t m, const uint64_t *x, uint64_t n, const uint64_t *y);

// Subtract modulo p_25519, z := (x - y) mod p_25519, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_sub_p25519 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Subtract modulo p_256, z := (x - y) mod p_256, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_sub_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Subtract modulo p_256k1, z := (x - y) mod p_256k1, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_sub_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Subtract modulo p_384, z := (x - y) mod p_384, assuming x and y reduced
// Inputs x[6], y[6]; output z[6]
extern void bignum_sub_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);

// Subtract modulo p_521, z := (x - y) mod p_521, assuming x and y reduced
// Inputs x[9], y[9]; output z[9]
extern void bignum_sub_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9], const uint64_t y[S2N_BIGNUM_STATIC 9]);

// Subtract modulo p_sm2, z := (x - y) mod p_sm2, assuming x and y reduced
// Inputs x[4], y[4]; output z[4]
extern void bignum_sub_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4], const uint64_t y[S2N_BIGNUM_STATIC 4]);

// Convert 4-digit (256-bit) bignum to big-endian bytes
// Input x[4]; output z[32] (bytes)
extern void bignum_tobebytes_4 (uint8_t z[S2N_BIGNUM_STATIC 32], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert 6-digit (384-bit) bignum to big-endian bytes
// Input x[6]; output z[48] (bytes)
extern void bignum_tobebytes_6 (uint8_t z[S2N_BIGNUM_STATIC 48], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Convert 4-digit (256-bit) bignum to little-endian bytes
// Input x[4]; output z[32] (bytes)
extern void bignum_tolebytes_4 (uint8_t z[S2N_BIGNUM_STATIC 32], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert 6-digit (384-bit) bignum to little-endian bytes
// Input x[6]; output z[48] (bytes)
extern void bignum_tolebytes_6 (uint8_t z[S2N_BIGNUM_STATIC 48], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Convert 9-digit 528-bit bignum to little-endian bytes
// Input x[6]; output z[66] (bytes)
extern void bignum_tolebytes_p521 (uint8_t z[S2N_BIGNUM_STATIC 66], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Convert to Montgomery form z := (2^256 * x) mod p_256
// Input x[4]; output z[4]
extern void bignum_tomont_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_tomont_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert to Montgomery form z := (2^256 * x) mod p_256k1
// Input x[4]; output z[4]
extern void bignum_tomont_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_tomont_p256k1_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Convert to Montgomery form z := (2^384 * x) mod p_384
// Input x[6]; output z[6]
extern void bignum_tomont_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);
extern void bignum_tomont_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Convert to Montgomery form z := (2^576 * x) mod p_521
// Input x[9]; output z[9]
extern void bignum_tomont_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Convert to Montgomery form z := (2^256 * x) mod p_sm2
// Input x[4]; output z[4]
extern void bignum_tomont_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Triple modulo p_256, z := (3 * x) mod p_256
// Input x[4]; output z[4]
extern void bignum_triple_p256 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_triple_p256_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Triple modulo p_256k1, z := (3 * x) mod p_256k1
// Input x[4]; output z[4]
extern void bignum_triple_p256k1 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_triple_p256k1_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Triple modulo p_384, z := (3 * x) mod p_384
// Input x[6]; output z[6]
extern void bignum_triple_p384 (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);
extern void bignum_triple_p384_alt (uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);

// Triple modulo p_521, z := (3 * x) mod p_521, assuming x reduced
// Input x[9]; output z[9]
extern void bignum_triple_p521 (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);
extern void bignum_triple_p521_alt (uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);

// Triple modulo p_sm2, z := (3 * x) mod p_sm2
// Input x[4]; output z[4]
extern void bignum_triple_sm2 (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
extern void bignum_triple_sm2_alt (uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);

// Montgomery ladder step for curve25519
// Inputs point[8], pp[16], b; output rr[16]
extern void curve25519_ladderstep(uint64_t rr[16],const uint64_t point[8],const uint64_t pp[16],uint64_t b);
extern void curve25519_ladderstep_alt(uint64_t rr[16],const uint64_t point[8],const uint64_t pp[16],uint64_t b);

// Projective scalar multiplication, x coordinate only, for curve25519
// Inputs scalar[4], point[4]; output res[8]
extern void curve25519_pxscalarmul(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 4]);
extern void curve25519_pxscalarmul_alt(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 4]);

// x25519 function for curve25519
// Inputs scalar[4], point[4]; output res[4]
extern void curve25519_x25519(uint64_t res[S2N_BIGNUM_STATIC 4],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 4]);
extern void curve25519_x25519_alt(uint64_t res[S2N_BIGNUM_STATIC 4],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 4]);

// x25519 function for curve25519 (byte array arguments)
// Inputs scalar[32] (bytes), point[32] (bytes); output res[32] (bytes)
extern void curve25519_x25519_byte(uint8_t res[S2N_BIGNUM_STATIC 32],const uint8_t scalar[S2N_BIGNUM_STATIC 32],const uint8_t point[S2N_BIGNUM_STATIC 32]);
extern void curve25519_x25519_byte_alt(uint8_t res[S2N_BIGNUM_STATIC 32],const uint8_t scalar[S2N_BIGNUM_STATIC 32],const uint8_t point[S2N_BIGNUM_STATIC 32]);

// x25519 function for curve25519 on base element 9
// Input scalar[4]; output res[4]
extern void curve25519_x25519base(uint64_t res[S2N_BIGNUM_STATIC 4],const uint64_t scalar[S2N_BIGNUM_STATIC 4]);
extern void curve25519_x25519base_alt(uint64_t res[S2N_BIGNUM_STATIC 4],const uint64_t scalar[S2N_BIGNUM_STATIC 4]);

// x25519 function for curve25519 on base element 9 (byte array arguments)
// Input scalar[32] (bytes); output res[32] (bytes)
extern void curve25519_x25519base_byte(uint8_t res[S2N_BIGNUM_STATIC 32],const uint8_t scalar[S2N_BIGNUM_STATIC 32]);
extern void curve25519_x25519base_byte_alt(uint8_t res[S2N_BIGNUM_STATIC 32],const uint8_t scalar[S2N_BIGNUM_STATIC 32]);

// Decode compressed 256-bit form of edwards25519 point
// Input c[32] (bytes); output function return and z[8]
extern uint64_t edwards25519_decode(uint64_t z[S2N_BIGNUM_STATIC 8], const uint8_t c[S2N_BIGNUM_STATIC 32]);
extern uint64_t edwards25519_decode_alt(uint64_t z[S2N_BIGNUM_STATIC 8], const uint8_t c[S2N_BIGNUM_STATIC 32]);

// Encode edwards25519 point into compressed form as 256-bit number
// Input p[8]; output z[32] (bytes)
extern void edwards25519_encode(uint8_t z[S2N_BIGNUM_STATIC 32], const uint64_t p[S2N_BIGNUM_STATIC 8]);

// Extended projective addition for edwards25519
// Inputs p1[16], p2[16]; output p3[16]
extern void edwards25519_epadd(uint64_t p3[S2N_BIGNUM_STATIC 16],const uint64_t p1[S2N_BIGNUM_STATIC 16],const uint64_t p2[S2N_BIGNUM_STATIC 16]);
extern void edwards25519_epadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 16],const uint64_t p1[S2N_BIGNUM_STATIC 16],const uint64_t p2[S2N_BIGNUM_STATIC 16]);

// Extended projective doubling for edwards25519
// Inputs p1[12]; output p3[16]
extern void edwards25519_epdouble(uint64_t p3[S2N_BIGNUM_STATIC 16],const uint64_t p1[S2N_BIGNUM_STATIC 12]);
extern void edwards25519_epdouble_alt(uint64_t p3[S2N_BIGNUM_STATIC 16],const uint64_t p1[S2N_BIGNUM_STATIC 12]);

// Projective doubling for edwards25519
// Inputs p1[12]; output p3[12]
extern void edwards25519_pdouble(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);
extern void edwards25519_pdouble_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);

// Extended projective + precomputed mixed addition for edwards25519
// Inputs p1[16], p2[12]; output p3[16]
extern void edwards25519_pepadd(uint64_t p3[S2N_BIGNUM_STATIC 16],const uint64_t p1[S2N_BIGNUM_STATIC 16],const uint64_t p2[S2N_BIGNUM_STATIC 12]);
extern void edwards25519_pepadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 16],const uint64_t p1[S2N_BIGNUM_STATIC 16],const uint64_t p2[S2N_BIGNUM_STATIC 12]);

// Scalar multiplication by standard basepoint for edwards25519 (Ed25519)
// Input scalar[4]; output res[8]
extern void edwards25519_scalarmulbase(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4]);
extern void edwards25519_scalarmulbase_alt(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4]);

// Double scalar multiplication for edwards25519, fresh and base point
// Input scalar[4], point[8], bscalar[4]; output res[8]
extern void edwards25519_scalarmuldouble(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4], const uint64_t point[S2N_BIGNUM_STATIC 8],const uint64_t bscalar[S2N_BIGNUM_STATIC 4]);
extern void edwards25519_scalarmuldouble_alt(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4], const uint64_t point[S2N_BIGNUM_STATIC 8],const uint64_t bscalar[S2N_BIGNUM_STATIC 4]);

// Scalar product of 2-element polynomial vectors in NTT domain, with mulcache
// Inputs a[512], b[512], bt[256] (signed 16-bit words); output r[256] (signed 16-bit words)
extern void mlkem_basemul_k2(int16_t r[S2N_BIGNUM_STATIC 256],const int16_t a[S2N_BIGNUM_STATIC 512],const int16_t b[S2N_BIGNUM_STATIC 512],const int16_t bt[S2N_BIGNUM_STATIC 256]);

// Scalar product of 3-element polynomial vectors in NTT domain, with mulcache
// Inputs a[768], b[768], bt[384] (signed 16-bit words); output r[256] (signed 16-bit words)
extern void mlkem_basemul_k3(int16_t r[S2N_BIGNUM_STATIC 256],const int16_t a[S2N_BIGNUM_STATIC 768],const int16_t b[S2N_BIGNUM_STATIC 768],const int16_t bt[S2N_BIGNUM_STATIC 384]);

// Scalar product of 4-element polynomial vectors in NTT domain, with mulcache
// Inputs a[1024], b[1024], bt[512] (signed 16-bit words); output r[256] (signed 16-bit words)
extern void mlkem_basemul_k4(int16_t r[S2N_BIGNUM_STATIC 256],const int16_t a[S2N_BIGNUM_STATIC 1024],const int16_t b[S2N_BIGNUM_STATIC 1024],const int16_t bt[S2N_BIGNUM_STATIC 512]);

// Inverse number-theoretic transform from ML-KEM
// Input a[256] (signed 16-bit words), z_01234[80] (signed 16-bit words), z_56[384] (signed 16-bit words); output a[256] (signed 16-bit words)
extern void mlkem_intt(int16_t a[S2N_BIGNUM_STATIC 256],const int16_t z_01234[S2N_BIGNUM_STATIC 80],const int16_t z_56[S2N_BIGNUM_STATIC 384]);

// Precompute the mulcache data for a polynomial in the NTT domain
// Inputs a[256], z[128] and t[128] (signed 16-bit words); output x[128] (signed 16-bit words)
extern void mlkem_mulcache_compute(int16_t x[S2N_BIGNUM_STATIC 128],const int16_t a[S2N_BIGNUM_STATIC 256],const int16_t z[S2N_BIGNUM_STATIC 128],const int16_t t[S2N_BIGNUM_STATIC 128]);

// Forward number-theoretic transform from ML-KEM
// Input a[256] (signed 16-bit words), z_01234[80] (signed 16-bit words), z_56[384] (signed 16-bit words); output a[256] (signed 16-bit words)
extern void mlkem_ntt(int16_t a[S2N_BIGNUM_STATIC 256],const int16_t z_01234[S2N_BIGNUM_STATIC 80],const int16_t z_56[S2N_BIGNUM_STATIC 384]);

// Canonical modular reduction of polynomial coefficients for ML-KEM
// Input a[256] (signed 16-bit words); output a[256] (signed 16-bit words)
extern void mlkem_reduce(int16_t a[S2N_BIGNUM_STATIC 256]);

// Pack ML-KEM polynomial coefficients as 12-bit numbers
// Input a[256] (signed 16-bit words); output r[384] (bytes)
extern void mlkem_tobytes(uint8_t r[S2N_BIGNUM_STATIC 384],const int16_t a[S2N_BIGNUM_STATIC 256]);

// Conversion of ML-KEM polynomial coefficients to Montgomery form
// Input a[256] (signed 16-bit words); output a[256] (signed 16-bit words)
extern void mlkem_tomont(int16_t a[S2N_BIGNUM_STATIC 256]);

// Uniform rejection sampling for ML-KEM
// Inputs *buf (unsigned bytes), buflen, table (unsigned bytes); output r[256] (signed 16-bit words), return
extern uint64_t mlkem_rej_uniform_VARIABLE_TIME(int16_t r[S2N_BIGNUM_STATIC 256],const uint8_t *buf,uint64_t buflen,const uint8_t *table);

// Point addition on NIST curve P-256 in Montgomery-Jacobian coordinates
// Inputs p1[12], p2[12]; output p3[12]
extern void p256_montjadd(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 12]);
extern void p256_montjadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 12]);

// Point doubling on NIST curve P-256 in Montgomery-Jacobian coordinates
// Inputs p1[12]; output p3[12]
extern void p256_montjdouble(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);
extern void p256_montjdouble_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);

// Point mixed addition on NIST curve P-256 in Montgomery-Jacobian coordinates
// Inputs p1[12], p2[8]; output p3[12]
extern void p256_montjmixadd(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 8]);
extern void p256_montjmixadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 8]);

// Montgomery-Jacobian form scalar multiplication for P-256
// Input scalar[4], point[12]; output res[12]
extern void p256_montjscalarmul(uint64_t res[S2N_BIGNUM_STATIC 12],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 12]);
extern void p256_montjscalarmul_alt(uint64_t res[S2N_BIGNUM_STATIC 12],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 12]);

// Scalar multiplication for NIST curve P-256
// Input scalar[4], point[8]; output res[8]
extern void p256_scalarmul(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 8]);
extern void p256_scalarmul_alt(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 8]);

// Scalar multiplication for precomputed point on NIST curve P-256
// Input scalar[4], blocksize, table[]; output res[8]
extern void p256_scalarmulbase(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4],uint64_t blocksize,const uint64_t *table);
extern void p256_scalarmulbase_alt(uint64_t res[S2N_BIGNUM_STATIC 8],const uint64_t scalar[S2N_BIGNUM_STATIC 4],uint64_t blocksize,const uint64_t *table);

// Point addition on NIST curve P-384 in Montgomery-Jacobian coordinates
// Inputs p1[18], p2[18]; output p3[18]
extern void p384_montjadd(uint64_t p3[S2N_BIGNUM_STATIC 18],const uint64_t p1[S2N_BIGNUM_STATIC 18],const uint64_t p2[S2N_BIGNUM_STATIC 18]);
extern void p384_montjadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 18],const uint64_t p1[S2N_BIGNUM_STATIC 18],const uint64_t p2[S2N_BIGNUM_STATIC 18]);

// Point doubling on NIST curve P-384 in Montgomery-Jacobian coordinates
// Inputs p1[18]; output p3[18]
extern void p384_montjdouble(uint64_t p3[S2N_BIGNUM_STATIC 18],const uint64_t p1[S2N_BIGNUM_STATIC 18]);
extern void p384_montjdouble_alt(uint64_t p3[S2N_BIGNUM_STATIC 18],const uint64_t p1[S2N_BIGNUM_STATIC 18]);

// Point mixed addition on NIST curve P-384 in Montgomery-Jacobian coordinates
// Inputs p1[18], p2[12]; output p3[18]
extern void p384_montjmixadd(uint64_t p3[S2N_BIGNUM_STATIC 18],const uint64_t p1[S2N_BIGNUM_STATIC 18],const uint64_t p2[S2N_BIGNUM_STATIC 12]);
extern void p384_montjmixadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 18],const uint64_t p1[S2N_BIGNUM_STATIC 18],const uint64_t p2[S2N_BIGNUM_STATIC 12]);

// Montgomery-Jacobian form scalar multiplication for P-384
// Input scalar[6], point[18]; output res[18]
extern void p384_montjscalarmul(uint64_t res[S2N_BIGNUM_STATIC 18],const uint64_t scalar[S2N_BIGNUM_STATIC 6],const uint64_t point[S2N_BIGNUM_STATIC 18]);
extern void p384_montjscalarmul_alt(uint64_t res[S2N_BIGNUM_STATIC 18],const uint64_t scalar[S2N_BIGNUM_STATIC 6],const uint64_t point[S2N_BIGNUM_STATIC 18]);

// Point addition on NIST curve P-521 in Jacobian coordinates
// Inputs p1[27], p2[27]; output p3[27]
extern void p521_jadd(uint64_t p3[S2N_BIGNUM_STATIC 27],const uint64_t p1[S2N_BIGNUM_STATIC 27],const uint64_t p2[S2N_BIGNUM_STATIC 27]);
extern void p521_jadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 27],const uint64_t p1[S2N_BIGNUM_STATIC 27],const uint64_t p2[S2N_BIGNUM_STATIC 27]);

// Point doubling on NIST curve P-521 in Jacobian coordinates
// Input p1[27]; output p3[27]
extern void p521_jdouble(uint64_t p3[S2N_BIGNUM_STATIC 27],const uint64_t p1[S2N_BIGNUM_STATIC 27]);
extern void p521_jdouble_alt(uint64_t p3[S2N_BIGNUM_STATIC 27],const uint64_t p1[S2N_BIGNUM_STATIC 27]);

// Point mixed addition on NIST curve P-521 in Jacobian coordinates
// Inputs p1[27], p2[18]; output p3[27]
extern void p521_jmixadd(uint64_t p3[S2N_BIGNUM_STATIC 27],const uint64_t p1[S2N_BIGNUM_STATIC 27],const uint64_t p2[S2N_BIGNUM_STATIC 18]);
extern void p521_jmixadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 27],const uint64_t p1[S2N_BIGNUM_STATIC 27],const uint64_t p2[S2N_BIGNUM_STATIC 18]);

// Jacobian form scalar multiplication for P-521
// Input scalar[9], point[27]; output res[27]
extern void p521_jscalarmul(uint64_t res[S2N_BIGNUM_STATIC 27],const uint64_t scalar[S2N_BIGNUM_STATIC 9],const uint64_t point[S2N_BIGNUM_STATIC 27]);
extern void p521_jscalarmul_alt(uint64_t res[S2N_BIGNUM_STATIC 27],const uint64_t scalar[S2N_BIGNUM_STATIC 9],const uint64_t point[S2N_BIGNUM_STATIC 27]);

// Point addition on SECG curve secp256k1 in Jacobian coordinates
// Inputs p1[12], p2[12]; output p3[12]
extern void secp256k1_jadd(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 12]);
extern void secp256k1_jadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 12]);

// Point doubling on SECG curve secp256k1 in Jacobian coordinates
// Input p1[12]; output p3[12]
extern void secp256k1_jdouble(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);
extern void secp256k1_jdouble_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);

// Point mixed addition on SECG curve secp256k1 in Jacobian coordinates
// Inputs p1[12], p2[8]; output p3[12]
extern void secp256k1_jmixadd(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 8]);
extern void secp256k1_jmixadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 8]);

// Keccak-f1600 permutation for SHA3
// Inputs a[25], rc[24]; output a[25]
extern void sha3_keccak_f1600(uint64_t a[S2N_BIGNUM_STATIC 25],const uint64_t rc[S2N_BIGNUM_STATIC 24]);
extern void sha3_keccak_f1600_alt(uint64_t a[S2N_BIGNUM_STATIC 25],const uint64_t rc[S2N_BIGNUM_STATIC 24]);

// Batched 2-way Keccak-f1600 permutation for SHA3
// Inputs a[50], rc[24]; output a[50]
extern void sha3_keccak2_f1600(uint64_t a[S2N_BIGNUM_STATIC 50],const uint64_t rc[S2N_BIGNUM_STATIC 24]);
extern void sha3_keccak2_f1600_alt(uint64_t a[S2N_BIGNUM_STATIC 50],const uint64_t rc[S2N_BIGNUM_STATIC 24]);

// Batched 4-way Keccak-f1600 permutation for SHA3
// Inputs a[100], rc[24]; output a[100]
extern void sha3_keccak4_f1600(uint64_t a[S2N_BIGNUM_STATIC 100],const uint64_t rc[S2N_BIGNUM_STATIC 24]);
extern void sha3_keccak4_f1600_alt(uint64_t a[S2N_BIGNUM_STATIC 100],const uint64_t rc[S2N_BIGNUM_STATIC 24]);
extern void sha3_keccak4_f1600_alt2(uint64_t a[S2N_BIGNUM_STATIC 100],const uint64_t rc[S2N_BIGNUM_STATIC 24]);

// Point addition on CC curve SM2 in Montgomery-Jacobian coordinates
// Inputs p1[12], p2[12]; output p3[12]
extern void sm2_montjadd(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 12]);
extern void sm2_montjadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 12]);

// Point doubling on CC curve SM2 in Montgomery-Jacobian coordinates
// Inputs p1[12]; output p3[12]
extern void sm2_montjdouble(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);
extern void sm2_montjdouble_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12]);

// Point mixed addition on CC curve SM2 in Montgomery-Jacobian coordinates
// Inputs p1[12], p2[8]; output p3[12]
extern void sm2_montjmixadd(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 8]);
extern void sm2_montjmixadd_alt(uint64_t p3[S2N_BIGNUM_STATIC 12],const uint64_t p1[S2N_BIGNUM_STATIC 12],const uint64_t p2[S2N_BIGNUM_STATIC 8]);

// Montgomery-Jacobian form scalar multiplication for CC curve SM2
// Input scalar[4], point[12]; output res[12]
extern void sm2_montjscalarmul(uint64_t res[S2N_BIGNUM_STATIC 12],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 12]);
extern void sm2_montjscalarmul_alt(uint64_t res[S2N_BIGNUM_STATIC 12],const uint64_t scalar[S2N_BIGNUM_STATIC 4],const uint64_t point[S2N_BIGNUM_STATIC 12]);

// Reverse the bytes in a single word
// Input a; output function return
extern uint64_t word_bytereverse (uint64_t a);

// Count leading zero bits in a single word
// Input a; output function return
extern uint64_t word_clz (uint64_t a);

// Count trailing zero bits in a single word
// Input a; output function return
extern uint64_t word_ctz (uint64_t a);

// Perform 59 "divstep" iterations and return signed matrix of updates
// Inputs d, f, g; output m[2][2] and function return
extern int64_t word_divstep59(int64_t m[2][2],int64_t d,uint64_t f,uint64_t g);

// Return maximum of two unsigned 64-bit words
// Inputs a, b; output function return
extern uint64_t word_max (uint64_t a, uint64_t b);

// Return minimum of two unsigned 64-bit words
// Inputs a, b; output function return
extern uint64_t word_min (uint64_t a, uint64_t b);

// Single-word negated modular inverse (-1/a) mod 2^64
// Input a; output function return
extern uint64_t word_negmodinv (uint64_t a);

// Count number of set bits in a single 64-bit word (population count)
// Input a; output function return
extern uint64_t word_popcount (uint64_t a);

// Single-word reciprocal, 2^64 + ret = ceil(2^128/a) - 1 if MSB of "a" is set
// Input a; output function return
extern uint64_t word_recip (uint64_t a);