/*
* Copyright (c) 2016 Thomas Pornin
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#ifndef BR_BEARSSL_EC_H__
#define BR_BEARSSL_EC_H__
#include
#include
/** \file bearssl_ec.h
*
* # Elliptic Curves
*
* This file documents the EC implementations provided with BearSSL, and
* ECDSA.
*
* ## Elliptic Curve API
*
* Only "named curves" are supported. Each EC implementation supports
* one or several named curves, identified by symbolic identifiers.
* These identifiers are small integers, that correspond to the values
* registered by the
* [IANA](http://www.iana.org/assignments/tls-parameters/tls-parameters.xhtml#tls-parameters-8).
*
* Since all currently defined elliptic curve identifiers are in the 0..31
* range, it is convenient to encode support of some curves in a 32-bit
* word, such that bit x corresponds to curve of identifier x.
*
* An EC implementation is incarnated by a `br_ec_impl` instance, that
* offers the following fields:
*
* - `supported_curves`
*
* A 32-bit word that documents the identifiers of the curves supported
* by this implementation.
*
* - `generator()`
*
* Callback method that returns a pointer to the conventional generator
* point for that curve.
*
* - `order()`
*
* Callback method that returns a pointer to the subgroup order for
* that curve. That value uses unsigned big-endian encoding.
*
* - `xoff()`
*
* Callback method that returns the offset and length of the X
* coordinate in an encoded point.
*
* - `mul()`
*
* Multiply a curve point with an integer.
*
* - `mulgen()`
*
* Multiply the curve generator with an integer. This may be faster
* than the generic `mul()`.
*
* - `muladd()`
*
* Multiply two curve points by two integers, and return the sum of
* the two products.
*
* All curve points are represented in uncompressed format. The `mul()`
* and `muladd()` methods take care to validate that the provided points
* are really part of the relevant curve subgroup.
*
* For all point multiplication functions, the following holds:
*
* - Functions validate that the provided points are valid members
* of the relevant curve subgroup. An error is reported if that is
* not the case.
*
* - Processing is constant-time, even if the point operands are not
* valid. This holds for both the source and resulting points, and
* the multipliers (integers). Only the byte length of the provided
* multiplier arrays (not their actual value length in bits) may
* leak through timing-based side channels.
*
* - The multipliers (integers) MUST be lower than the subgroup order.
* If this property is not met, then the result is indeterminate,
* but an error value is not ncessearily returned.
*
*
* ## ECDSA
*
* ECDSA signatures have two standard formats, called "raw" and "asn1".
* Internally, such a signature is a pair of modular integers `(r,s)`.
* The "raw" format is the concatenation of the unsigned big-endian
* encodings of these two integers, possibly left-padded with zeros so
* that they have the same encoded length. The "asn1" format is the
* DER encoding of an ASN.1 structure that contains the two integer
* values:
*
* ECDSASignature ::= SEQUENCE {
* r INTEGER,
* s INTEGER
* }
*
* In general, in all of X.509 and SSL/TLS, the "asn1" format is used.
* BearSSL offers ECDSA implementations for both formats; conversion
* functions between the two formats are also provided. Conversion of a
* "raw" format signature into "asn1" may enlarge a signature by no more
* than 9 bytes for all supported curves; conversely, conversion of an
* "asn1" signature to "raw" may expand the signature but the "raw"
* length will never be more than twice the length of the "asn1" length
* (and usually it will be shorter).
*
* Note that for a given signature, the "raw" format is not fully
* deterministic, in that it does not enforce a minimal common length.
*/
/*
* Standard curve ID. These ID are equal to the assigned numerical
* identifiers assigned to these curves for TLS:
* http://www.iana.org/assignments/tls-parameters/tls-parameters.xhtml#tls-parameters-8
*/
/** \brief Identifier for named curve sect163k1. */
#define BR_EC_sect163k1 1
/** \brief Identifier for named curve sect163r1. */
#define BR_EC_sect163r1 2
/** \brief Identifier for named curve sect163r2. */
#define BR_EC_sect163r2 3
/** \brief Identifier for named curve sect193r1. */
#define BR_EC_sect193r1 4
/** \brief Identifier for named curve sect193r2. */
#define BR_EC_sect193r2 5
/** \brief Identifier for named curve sect233k1. */
#define BR_EC_sect233k1 6
/** \brief Identifier for named curve sect233r1. */
#define BR_EC_sect233r1 7
/** \brief Identifier for named curve sect239k1. */
#define BR_EC_sect239k1 8
/** \brief Identifier for named curve sect283k1. */
#define BR_EC_sect283k1 9
/** \brief Identifier for named curve sect283r1. */
#define BR_EC_sect283r1 10
/** \brief Identifier for named curve sect409k1. */
#define BR_EC_sect409k1 11
/** \brief Identifier for named curve sect409r1. */
#define BR_EC_sect409r1 12
/** \brief Identifier for named curve sect571k1. */
#define BR_EC_sect571k1 13
/** \brief Identifier for named curve sect571r1. */
#define BR_EC_sect571r1 14
/** \brief Identifier for named curve secp160k1. */
#define BR_EC_secp160k1 15
/** \brief Identifier for named curve secp160r1. */
#define BR_EC_secp160r1 16
/** \brief Identifier for named curve secp160r2. */
#define BR_EC_secp160r2 17
/** \brief Identifier for named curve secp192k1. */
#define BR_EC_secp192k1 18
/** \brief Identifier for named curve secp192r1. */
#define BR_EC_secp192r1 19
/** \brief Identifier for named curve secp224k1. */
#define BR_EC_secp224k1 20
/** \brief Identifier for named curve secp224r1. */
#define BR_EC_secp224r1 21
/** \brief Identifier for named curve secp256k1. */
#define BR_EC_secp256k1 22
/** \brief Identifier for named curve secp256r1. */
#define BR_EC_secp256r1 23
/** \brief Identifier for named curve secp384r1. */
#define BR_EC_secp384r1 24
/** \brief Identifier for named curve secp521r1. */
#define BR_EC_secp521r1 25
/** \brief Identifier for named curve brainpoolP256r1. */
#define BR_EC_brainpoolP256r1 26
/** \brief Identifier for named curve brainpoolP384r1. */
#define BR_EC_brainpoolP384r1 27
/** \brief Identifier for named curve brainpoolP512r1. */
#define BR_EC_brainpoolP512r1 28
/** \brief Identifier for named curve Curve25519. */
#define BR_EC_curve25519 29
/** \brief Identifier for named curve Curve448. */
#define BR_EC_curve448 30
/**
* \brief Structure for an EC public key.
*/
typedef struct {
/** \brief Identifier for the curve used by this key. */
int curve;
/** \brief Public curve point (uncompressed format). */
unsigned char *q;
/** \brief Length of public curve point (in bytes). */
size_t qlen;
} br_ec_public_key;
/**
* \brief Structure for an EC private key.
*
* The private key is an integer modulo the curve subgroup order. The
* encoding below tolerates extra leading zeros. In general, it is
* recommended that the private key has the same length as the curve
* subgroup order.
*/
typedef struct {
/** \brief Identifier for the curve used by this key. */
int curve;
/** \brief Private key (integer, unsigned big-endian encoding). */
unsigned char *x;
/** \brief Private key length (in bytes). */
size_t xlen;
} br_ec_private_key;
/**
* \brief Type for an EC implementation.
*/
typedef struct {
/**
* \brief Supported curves.
*
* This word is a bitfield: bit `x` is set if the curve of ID `x`
* is supported. E.g. an implementation supporting both NIST P-256
* (secp256r1, ID 23) and NIST P-384 (secp384r1, ID 24) will have
* value `0x01800000` in this field.
*/
uint32_t supported_curves;
/**
* \brief Get the conventional generator.
*
* This function returns the conventional generator (encoded
* curve point) for the specified curve. This function MUST NOT
* be called if the curve is not supported.
*
* \param curve curve identifier.
* \param len receiver for the encoded generator length (in bytes).
* \return the encoded generator.
*/
const unsigned char *(*generator)(int curve, size_t *len);
/**
* \brief Get the subgroup order.
*
* This function returns the order of the subgroup generated by
* the conventional generator, for the specified curve. Unsigned
* big-endian encoding is used. This function MUST NOT be called
* if the curve is not supported.
*
* \param curve curve identifier.
* \param len receiver for the encoded order length (in bytes).
* \return the encoded order.
*/
const unsigned char *(*order)(int curve, size_t *len);
/**
* \brief Get the offset and length for the X coordinate.
*
* This function returns the offset and length (in bytes) of
* the X coordinate in an encoded non-zero point.
*
* \param curve curve identifier.
* \param len receiver for the X coordinate length (in bytes).
* \return the offset for the X coordinate (in bytes).
*/
size_t (*xoff)(int curve, size_t *len);
/**
* \brief Multiply a curve point by an integer.
*
* The source point is provided in array `G` (of size `Glen` bytes);
* the multiplication result is written over it. The multiplier
* `x` (of size `xlen` bytes) uses unsigned big-endian encoding.
*
* Rules:
*
* - The specified curve MUST be supported.
*
* - The source point must be a valid point on the relevant curve
* subgroup (and not the "point at infinity" either). If this is
* not the case, then this function returns an error (0).
*
* - The multiplier integer MUST be non-zero and less than the
* curve subgroup order. If this property does not hold, then
* the result is indeterminate and an error code is not
* guaranteed.
*
* Returned value is 1 on success, 0 on error. On error, the
* contents of `G` are indeterminate.
*
* \param G point to multiply.
* \param Glen length of the encoded point (in bytes).
* \param x multiplier (unsigned big-endian).
* \param xlen multiplier length (in bytes).
* \param curve curve identifier.
* \return 1 on success, 0 on error.
*/
uint32_t (*mul)(unsigned char *G, size_t Glen,
const unsigned char *x, size_t xlen, int curve);
/**
* \brief Multiply the generator by an integer.
*
* The multiplier MUST be non-zero and less than the curve
* subgroup order. Results are indeterminate if this property
* does not hold.
*
* \param R output buffer for the point.
* \param x multiplier (unsigned big-endian).
* \param xlen multiplier length (in bytes).
* \param curve curve identifier.
* \return encoded result point length (in bytes).
*/
size_t (*mulgen)(unsigned char *R,
const unsigned char *x, size_t xlen, int curve);
/**
* \brief Multiply two points by two integers and add the
* results.
*
* The point `x*A + y*B` is computed and written back in the `A`
* array.
*
* Rules:
*
* - The specified curve MUST be supported.
*
* - The source points (`A` and `B`) must be valid points on
* the relevant curve subgroup (and not the "point at
* infinity" either). If this is not the case, then this
* function returns an error (0).
*
* - If the `B` pointer is `NULL`, then the conventional
* subgroup generator is used. With some implementations,
* this may be faster than providing a pointer to the
* generator.
*
* - The multiplier integers (`x` and `y`) MUST be non-zero
* and less than the curve subgroup order. If either integer
* is zero, then an error is reported, but if one of them is
* not lower than the subgroup order, then the result is
* indeterminate and an error code is not guaranteed.
*
* - If the final result is the point at infinity, then an
* error is returned.
*
* Returned value is 1 on success, 0 on error. On error, the
* contents of `A` are indeterminate.
*
* \param A first point to multiply.
* \param B second point to multiply (`NULL` for the generator).
* \param len common length of the encoded points (in bytes).
* \param x multiplier for `A` (unsigned big-endian).
* \param xlen length of multiplier for `A` (in bytes).
* \param y multiplier for `A` (unsigned big-endian).
* \param ylen length of multiplier for `A` (in bytes).
* \param curve curve identifier.
* \return 1 on success, 0 on error.
*/
uint32_t (*muladd)(unsigned char *A, const unsigned char *B, size_t len,
const unsigned char *x, size_t xlen,
const unsigned char *y, size_t ylen, int curve);
} br_ec_impl;
/**
* \brief EC implementation "i31".
*
* This implementation internally uses generic code for modular integers,
* with a representation as sequences of 31-bit words. It supports secp256r1,
* secp384r1 and secp521r1 (aka NIST curves P-256, P-384 and P-521).
*/
extern const br_ec_impl br_ec_prime_i31;
/**
* \brief EC implementation "i15".
*
* This implementation internally uses generic code for modular integers,
* with a representation as sequences of 15-bit words. It supports secp256r1,
* secp384r1 and secp521r1 (aka NIST curves P-256, P-384 and P-521).
*/
extern const br_ec_impl br_ec_prime_i15;
/**
* \brief EC implementation "m15" for P-256.
*
* This implementation uses specialised code for curve secp256r1 (also
* known as NIST P-256), with optional Karatsuba decomposition, and fast
* modular reduction thanks to the field modulus special format. Only
* 32-bit multiplications are used (with 32-bit results, not 64-bit).
*/
extern const br_ec_impl br_ec_p256_m15;
/**
* \brief EC implementation "m31" for P-256.
*
* This implementation uses specialised code for curve secp256r1 (also
* known as NIST P-256), relying on multiplications of 31-bit values
* (MUL31).
*/
extern const br_ec_impl br_ec_p256_m31;
/**
* \brief EC implementation "i15" (generic code) for Curve25519.
*
* This implementation uses the generic code for modular integers (with
* 15-bit words) to support Curve25519. Due to the specificities of the
* curve definition, the following applies:
*
* - `muladd()` is not implemented (the function returns 0 systematically).
* - `order()` returns 2^255-1, since the point multiplication algorithm
* accepts any 32-bit integer as input (it clears the top bit and low
* three bits systematically).
*/
extern const br_ec_impl br_ec_c25519_i15;
/**
* \brief EC implementation "i31" (generic code) for Curve25519.
*
* This implementation uses the generic code for modular integers (with
* 31-bit words) to support Curve25519. Due to the specificities of the
* curve definition, the following applies:
*
* - `muladd()` is not implemented (the function returns 0 systematically).
* - `order()` returns 2^255-1, since the point multiplication algorithm
* accepts any 32-bit integer as input (it clears the top bit and low
* three bits systematically).
*/
extern const br_ec_impl br_ec_c25519_i31;
/**
* \brief EC implementation "m15" (specialised code) for Curve25519.
*
* This implementation uses custom code relying on multiplication of
* integers up to 15 bits. Due to the specificities of the curve
* definition, the following applies:
*
* - `muladd()` is not implemented (the function returns 0 systematically).
* - `order()` returns 2^255-1, since the point multiplication algorithm
* accepts any 32-bit integer as input (it clears the top bit and low
* three bits systematically).
*/
extern const br_ec_impl br_ec_c25519_m15;
/**
* \brief EC implementation "m31" (specialised code) for Curve25519.
*
* This implementation uses custom code relying on multiplication of
* integers up to 31 bits. Due to the specificities of the curve
* definition, the following applies:
*
* - `muladd()` is not implemented (the function returns 0 systematically).
* - `order()` returns 2^255-1, since the point multiplication algorithm
* accepts any 32-bit integer as input (it clears the top bit and low
* three bits systematically).
*/
extern const br_ec_impl br_ec_c25519_m31;
/**
* \brief Aggregate EC implementation "m15".
*
* This implementation is a wrapper for:
*
* - `br_ec_c25519_m15` for Curve25519
* - `br_ec_p256_m15` for NIST P-256
* - `br_ec_prime_i15` for other curves (NIST P-384 and NIST-P512)
*/
extern const br_ec_impl br_ec_all_m15;
/**
* \brief Convert a signature from "raw" to "asn1".
*
* Conversion is done "in place" and the new length is returned.
* Conversion may enlarge the signature, but by no more than 9 bytes at
* most. On error, 0 is returned (error conditions include an odd raw
* signature length, or an oversized integer).
*
* \param sig signature to convert.
* \param sig_len signature length (in bytes).
* \return the new signature length, or 0 on error.
*/
size_t br_ecdsa_raw_to_asn1(void *sig, size_t sig_len);
/**
* \brief Convert a signature from "asn1" to "raw".
*
* Conversion is done "in place" and the new length is returned.
* Conversion may enlarge the signature, but the new signature length
* will be less than twice the source length at most. On error, 0 is
* returned (error conditions include an invalid ASN.1 structure or an
* oversized integer).
*
* \param sig signature to convert.
* \param sig_len signature length (in bytes).
* \return the new signature length, or 0 on error.
*/
size_t br_ecdsa_asn1_to_raw(void *sig, size_t sig_len);
/**
* \brief Type for an ECDSA signer function.
*
* A pointer to the EC implementation is provided. The hash value is
* assumed to have the length inferred from the designated hash function
* class.
*
* Signature is written in the buffer pointed to by `sig`, and the length
* (in bytes) is returned. On error, nothing is written in the buffer,
* and 0 is returned. This function returns 0 if the specified curve is
* not supported by the provided EC implementation.
*
* The signature format is either "raw" or "asn1", depending on the
* implementation; maximum length is predictable from the implemented
* curve:
*
* | curve | raw | asn1 |
* | :--------- | --: | ---: |
* | NIST P-256 | 64 | 72 |
* | NIST P-384 | 96 | 104 |
* | NIST P-521 | 132 | 139 |
*
* \param impl EC implementation to use.
* \param hf hash function used to process the data.
* \param hash_value signed data (hashed).
* \param sk EC private key.
* \param sig destination buffer.
* \return the signature length (in bytes), or 0 on error.
*/
typedef size_t (*br_ecdsa_sign)(const br_ec_impl *impl,
const br_hash_class *hf, const void *hash_value,
const br_ec_private_key *sk, void *sig);
/**
* \brief Type for an ECDSA signature verification function.
*
* A pointer to the EC implementation is provided. The hashed value,
* computed over the purportedly signed data, is also provided with
* its length.
*
* The signature format is either "raw" or "asn1", depending on the
* implementation.
*
* Returned value is 1 on success (valid signature), 0 on error. This
* function returns 0 if the specified curve is not supported by the
* provided EC implementation.
*
* \param impl EC implementation to use.
* \param hash signed data (hashed).
* \param hash_len hash value length (in bytes).
* \param pk EC public key.
* \param sig signature.
* \param sig_len signature length (in bytes).
* \return 1 on success, 0 on error.
*/
typedef uint32_t (*br_ecdsa_vrfy)(const br_ec_impl *impl,
const void *hash, size_t hash_len,
const br_ec_public_key *pk, const void *sig, size_t sig_len);
/**
* \brief ECDSA signature generator, "i31" implementation, "asn1" format.
*
* \see br_ecdsa_sign()
*
* \param impl EC implementation to use.
* \param hf hash function used to process the data.
* \param hash_value signed data (hashed).
* \param sk EC private key.
* \param sig destination buffer.
* \return the signature length (in bytes), or 0 on error.
*/
size_t br_ecdsa_i31_sign_asn1(const br_ec_impl *impl,
const br_hash_class *hf, const void *hash_value,
const br_ec_private_key *sk, void *sig);
/**
* \brief ECDSA signature generator, "i31" implementation, "raw" format.
*
* \see br_ecdsa_sign()
*
* \param impl EC implementation to use.
* \param hf hash function used to process the data.
* \param hash_value signed data (hashed).
* \param sk EC private key.
* \param sig destination buffer.
* \return the signature length (in bytes), or 0 on error.
*/
size_t br_ecdsa_i31_sign_raw(const br_ec_impl *impl,
const br_hash_class *hf, const void *hash_value,
const br_ec_private_key *sk, void *sig);
/**
* \brief ECDSA signature verifier, "i31" implementation, "asn1" format.
*
* \see br_ecdsa_vrfy()
*
* \param impl EC implementation to use.
* \param hash signed data (hashed).
* \param hash_len hash value length (in bytes).
* \param pk EC public key.
* \param sig signature.
* \param sig_len signature length (in bytes).
* \return 1 on success, 0 on error.
*/
uint32_t br_ecdsa_i31_vrfy_asn1(const br_ec_impl *impl,
const void *hash, size_t hash_len,
const br_ec_public_key *pk, const void *sig, size_t sig_len);
/**
* \brief ECDSA signature verifier, "i31" implementation, "raw" format.
*
* \see br_ecdsa_vrfy()
*
* \param impl EC implementation to use.
* \param hash signed data (hashed).
* \param hash_len hash value length (in bytes).
* \param pk EC public key.
* \param sig signature.
* \param sig_len signature length (in bytes).
* \return 1 on success, 0 on error.
*/
uint32_t br_ecdsa_i31_vrfy_raw(const br_ec_impl *impl,
const void *hash, size_t hash_len,
const br_ec_public_key *pk, const void *sig, size_t sig_len);
/**
* \brief ECDSA signature generator, "i15" implementation, "asn1" format.
*
* \see br_ecdsa_sign()
*
* \param impl EC implementation to use.
* \param hf hash function used to process the data.
* \param hash_value signed data (hashed).
* \param sk EC private key.
* \param sig destination buffer.
* \return the signature length (in bytes), or 0 on error.
*/
size_t br_ecdsa_i15_sign_asn1(const br_ec_impl *impl,
const br_hash_class *hf, const void *hash_value,
const br_ec_private_key *sk, void *sig);
/**
* \brief ECDSA signature generator, "i15" implementation, "raw" format.
*
* \see br_ecdsa_sign()
*
* \param impl EC implementation to use.
* \param hf hash function used to process the data.
* \param hash_value signed data (hashed).
* \param sk EC private key.
* \param sig destination buffer.
* \return the signature length (in bytes), or 0 on error.
*/
size_t br_ecdsa_i15_sign_raw(const br_ec_impl *impl,
const br_hash_class *hf, const void *hash_value,
const br_ec_private_key *sk, void *sig);
/**
* \brief ECDSA signature verifier, "i15" implementation, "asn1" format.
*
* \see br_ecdsa_vrfy()
*
* \param impl EC implementation to use.
* \param hash signed data (hashed).
* \param hash_len hash value length (in bytes).
* \param pk EC public key.
* \param sig signature.
* \param sig_len signature length (in bytes).
* \return 1 on success, 0 on error.
*/
uint32_t br_ecdsa_i15_vrfy_asn1(const br_ec_impl *impl,
const void *hash, size_t hash_len,
const br_ec_public_key *pk, const void *sig, size_t sig_len);
/**
* \brief ECDSA signature verifier, "i15" implementation, "raw" format.
*
* \see br_ecdsa_vrfy()
*
* \param impl EC implementation to use.
* \param hash signed data (hashed).
* \param hash_len hash value length (in bytes).
* \param pk EC public key.
* \param sig signature.
* \param sig_len signature length (in bytes).
* \return 1 on success, 0 on error.
*/
uint32_t br_ecdsa_i15_vrfy_raw(const br_ec_impl *impl,
const void *hash, size_t hash_len,
const br_ec_public_key *pk, const void *sig, size_t sig_len);
#endif