/* LibTomCrypt, modular cryptographic library -- Tom St Denis */ /* SPDX-License-Identifier: Unlicense */ /** math functions **/ #define LTC_MP_LT -1 #define LTC_MP_EQ 0 #define LTC_MP_GT 1 #define LTC_MP_NO 0 #define LTC_MP_YES 1 #ifndef LTC_MECC typedef void ecc_point; #endif #ifndef LTC_MRSA typedef void rsa_key; #endif #ifndef LTC_MILLER_RABIN_REPS /* Number of rounds of the Miller-Rabin test * "Reasonable values of reps are between 15 and 50." c.f. gmp doc of mpz_probab_prime_p() * As of https://security.stackexchange.com/a/4546 we should use 40 rounds */ #define LTC_MILLER_RABIN_REPS 40 #endif int radix_to_bin(const void *in, int radix, void *out, unsigned long *len); /** math descriptor */ typedef struct { /** Name of the math provider */ const char *name; /** Bits per digit, amount of bits must fit in an unsigned long */ int bits_per_digit; /* ---- init/deinit functions ---- */ /** initialize a bignum @param a The number to initialize @return CRYPT_OK on success */ int (*init)(void **a); /** initialize a bignum @param size_bits The size of the number we compute on @param a The number to initialize @return CRYPT_OK on success */ int (*init_size)(int size_bits, void **a); /** init copy @param dst The number to initialize and write to @param src The number to copy from @return CRYPT_OK on success */ int (*init_copy)(void **dst, void *src); /** deinit @param a The number to free @return CRYPT_OK on success */ void (*deinit)(void *a); /* ---- data movement ---- */ /** negate @param src The number to negate @param dst The destination @return CRYPT_OK on success */ int (*neg)(void *src, void *dst); /** copy @param src The number to copy from @param dst The number to write to @return CRYPT_OK on success */ int (*copy)(void *src, void *dst); /* ---- trivial low level functions ---- */ /** set small constant @param a Number to write to @param n Source upto bits_per_digit (actually meant for very small constants) @return CRYPT_OK on success */ int (*set_int)(void *a, ltc_mp_digit n); /** get small constant @param a Small number to read, only fetches up to bits_per_digit from the number @return The lower bits_per_digit of the integer (unsigned) */ unsigned long (*get_int)(void *a); /** get digit n @param a The number to read from @param n The number of the digit to fetch @return The bits_per_digit sized n'th digit of a */ ltc_mp_digit (*get_digit)(void *a, int n); /** Get the number of digits that represent the number @param a The number to count @return The number of digits used to represent the number */ int (*get_digit_count)(void *a); /** compare two integers @param a The left side integer @param b The right side integer @return LTC_MP_LT if a < b, LTC_MP_GT if a > b and LTC_MP_EQ otherwise. (signed comparison) */ int (*compare)(void *a, void *b); /** compare against int @param a The left side integer @param b The right side integer (upto bits_per_digit) @return LTC_MP_LT if a < b, LTC_MP_GT if a > b and LTC_MP_EQ otherwise. (signed comparison) */ int (*compare_d)(void *a, ltc_mp_digit n); /** Count the number of bits used to represent the integer @param a The integer to count @return The number of bits required to represent the integer */ int (*count_bits)(void * a); /** Count the number of LSB bits which are zero @param a The integer to count @return The number of contiguous zero LSB bits */ int (*count_lsb_bits)(void *a); /** Compute a power of two @param a The integer to store the power in @param n The power of two you want to store (a = 2^n) @return CRYPT_OK on success */ int (*twoexpt)(void *a , int n); /* ---- radix conversions ---- */ /** read ascii string @param a The integer to store into @param str The string to read @param radix The radix the integer has been represented in (2-64) @return CRYPT_OK on success */ int (*read_radix)(void *a, const char *str, int radix); /** write number to string @param a The integer to store @param str The destination for the string @param radix The radix the integer is to be represented in (2-64) @return CRYPT_OK on success */ int (*write_radix)(void *a, char *str, int radix); /** get size as unsigned char string @param a The integer to get the size (when stored in array of octets) @return The length of the integer in octets */ unsigned long (*unsigned_size)(void *a); /** store an integer as an array of octets @param src The integer to store @param dst The buffer to store the integer in @return CRYPT_OK on success */ int (*unsigned_write)(void *src, unsigned char *dst); /** read an array of octets and store as integer @param dst The integer to load @param src The array of octets @param len The number of octets @return CRYPT_OK on success */ int (*unsigned_read)( void *dst, unsigned char *src, unsigned long len); /* ---- basic math ---- */ /** add two integers @param a The first source integer @param b The second source integer @param c The destination of "a + b" @return CRYPT_OK on success */ int (*add)(void *a, void *b, void *c); /** add two integers @param a The first source integer @param b The second source integer (single digit of upto bits_per_digit in length) @param c The destination of "a + b" @return CRYPT_OK on success */ int (*addi)(void *a, ltc_mp_digit b, void *c); /** subtract two integers @param a The first source integer @param b The second source integer @param c The destination of "a - b" @return CRYPT_OK on success */ int (*sub)(void *a, void *b, void *c); /** subtract two integers @param a The first source integer @param b The second source integer (single digit of upto bits_per_digit in length) @param c The destination of "a - b" @return CRYPT_OK on success */ int (*subi)(void *a, ltc_mp_digit b, void *c); /** multiply two integers @param a The first source integer @param b The second source integer (single digit of upto bits_per_digit in length) @param c The destination of "a * b" @return CRYPT_OK on success */ int (*mul)(void *a, void *b, void *c); /** multiply two integers @param a The first source integer @param b The second source integer (single digit of upto bits_per_digit in length) @param c The destination of "a * b" @return CRYPT_OK on success */ int (*muli)(void *a, ltc_mp_digit b, void *c); /** Square an integer @param a The integer to square @param b The destination @return CRYPT_OK on success */ int (*sqr)(void *a, void *b); /** Square root (mod prime) @param a The integer to compute square root mod prime from @param b The prime @param c The destination @return CRYPT_OK on success */ int (*sqrtmod_prime)(void *a, void *b, void *c); /** Divide an integer @param a The dividend @param b The divisor @param c The quotient (can be NULL to signify don't care) @param d The remainder (can be NULL to signify don't care) @return CRYPT_OK on success */ int (*mpdiv)(void *a, void *b, void *c, void *d); /** divide by two @param a The integer to divide (shift right) @param b The destination @return CRYPT_OK on success */ int (*div_2)(void *a, void *b); /** Get remainder (small value) @param a The integer to reduce @param b The modulus (upto bits_per_digit in length) @param c The destination for the residue @return CRYPT_OK on success */ int (*modi)(void *a, ltc_mp_digit b, ltc_mp_digit *c); /** gcd @param a The first integer @param b The second integer @param c The destination for (a, b) @return CRYPT_OK on success */ int (*gcd)(void *a, void *b, void *c); /** lcm @param a The first integer @param b The second integer @param c The destination for [a, b] @return CRYPT_OK on success */ int (*lcm)(void *a, void *b, void *c); /** Modular multiplication @param a The first source @param b The second source @param c The modulus @param d The destination (a*b mod c) @return CRYPT_OK on success */ int (*mulmod)(void *a, void *b, void *c, void *d); /** Modular squaring @param a The first source @param b The modulus @param c The destination (a*a mod b) @return CRYPT_OK on success */ int (*sqrmod)(void *a, void *b, void *c); /** Modular inversion @param a The value to invert @param b The modulus @param c The destination (1/a mod b) @return CRYPT_OK on success */ int (*invmod)(void *, void *, void *); /* ---- reduction ---- */ /** setup Montgomery @param a The modulus @param b The destination for the reduction digit @return CRYPT_OK on success */ int (*montgomery_setup)(void *a, void **b); /** get normalization value @param a The destination for the normalization value @param b The modulus @return CRYPT_OK on success */ int (*montgomery_normalization)(void *a, void *b); /** reduce a number @param a The number [and dest] to reduce @param b The modulus @param c The value "b" from montgomery_setup() @return CRYPT_OK on success */ int (*montgomery_reduce)(void *a, void *b, void *c); /** clean up (frees memory) @param a The value "b" from montgomery_setup() @return CRYPT_OK on success */ void (*montgomery_deinit)(void *a); /* ---- exponentiation ---- */ /** Modular exponentiation @param a The base integer @param b The power (can be negative) integer @param c The modulus integer @param d The destination @return CRYPT_OK on success */ int (*exptmod)(void *a, void *b, void *c, void *d); /** Primality testing @param a The integer to test @param b The number of Miller-Rabin tests that shall be executed @param c The destination of the result (FP_YES if prime) @return CRYPT_OK on success */ int (*isprime)(void *a, int b, int *c); /* ---- (optional) ecc point math ---- */ /** ECC GF(p) point multiplication (from the NIST curves) @param k The integer to multiply the point by @param G The point to multiply @param R The destination for kG @param a ECC curve parameter a @param modulus The modulus for the field @param map Boolean indicated whether to map back to affine or not (can be ignored if you work in affine only) @return CRYPT_OK on success */ int (*ecc_ptmul)( void *k, const ecc_point *G, ecc_point *R, void *a, void *modulus, int map); /** ECC GF(p) point addition @param P The first point @param Q The second point @param R The destination of P + Q @param ma The curve parameter "a" in montgomery form @param modulus The modulus @param mp The "b" value from montgomery_setup() @return CRYPT_OK on success */ int (*ecc_ptadd)(const ecc_point *P, const ecc_point *Q, ecc_point *R, void *ma, void *modulus, void *mp); /** ECC GF(p) point double @param P The first point @param R The destination of 2P @param ma The curve parameter "a" in montgomery form @param modulus The modulus @param mp The "b" value from montgomery_setup() @return CRYPT_OK on success */ int (*ecc_ptdbl)(const ecc_point *P, ecc_point *R, void *ma, void *modulus, void *mp); /** ECC mapping from projective to affine, currently uses (x,y,z) => (x/z^2, y/z^3, 1) @param P The point to map @param modulus The modulus @param mp The "b" value from montgomery_setup() @return CRYPT_OK on success @remark The mapping can be different but keep in mind a ecc_point only has three integers (x,y,z) so if you use a different mapping you have to make it fit. */ int (*ecc_map)(ecc_point *P, void *modulus, void *mp); /** Computes kA*A + kB*B = C using Shamir's Trick @param A First point to multiply @param kA What to multiple A by @param B Second point to multiply @param kB What to multiple B by @param C [out] Destination point (can overlap with A or B) @param ma The curve parameter "a" in montgomery form @param modulus Modulus for curve @return CRYPT_OK on success */ int (*ecc_mul2add)(const ecc_point *A, void *kA, const ecc_point *B, void *kB, ecc_point *C, void *ma, void *modulus); /* ---- (optional) rsa optimized math (for internal CRT) ---- */ /** RSA Key Generation @param prng An active PRNG state @param wprng The index of the PRNG desired @param size The size of the key in octets @param e The "e" value (public key). e==65537 is a good choice @param key [out] Destination of a newly created private key pair @return CRYPT_OK if successful, upon error all allocated ram is freed */ int (*rsa_keygen)(prng_state *prng, int wprng, int size, long e, rsa_key *key); /** RSA exponentiation @param in The octet array representing the base @param inlen The length of the input @param out The destination (to be stored in an octet array format) @param outlen The length of the output buffer and the resulting size (zero padded to the size of the modulus) @param which PK_PUBLIC for public RSA and PK_PRIVATE for private RSA @param key The RSA key to use @return CRYPT_OK on success */ int (*rsa_me)(const unsigned char *in, unsigned long inlen, unsigned char *out, unsigned long *outlen, int which, const rsa_key *key); /* ---- basic math continued ---- */ /** Modular addition @param a The first source @param b The second source @param c The modulus @param d The destination (a + b mod c) @return CRYPT_OK on success */ int (*addmod)(void *a, void *b, void *c, void *d); /** Modular substraction @param a The first source @param b The second source @param c The modulus @param d The destination (a - b mod c) @return CRYPT_OK on success */ int (*submod)(void *a, void *b, void *c, void *d); /* ---- misc stuff ---- */ /** Make a pseudo-random mpi @param a The mpi to make random @param size The desired length @return CRYPT_OK on success */ int (*rand)(void *a, int size); } ltc_math_descriptor; extern ltc_math_descriptor ltc_mp; int ltc_init_multi(void **a, ...) LTC_NULL_TERMINATED; int ltc_init_multi_size(int size_bits, void **a, ...) LTC_NULL_TERMINATED; void ltc_deinit_multi(void *a, ...) LTC_NULL_TERMINATED; void ltc_cleanup_multi(void **a, ...) LTC_NULL_TERMINATED; #ifdef LTM_DESC extern const ltc_math_descriptor ltm_desc; #endif #ifdef TFM_DESC extern const ltc_math_descriptor tfm_desc; #endif #ifdef GMP_DESC extern const ltc_math_descriptor gmp_desc; #endif