=pod

=head1 NAME

EVP_PKEY-RSA, EVP_KEYMGMT-RSA, RSA
- EVP_PKEY RSA keytype and algorithm support

=head1 DESCRIPTION

The B<RSA> keytype is implemented in OpenSSL's default and FIPS providers.
That implementation supports the basic RSA keys, containing the modulus I<n>,
the public exponent I<e>, the private exponent I<d>, and a collection of prime
factors, exponents and coefficient for CRT calculations, of which the first
few are known as I<p> and I<q>, I<dP> and I<dQ>, and I<qInv>.

RSA key generation uses FIPS 186-5 Section A.1.6 "Generation of Probable
Primes with Conditions Based on Auxiliary Probable Primes" for the OpenSSL FIPS
provider. It is also used for the OpenSSL default provider when the generation
parameters satisfy the following conditions:

=over 4

=item There are 2 "primes" (p, q)

=item The exponent "e" >= 65537 and is odd

=item The cryptographic length "bits" >= 2048

=back

Otherwise the OpenSSL default provider uses an older general multi-prime key
generator.

=head2 Common RSA parameters

In addition to the common parameters that all keytypes should support (see
L<provider-keymgmt(7)/Common parameters>), the B<RSA> keytype implementation
supports the following.

=over 4

=item "n" (B<OSSL_PKEY_PARAM_RSA_N>) <unsigned integer>

The RSA modulus "n" value.

=item "e" (B<OSSL_PKEY_PARAM_RSA_E>) <unsigned integer>

The RSA public exponent "e" value.
This value must always be set when creating a raw key using L<EVP_PKEY_fromdata(3)>.
Note that when a decryption operation is performed, that this value is used for
blinding purposes to prevent timing attacks.

=item "d" (B<OSSL_PKEY_PARAM_RSA_D>) <unsigned integer>

The RSA private exponent "d" value.

=item "rsa-factor1" (B<OSSL_PKEY_PARAM_RSA_FACTOR1>) <unsigned integer>

=item "rsa-factor2" (B<OSSL_PKEY_PARAM_RSA_FACTOR2>) <unsigned integer>

=item "rsa-factor3" (B<OSSL_PKEY_PARAM_RSA_FACTOR3>) <unsigned integer>

=item "rsa-factor4" (B<OSSL_PKEY_PARAM_RSA_FACTOR4>) <unsigned integer>

=item "rsa-factor5" (B<OSSL_PKEY_PARAM_RSA_FACTOR5>) <unsigned integer>

=item "rsa-factor6" (B<OSSL_PKEY_PARAM_RSA_FACTOR6>) <unsigned integer>

=item "rsa-factor7" (B<OSSL_PKEY_PARAM_RSA_FACTOR7>) <unsigned integer>

=item "rsa-factor8" (B<OSSL_PKEY_PARAM_RSA_FACTOR8>) <unsigned integer>

=item "rsa-factor9" (B<OSSL_PKEY_PARAM_RSA_FACTOR9>) <unsigned integer>

=item "rsa-factor10" (B<OSSL_PKEY_PARAM_RSA_FACTOR10>) <unsigned integer>

RSA prime factors. The factors are known as "p", "q" and "r_i" in RFC8017.
Up to eight additional "r_i" prime factors are supported.

=item "rsa-exponent1" (B<OSSL_PKEY_PARAM_RSA_EXPONENT1>) <unsigned integer>

=item "rsa-exponent2" (B<OSSL_PKEY_PARAM_RSA_EXPONENT2>) <unsigned integer>

=item "rsa-exponent3" (B<OSSL_PKEY_PARAM_RSA_EXPONENT3>) <unsigned integer>

=item "rsa-exponent4" (B<OSSL_PKEY_PARAM_RSA_EXPONENT4>) <unsigned integer>

=item "rsa-exponent5" (B<OSSL_PKEY_PARAM_RSA_EXPONENT5>) <unsigned integer>

=item "rsa-exponent6" (B<OSSL_PKEY_PARAM_RSA_EXPONENT6>) <unsigned integer>

=item "rsa-exponent7" (B<OSSL_PKEY_PARAM_RSA_EXPONENT7>) <unsigned integer>

=item "rsa-exponent8" (B<OSSL_PKEY_PARAM_RSA_EXPONENT8>) <unsigned integer>

=item "rsa-exponent9" (B<OSSL_PKEY_PARAM_RSA_EXPONENT9>) <unsigned integer>

=item "rsa-exponent10" (B<OSSL_PKEY_PARAM_RSA_EXPONENT10>) <unsigned integer>

RSA CRT (Chinese Remainder Theorem) exponents. The exponents are known
as "dP", "dQ" and "d_i" in RFC8017.
Up to eight additional "d_i" exponents are supported.

=item "rsa-coefficient1" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT1>) <unsigned integer>

=item "rsa-coefficient2" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT2>) <unsigned integer>

=item "rsa-coefficient3" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT3>) <unsigned integer>

=item "rsa-coefficient4" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT4>) <unsigned integer>

=item "rsa-coefficient5" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT5>) <unsigned integer>

=item "rsa-coefficient6" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT6>) <unsigned integer>

=item "rsa-coefficient7" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT7>) <unsigned integer>

=item "rsa-coefficient8" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT8>) <unsigned integer>

=item "rsa-coefficient9" (B<OSSL_PKEY_PARAM_RSA_COEFFICIENT9>) <unsigned integer>

RSA CRT (Chinese Remainder Theorem) coefficients. The coefficients are known as
"qInv" and "t_i".
Up to eight additional "t_i" exponents are supported.

=back

=head2 RSA key generation parameters

When generating RSA keys, the following key generation parameters may be used.

=over 4

=item "bits" (B<OSSL_PKEY_PARAM_RSA_BITS>) <unsigned integer>

The value should be the cryptographic length for the B<RSA> cryptosystem, in
bits.

=item "primes" (B<OSSL_PKEY_PARAM_RSA_PRIMES>) <unsigned integer>

The value should be the number of primes for the generated B<RSA> key.  The
default is 2.  It isn't permitted to specify a larger number of primes than
10.  Additionally, the number of primes is limited by the length of the key
being generated so the maximum number could be less.
Some providers may only support a value of 2.

=item "e" (B<OSSL_PKEY_PARAM_RSA_E>) <unsigned integer>

The RSA "e" value. The value may be any odd number greater than or equal to
65537. The default value is 65537.
For legacy reasons a value of 3 is currently accepted but is deprecated.

=item "rsa-derive-from-pq"  (B<OSSL_PKEY_PARAM_RSA_DERIVE_FROM_PQ>) <unsigned integer>

Indicate that missing parameters not passed in the parameter list should be
derived if not provided.  Setting a nonzero value will cause all
needed exponents and coefficients to be derived if not available.  Setting this
option requires at least OSSL_PARAM_RSA_FACTOR1, OSSL_PARAM_RSA_FACTOR2,
and OSSL_PARAM_RSA_N to be provided.  This option is ignored if
OSSL_KEYMGMT_SELECT_PRIVATE_KEY is not set in the selection parameter.

=item "rsa-a" (B<OSSL_PKEY_PARAM_RSA_A>) <unsigned integer>

Setting this value to one of 1, 3, 5 or 7 applies an additional constraint
requiring that the computed prime p is congruent to this value mod 8. 
If this value is zero then it is ignored. An error will occur if the value is not
set to one of the above values.

=item "rsa-b" (B<OSSL_PKEY_PARAM_RSA_B>) <unsigned integer>

Setting this value to one of 1, 3, 5 or 7 applies an additional constraint
requiring that the computed prime q is congruent to this value mod 8. 
If this value is zero then it is ignored. An error will occur if the value is not
set to one of the above values.

=back

=head2 RSA key generation parameters for FIPS module testing

When generating RSA keys, the following additional key generation parameters may
be used for algorithm testing purposes only. Do not use these to generate
RSA keys for a production environment.

=over 4

=item "xp" (B<OSSL_PKEY_PARAM_RSA_TEST_XP>) <unsigned integer>

=item "xq" (B<OSSL_PKEY_PARAM_RSA_TEST_XQ>) <unsigned integer>

These 2 fields are normally randomly generated and are used to generate "p" and
"q".

=item "xp1" (B<OSSL_PKEY_PARAM_RSA_TEST_XP1>) <unsigned integer>

=item "xp2" (B<OSSL_PKEY_PARAM_RSA_TEST_XP2>) <unsigned integer>

=item "xq1" (B<OSSL_PKEY_PARAM_RSA_TEST_XQ1>) <unsigned integer>

=item "xq2" (B<OSSL_PKEY_PARAM_RSA_TEST_XQ2>) <unsigned integer>

These 4 fields are normally randomly generated. The prime factors "p1", "p2",
"q1" and "q2" are determined from these values.

=back

=head2 RSA key parameters for FIPS module testing

The following intermediate values can be retrieved only if the values
specified in L</"RSA key generation parameters for FIPS module testing"> are set.
These should not be accessed in a production environment.

=over 4

=item "p1" (B<OSSL_PKEY_PARAM_RSA_TEST_P1>) <unsigned integer>

=item "p2" (B<OSSL_PKEY_PARAM_RSA_TEST_P2>) <unsigned integer>

=item "q1" (B<OSSL_PKEY_PARAM_RSA_TEST_Q1>) <unsigned integer>

=item "q2" (B<OSSL_PKEY_PARAM_RSA_TEST_Q2>) <unsigned integer>

The auxiliary probable primes.

=back

=head2 RSA key validation

For RSA keys, L<EVP_PKEY_param_check(3)> and L<EVP_PKEY_param_check_quick(3)>
both return 1 unconditionally.

For RSA keys, L<EVP_PKEY_public_check(3)> conforms to the SP800-56Br1 I<public key
check> when the OpenSSL FIPS provider is used. The OpenSSL default provider
performs similar tests but relaxes the keysize restrictions for backwards
compatibility.

For RSA keys, L<EVP_PKEY_public_check_quick(3)> is the same as
L<EVP_PKEY_public_check(3)>.

For RSA keys, L<EVP_PKEY_private_check(3)> conforms to the SP800-56Br1
I<private key test>.

For RSA keys, L<EVP_PKEY_pairwise_check(3)> conforms to the
SP800-56Br1 I<KeyPair Validation check> for the OpenSSL FIPS provider. The
OpenSSL default provider allows testing of the validity of multi-primes.

=head1 CONFORMING TO

=over 4

=item FIPS186-5

Section A.1.6 Generation of Probable Primes with Conditions Based on
Auxiliary Probable Primes

=item RFC 8017, excluding RSA-PSS and RSA-OAEP

=for comment RSA-PSS, and probably also RSA-OAEP, need separate keytypes,
and will be described in separate pages for those RSA keytypes.

=back

=head1 EXAMPLES

An B<EVP_PKEY> context can be obtained by calling:

    EVP_PKEY_CTX *pctx =
        EVP_PKEY_CTX_new_from_name(NULL, "RSA", NULL);

An B<RSA> key can be generated simply like this:

    pkey = EVP_RSA_gen(4096);

or like this:

    EVP_PKEY *pkey = NULL;
    EVP_PKEY_CTX *pctx =
        EVP_PKEY_CTX_new_from_name(NULL, "RSA", NULL);

    EVP_PKEY_keygen_init(pctx);
    EVP_PKEY_generate(pctx, &pkey);
    EVP_PKEY_CTX_free(pctx);

An B<RSA> key can be generated with key generation parameters:

    unsigned int primes = 3;
    unsigned int bits = 4096;
    OSSL_PARAM params[3];
    EVP_PKEY *pkey = NULL;
    EVP_PKEY_CTX *pctx = EVP_PKEY_CTX_new_from_name(NULL, "RSA", NULL);

    EVP_PKEY_keygen_init(pctx);

    params[0] = OSSL_PARAM_construct_uint("bits", &bits);
    params[1] = OSSL_PARAM_construct_uint("primes", &primes);
    params[2] = OSSL_PARAM_construct_end();
    EVP_PKEY_CTX_set_params(pctx, params);

    EVP_PKEY_generate(pctx, &pkey);
    EVP_PKEY_print_private(bio_out, pkey, 0, NULL);
    EVP_PKEY_CTX_free(pctx);

=head1 SEE ALSO

L<EVP_RSA_gen(3)>, L<EVP_KEYMGMT(3)>, L<EVP_PKEY(3)>, L<provider-keymgmt(7)>

=head1 HISTORY

The RSA key generation parameters "a" and "b" were added in OpenSSL 4.0.

=head1 COPYRIGHT

Copyright 2020-2024 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the Apache License 2.0 (the "License").  You may not use
this file except in compliance with the License.  You can obtain a copy
in the file LICENSE in the source distribution or at
L<https://www.openssl.org/source/license.html>.

=cut
