/*
* 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_RSA_H__
#define BR_BEARSSL_RSA_H__
#include
#include
/** \file bearssl_rsa.h
*
* # RSA
*
* This file documents the RSA implementations provided with BearSSL.
* Note that the SSL engine accesses these implementations through a
* configurable API, so it is possible to, for instance, run a SSL
* server which uses a RSA engine which is not based on this code.
*
* ## Key Elements
*
* RSA public and private keys consist in lists of big integers. All
* such integers are represented with big-endian unsigned notation:
* first byte is the most significant, and the value is positive (so
* there is no dedicated "sign bit"). Public and private key structures
* thus contain, for each such integer, a pointer to the first value byte
* (`unsigned char *`), and a length (`size_t`) which is the number of
* relevant bytes. As a general rule, minimal-length encoding is not
* enforced: values may have extra leading bytes of value 0.
*
* RSA public keys consist in two integers:
*
* - the modulus (`n`);
* - the public exponent (`e`).
*
* RSA private keys, as defined in
* [PKCS#1](https://tools.ietf.org/html/rfc3447), contain eight integers:
*
* - the modulus (`n`);
* - the public exponent (`e`);
* - the private exponent (`d`);
* - the first prime factor (`p`);
* - the second prime factor (`q`);
* - the first reduced exponent (`dp`, which is `d` modulo `p-1`);
* - the second reduced exponent (`dq`, which is `d` modulo `q-1`);
* - the CRT coefficient (`iq`, the inverse of `q` modulo `p`).
*
* However, the implementations defined in BearSSL use only five of
* these integers: `p`, `q`, `dp`, `dq` and `iq`.
*
* ## Security Features and Limitations
*
* The implementations contained in BearSSL have the following limitations
* and features:
*
* - They are constant-time. This means that the execution time and
* memory access pattern may depend on the _lengths_ of the private
* key components, but not on their value, nor on the value of
* the operand. Note that this property is not achieved through
* random masking, but "true" constant-time code.
*
* - They support only private keys with two prime factors. RSA private
* key with three or more prime factors are nominally supported, but
* rarely used; they may offer faster operations, at the expense of
* more code and potentially a reduction in security if there are
* "too many" prime factors.
*
* - The public exponent may have arbitrary length. Of course, it is
* a good idea to keep public exponents small, so that public key
* operations are fast; but, contrary to some widely deployed
* implementations, BearSSL has no problem with public exponent
* longer than 32 bits.
*
* - The two prime factors of the modulus need not have the same length
* (but severely imbalanced factor lengths might reduce security).
* Similarly, there is no requirement that the first factor (`p`)
* be greater than the second factor (`q`).
*
* - Prime factors and modulus must be smaller than a compile-time limit.
* This is made necessary by the use of fixed-size stack buffers, and
* the limit has been adjusted to keep stack usage under 2 kB for the
* RSA operations. Currently, the maximum modulus size is 4096 bits,
* and the maximum prime factor size is 2080 bits.
*
* - The RSA functions themselves do not enforce lower size limits,
* except that which is absolutely necessary for the operation to
* mathematically make sense (e.g. a PKCS#1 v1.5 signature with
* SHA-1 requires a modulus of at least 361 bits). It is up to users
* of this code to enforce size limitations when appropriate (e.g.
* the X.509 validation engine, by default, rejects RSA keys of
* less than 1017 bits).
*
* - Within the size constraints expressed above, arbitrary bit lengths
* are supported. There is no requirement that prime factors or
* modulus have a size multiple of 8 or 16.
*
* - When verifying PKCS#1 v1.5 signatures, both variants of the hash
* function identifying header (with and without the ASN.1 NULL) are
* supported. When producing such signatures, the variant with the
* ASN.1 NULL is used.
*
* ## Implementations
*
* Three RSA implementations are included:
*
* - The **i32** implementation internally represents big integers
* as arrays of 32-bit integers. It is perfunctory and portable,
* but not very efficient.
*
* - The **i31** implementation uses 32-bit integers, each containing
* 31 bits worth of integer data. The i31 implementation is somewhat
* faster than the i32 implementation (the reduced integer size makes
* carry propagation easier) for a similar code footprint, but uses
* very slightly larger stack buffers (about 4% bigger).
*
* - The **i15** implementation uses 16-bit integers, each containing
* 15 bits worth of integer data. Multiplication results fit on
* 32 bits, so this won't use the "widening" multiplication routine
* on ARM Cortex M0/M0+, for much better performance and constant-time
* execution.
*/
/**
* \brief RSA public key.
*
* The structure references the modulus and the public exponent. Both
* integers use unsigned big-endian representation; extra leading bytes
* of value 0 are allowed.
*/
typedef struct {
/** \brief Modulus. */
unsigned char *n;
/** \brief Modulus length (in bytes). */
size_t nlen;
/** \brief Public exponent. */
unsigned char *e;
/** \brief Public exponent length (in bytes). */
size_t elen;
} br_rsa_public_key;
/**
* \brief RSA private key.
*
* The structure references the primvate factors, reduced private
* exponents, and CRT coefficient. It also contains the bit length of
* the modulus. The big integers use unsigned big-endian representation;
* extra leading bytes of value 0 are allowed. However, the modulus bit
* length (`n_bitlen`) MUST be exact.
*/
typedef struct {
/** \brief Modulus bit length (in bits, exact value). */
uint32_t n_bitlen;
/** \brief First prime factor. */
unsigned char *p;
/** \brief First prime factor length (in bytes). */
size_t plen;
/** \brief Second prime factor. */
unsigned char *q;
/** \brief Second prime factor length (in bytes). */
size_t qlen;
/** \brief First reduced private exponent. */
unsigned char *dp;
/** \brief First reduced private exponent length (in bytes). */
size_t dplen;
/** \brief Second reduced private exponent. */
unsigned char *dq;
/** \brief Second reduced private exponent length (in bytes). */
size_t dqlen;
/** \brief CRT coefficient. */
unsigned char *iq;
/** \brief CRT coefficient length (in bytes). */
size_t iqlen;
} br_rsa_private_key;
/**
* \brief Type for a RSA public key engine.
*
* The public key engine performs the modular exponentiation of the
* provided value with the public exponent. The value is modified in
* place.
*
* The value length (`xlen`) is verified to have _exactly_ the same
* length as the modulus (actual modulus length, without extra leading
* zeros in the modulus representation in memory). If the length does
* not match, then this function returns 0 and `x[]` is unmodified.
*
* It `xlen` is correct, then `x[]` is modified. Returned value is 1
* on success, 0 on error. Error conditions include an oversized `x[]`
* (the array has the same length as the modulus, but the numerical value
* is not lower than the modulus) and an invalid modulus (e.g. an even
* integer). If an error is reported, then the new contents of `x[]` are
* unspecified.
*
* \param x operand to exponentiate.
* \param xlen length of the operand (in bytes).
* \param pk RSA public key.
* \return 1 on success, 0 on error.
*/
typedef uint32_t (*br_rsa_public)(unsigned char *x, size_t xlen,
const br_rsa_public_key *pk);
/**
* \brief Type for a RSA signature verification engine (PKCS#1 v1.5).
*
* Parameters are:
*
* - The signature itself. The provided array is NOT modified.
*
* - The encoded OID for the hash function. The provided array must begin
* with a single byte that contains the length of the OID value (in
* bytes), followed by exactly that many bytes. This parameter may
* also be `NULL`, in which case the raw hash value should be used
* with the PKCS#1 v1.5 "type 1" padding (as used in SSL/TLS up
* to TLS-1.1, with a 36-byte hash value).
*
* - The hash output length, in bytes.
*
* - The public key.
*
* - An output buffer for the hash value. The caller must still compare
* it with the hash of the data over which the signature is computed.
*
* **Constraints:**
*
* - Hash length MUST be no more than 64 bytes.
*
* - OID value length MUST be no more than 32 bytes (i.e. `hash_oid[0]`
* must have a value in the 0..32 range, inclusive).
*
* This function verifies that the signature length (`xlen`) matches the
* modulus length (this function returns 0 on mismatch). If the modulus
* size exceeds the maximum supported RSA size, then the function also
* returns 0.
*
* Returned value is 1 on success, 0 on error.
*
* Implementations of this type need not be constant-time.
*
* \param x signature buffer.
* \param xlen signature length (in bytes).
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash_len expected hash value length (in bytes).
* \param pk RSA public key.
* \param hash_out output buffer for the hash value.
* \return 1 on success, 0 on error.
*/
typedef uint32_t (*br_rsa_pkcs1_vrfy)(const unsigned char *x, size_t xlen,
const unsigned char *hash_oid, size_t hash_len,
const br_rsa_public_key *pk, unsigned char *hash_out);
/**
* \brief Type for a RSA private key engine.
*
* The `x[]` buffer is modified in place, and its length is inferred from
* the modulus length (`x[]` is assumed to have a length of
* `(sk->n_bitlen+7)/8` bytes).
*
* Returned value is 1 on success, 0 on error.
*
* \param x operand to exponentiate.
* \param sk RSA private key.
* \return 1 on success, 0 on error.
*/
typedef uint32_t (*br_rsa_private)(unsigned char *x,
const br_rsa_private_key *sk);
/**
* \brief Type for a RSA signature generation engine (PKCS#1 v1.5).
*
* Parameters are:
*
* - The encoded OID for the hash function. The provided array must begin
* with a single byte that contains the length of the OID value (in
* bytes), followed by exactly that many bytes. This parameter may
* also be `NULL`, in which case the raw hash value should be used
* with the PKCS#1 v1.5 "type 1" padding (as used in SSL/TLS up
* to TLS-1.1, with a 36-byte hash value).
*
* - The hash value computes over the data to sign (its length is
* expressed in bytes).
*
* - The RSA private key.
*
* - The output buffer, that receives the signature.
*
* Returned value is 1 on success, 0 on error. Error conditions include
* a too small modulus for the provided hash OID and value, or some
* invalid key parameters. The signature length is exactly
* `(sk->n_bitlen+7)/8` bytes.
*
* This function is expected to be constant-time with regards to the
* private key bytes (lengths of the modulus and the individual factors
* may leak, though) and to the hashed data.
*
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash hash value.
* \param hash_len hash value length (in bytes).
* \param sk RSA private key.
* \param x output buffer for the signature value.
* \return 1 on success, 0 on error.
*/
typedef uint32_t (*br_rsa_pkcs1_sign)(const unsigned char *hash_oid,
const unsigned char *hash, size_t hash_len,
const br_rsa_private_key *sk, unsigned char *x);
/*
* RSA "i32" engine. Integers are internally represented as arrays of
* 32-bit integers, and the core multiplication primitive is the
* 32x32->64 multiplication.
*/
/**
* \brief RSA public key engine "i32".
*
* \see br_rsa_public
*
* \param x operand to exponentiate.
* \param xlen length of the operand (in bytes).
* \param pk RSA public key.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i32_public(unsigned char *x, size_t xlen,
const br_rsa_public_key *pk);
/**
* \brief RSA signature verification engine "i32".
*
* \see br_rsa_pkcs1_vrfy
*
* \param x signature buffer.
* \param xlen signature length (in bytes).
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash_len expected hash value length (in bytes).
* \param pk RSA public key.
* \param hash_out output buffer for the hash value.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i32_pkcs1_vrfy(const unsigned char *x, size_t xlen,
const unsigned char *hash_oid, size_t hash_len,
const br_rsa_public_key *pk, unsigned char *hash_out);
/**
* \brief RSA private key engine "i32".
*
* \see br_rsa_private
*
* \param x operand to exponentiate.
* \param sk RSA private key.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i32_private(unsigned char *x,
const br_rsa_private_key *sk);
/**
* \brief RSA signature generation engine "i32".
*
* \see br_rsa_pkcs1_sign
*
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash hash value.
* \param hash_len hash value length (in bytes).
* \param sk RSA private key.
* \param x output buffer for the hash value.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i32_pkcs1_sign(const unsigned char *hash_oid,
const unsigned char *hash, size_t hash_len,
const br_rsa_private_key *sk, unsigned char *x);
/*
* RSA "i31" engine. Similar to i32, but only 31 bits are used per 32-bit
* word. This uses slightly more stack space (about 4% more) and code
* space, but it quite faster.
*/
/**
* \brief RSA public key engine "i31".
*
* \see br_rsa_public
*
* \param x operand to exponentiate.
* \param xlen length of the operand (in bytes).
* \param pk RSA public key.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i31_public(unsigned char *x, size_t xlen,
const br_rsa_public_key *pk);
/**
* \brief RSA signature verification engine "i31".
*
* \see br_rsa_pkcs1_vrfy
*
* \param x signature buffer.
* \param xlen signature length (in bytes).
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash_len expected hash value length (in bytes).
* \param pk RSA public key.
* \param hash_out output buffer for the hash value.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i31_pkcs1_vrfy(const unsigned char *x, size_t xlen,
const unsigned char *hash_oid, size_t hash_len,
const br_rsa_public_key *pk, unsigned char *hash_out);
/**
* \brief RSA private key engine "i31".
*
* \see br_rsa_private
*
* \param x operand to exponentiate.
* \param sk RSA private key.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i31_private(unsigned char *x,
const br_rsa_private_key *sk);
/**
* \brief RSA signature generation engine "i31".
*
* \see br_rsa_pkcs1_sign
*
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash hash value.
* \param hash_len hash value length (in bytes).
* \param sk RSA private key.
* \param x output buffer for the hash value.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i31_pkcs1_sign(const unsigned char *hash_oid,
const unsigned char *hash, size_t hash_len,
const br_rsa_private_key *sk, unsigned char *x);
/*
* RSA "i15" engine. Integers are represented as 15-bit integers, so
* the code uses only 32-bit multiplication (no 64-bit result), which
* is vastly faster (and constant-time) on the ARM Cortex M0/M0+.
*/
/**
* \brief RSA public key engine "i15".
*
* \see br_rsa_public
*
* \param x operand to exponentiate.
* \param xlen length of the operand (in bytes).
* \param pk RSA public key.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i15_public(unsigned char *x, size_t xlen,
const br_rsa_public_key *pk);
/**
* \brief RSA signature verification engine "i15".
*
* \see br_rsa_pkcs1_vrfy
*
* \param x signature buffer.
* \param xlen signature length (in bytes).
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash_len expected hash value length (in bytes).
* \param pk RSA public key.
* \param hash_out output buffer for the hash value.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i15_pkcs1_vrfy(const unsigned char *x, size_t xlen,
const unsigned char *hash_oid, size_t hash_len,
const br_rsa_public_key *pk, unsigned char *hash_out);
/**
* \brief RSA private key engine "i15".
*
* \see br_rsa_private
*
* \param x operand to exponentiate.
* \param sk RSA private key.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i15_private(unsigned char *x,
const br_rsa_private_key *sk);
/**
* \brief RSA signature generation engine "i15".
*
* \see br_rsa_pkcs1_sign
*
* \param hash_oid encoded hash algorithm OID (or `NULL`).
* \param hash hash value.
* \param hash_len hash value length (in bytes).
* \param sk RSA private key.
* \param x output buffer for the hash value.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_i15_pkcs1_sign(const unsigned char *hash_oid,
const unsigned char *hash, size_t hash_len,
const br_rsa_private_key *sk, unsigned char *x);
/**
* \brief RSA decryption helper, for SSL/TLS.
*
* This function performs the RSA decryption for a RSA-based key exchange
* in a SSL/TLS server. The provided RSA engine is used. The `data`
* parameter points to the value to decrypt, of length `len` bytes. On
* success, the 48-byte pre-master secret is copied into `data`, starting
* at the first byte of that buffer; on error, the contents of `data`
* become indeterminate.
*
* This function first checks that the provided value length (`len`) is
* not lower than 59 bytes, and matches the RSA modulus length; if neither
* of this property is met, then this function returns 0 and the buffer
* is unmodified.
*
* Otherwise, decryption and then padding verification are performed, both
* in constant-time. A decryption error, or a bad padding, or an
* incorrect decrypted value length are reported with a returned value of
* 0; on success, 1 is returned. The caller (SSL server engine) is supposed
* to proceed with a random pre-master secret in case of error.
*
* \param core RSA private key engine.
* \param sk RSA private key.
* \param data input/output buffer.
* \param len length (in bytes) of the data to decrypt.
* \return 1 on success, 0 on error.
*/
uint32_t br_rsa_ssl_decrypt(br_rsa_private core, const br_rsa_private_key *sk,
unsigned char *data, size_t len);
#endif