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+.\"	$NetBSD: EVP_PKEY-RSA.7,v 1.5 2026/04/08 17:06:43 christos Exp $
+.\"
+.\" -*- mode: troff; coding: utf-8 -*-
+.\" Automatically generated by Pod::Man v6.0.2 (Pod::Simple 3.45)
+.\"
+.\" Standard preamble:
+.\" ========================================================================
+.de Sp \" Vertical space (when we can't use .PP)
+.if t .sp .5v
+.if n .sp
+..
+.de Vb \" Begin verbatim text
+.ft CW
+.nf
+.ne \\$1
+..
+.de Ve \" End verbatim text
+.ft R
+.fi
+..
+.\" \*(C` and \*(C' are quotes in nroff, nothing in troff, for use with C<>.
+.ie n \{\
+.    ds C` ""
+.    ds C' ""
+'br\}
+.el\{\
+.    ds C`
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+'br\}
+.\"
+.\" Escape single quotes in literal strings from groff's Unicode transform.
+.ie \n(.g .ds Aq \(aq
+.el       .ds Aq '
+.\"
+.\" If the F register is >0, we'll generate index entries on stderr for
+.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
+.\" entries marked with X<> in POD.  Of course, you'll have to process the
+.\" output yourself in some meaningful fashion.
+.\"
+.\" Avoid warning from groff about undefined register 'F'.
+.de IX
+..
+.nr rF 0
+.if \n(.g .if rF .nr rF 1
+.if (\n(rF:(\n(.g==0)) \{\
+.    if \nF \{\
+.        de IX
+.        tm Index:\\$1\t\\n%\t"\\$2"
+..
+.        if !\nF==2 \{\
+.            nr % 0
+.            nr F 2
+.        \}
+.    \}
+.\}
+.rr rF
+.\"
+.\" Required to disable full justification in groff 1.23.0.
+.if n .ds AD l
+.\" ========================================================================
+.\"
+.IX Title "EVP_PKEY-RSA 7"
+.TH EVP_PKEY-RSA 7 2026-04-07 3.5.6 OpenSSL
+.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
+.\" way too many mistakes in technical documents.
+.if n .ad l
+.nh
+.SH NAME
+EVP_PKEY\-RSA, EVP_KEYMGMT\-RSA, RSA
+\&\- EVP_PKEY RSA keytype and algorithm support
+.SH DESCRIPTION
+.IX Header "DESCRIPTION"
+The \fBRSA\fR keytype is implemented in OpenSSL\*(Aqs default and FIPS providers.
+That implementation supports the basic RSA keys, containing the modulus \fIn\fR,
+the public exponent \fIe\fR, the private exponent \fId\fR, and a collection of prime
+factors, exponents and coefficient for CRT calculations, of which the first
+few are known as \fIp\fR and \fIq\fR, \fIdP\fR and \fIdQ\fR, and \fIqInv\fR.
+.SS "Common RSA parameters"
+.IX Subsection "Common RSA parameters"
+In addition to the common parameters that all keytypes should support (see
+"Common parameters" in \fBprovider\-keymgmt\fR\|(7)), the \fBRSA\fR keytype implementation
+supports the following.
+.IP """n"" (\fBOSSL_PKEY_PARAM_RSA_N\fR) <unsigned integer>" 4
+.IX Item """n"" (OSSL_PKEY_PARAM_RSA_N) <unsigned integer>"
+The RSA modulus "n" value.
+.IP """e"" (\fBOSSL_PKEY_PARAM_RSA_E\fR) <unsigned integer>" 4
+.IX Item """e"" (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 \fBEVP_PKEY_fromdata\fR\|(3).
+Note that when a decryption operation is performed, that this value is used for
+blinding purposes to prevent timing attacks.
+.IP """d"" (\fBOSSL_PKEY_PARAM_RSA_D\fR) <unsigned integer>" 4
+.IX Item """d"" (OSSL_PKEY_PARAM_RSA_D) <unsigned integer>"
+The RSA private exponent "d" value.
+.IP """rsa\-factor1"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR1\fR) <unsigned integer>" 4
+.IX Item """rsa-factor1"" (OSSL_PKEY_PARAM_RSA_FACTOR1) <unsigned integer>"
+.PD 0
+.IP """rsa\-factor2"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR2\fR) <unsigned integer>" 4
+.IX Item """rsa-factor2"" (OSSL_PKEY_PARAM_RSA_FACTOR2) <unsigned integer>"
+.IP """rsa\-factor3"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR3\fR) <unsigned integer>" 4
+.IX Item """rsa-factor3"" (OSSL_PKEY_PARAM_RSA_FACTOR3) <unsigned integer>"
+.IP """rsa\-factor4"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR4\fR) <unsigned integer>" 4
+.IX Item """rsa-factor4"" (OSSL_PKEY_PARAM_RSA_FACTOR4) <unsigned integer>"
+.IP """rsa\-factor5"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR5\fR) <unsigned integer>" 4
+.IX Item """rsa-factor5"" (OSSL_PKEY_PARAM_RSA_FACTOR5) <unsigned integer>"
+.IP """rsa\-factor6"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR6\fR) <unsigned integer>" 4
+.IX Item """rsa-factor6"" (OSSL_PKEY_PARAM_RSA_FACTOR6) <unsigned integer>"
+.IP """rsa\-factor7"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR7\fR) <unsigned integer>" 4
+.IX Item """rsa-factor7"" (OSSL_PKEY_PARAM_RSA_FACTOR7) <unsigned integer>"
+.IP """rsa\-factor8"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR8\fR) <unsigned integer>" 4
+.IX Item """rsa-factor8"" (OSSL_PKEY_PARAM_RSA_FACTOR8) <unsigned integer>"
+.IP """rsa\-factor9"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR9\fR) <unsigned integer>" 4
+.IX Item """rsa-factor9"" (OSSL_PKEY_PARAM_RSA_FACTOR9) <unsigned integer>"
+.IP """rsa\-factor10"" (\fBOSSL_PKEY_PARAM_RSA_FACTOR10\fR) <unsigned integer>" 4
+.IX Item """rsa-factor10"" (OSSL_PKEY_PARAM_RSA_FACTOR10) <unsigned integer>"
+.PD
+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.
+.IP """rsa\-exponent1"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT1\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent1"" (OSSL_PKEY_PARAM_RSA_EXPONENT1) <unsigned integer>"
+.PD 0
+.IP """rsa\-exponent2"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT2\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent2"" (OSSL_PKEY_PARAM_RSA_EXPONENT2) <unsigned integer>"
+.IP """rsa\-exponent3"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT3\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent3"" (OSSL_PKEY_PARAM_RSA_EXPONENT3) <unsigned integer>"
+.IP """rsa\-exponent4"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT4\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent4"" (OSSL_PKEY_PARAM_RSA_EXPONENT4) <unsigned integer>"
+.IP """rsa\-exponent5"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT5\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent5"" (OSSL_PKEY_PARAM_RSA_EXPONENT5) <unsigned integer>"
+.IP """rsa\-exponent6"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT6\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent6"" (OSSL_PKEY_PARAM_RSA_EXPONENT6) <unsigned integer>"
+.IP """rsa\-exponent7"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT7\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent7"" (OSSL_PKEY_PARAM_RSA_EXPONENT7) <unsigned integer>"
+.IP """rsa\-exponent8"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT8\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent8"" (OSSL_PKEY_PARAM_RSA_EXPONENT8) <unsigned integer>"
+.IP """rsa\-exponent9"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT9\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent9"" (OSSL_PKEY_PARAM_RSA_EXPONENT9) <unsigned integer>"
+.IP """rsa\-exponent10"" (\fBOSSL_PKEY_PARAM_RSA_EXPONENT10\fR) <unsigned integer>" 4
+.IX Item """rsa-exponent10"" (OSSL_PKEY_PARAM_RSA_EXPONENT10) <unsigned integer>"
+.PD
+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.
+.IP """rsa\-coefficient1"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT1\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient1"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT1) <unsigned integer>"
+.PD 0
+.IP """rsa\-coefficient2"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT2\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient2"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT2) <unsigned integer>"
+.IP """rsa\-coefficient3"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT3\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient3"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT3) <unsigned integer>"
+.IP """rsa\-coefficient4"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT4\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient4"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT4) <unsigned integer>"
+.IP """rsa\-coefficient5"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT5\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient5"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT5) <unsigned integer>"
+.IP """rsa\-coefficient6"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT6\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient6"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT6) <unsigned integer>"
+.IP """rsa\-coefficient7"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT7\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient7"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT7) <unsigned integer>"
+.IP """rsa\-coefficient8"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT8\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient8"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT8) <unsigned integer>"
+.IP """rsa\-coefficient9"" (\fBOSSL_PKEY_PARAM_RSA_COEFFICIENT9\fR) <unsigned integer>" 4
+.IX Item """rsa-coefficient9"" (OSSL_PKEY_PARAM_RSA_COEFFICIENT9) <unsigned integer>"
+.PD
+RSA CRT (Chinese Remainder Theorem) coefficients. The coefficients are known as
+"qInv" and "t_i".
+Up to eight additional "t_i" exponents are supported.
+.SS "RSA key generation parameters"
+.IX Subsection "RSA key generation parameters"
+When generating RSA keys, the following key generation parameters may be used.
+.IP """bits"" (\fBOSSL_PKEY_PARAM_RSA_BITS\fR) <unsigned integer>" 4
+.IX Item """bits"" (OSSL_PKEY_PARAM_RSA_BITS) <unsigned integer>"
+The value should be the cryptographic length for the \fBRSA\fR cryptosystem, in
+bits.
+.IP """primes"" (\fBOSSL_PKEY_PARAM_RSA_PRIMES\fR) <unsigned integer>" 4
+.IX Item """primes"" (OSSL_PKEY_PARAM_RSA_PRIMES) <unsigned integer>"
+The value should be the number of primes for the generated \fBRSA\fR key.  The
+default is 2.  It isn\*(Aqt 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.
+.IP """e"" (\fBOSSL_PKEY_PARAM_RSA_E\fR) <unsigned integer>" 4
+.IX Item """e"" (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.
+.IP """rsa\-derive\-from\-pq""  (\fBOSSL_PKEY_PARAM_RSA_DERIVE_FROM_PQ\fR) <unsigned integer>" 4
+.IX Item """rsa-derive-from-pq"" (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.
+.SS "RSA key generation parameters for FIPS module testing"
+.IX Subsection "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.
+.IP """xp"" (\fBOSSL_PKEY_PARAM_RSA_TEST_XP\fR) <unsigned integer>" 4
+.IX Item """xp"" (OSSL_PKEY_PARAM_RSA_TEST_XP) <unsigned integer>"
+.PD 0
+.IP """xq"" (\fBOSSL_PKEY_PARAM_RSA_TEST_XQ\fR) <unsigned integer>" 4
+.IX Item """xq"" (OSSL_PKEY_PARAM_RSA_TEST_XQ) <unsigned integer>"
+.PD
+These 2 fields are normally randomly generated and are used to generate "p" and
+"q".
+.IP """xp1"" (\fBOSSL_PKEY_PARAM_RSA_TEST_XP1\fR) <unsigned integer>" 4
+.IX Item """xp1"" (OSSL_PKEY_PARAM_RSA_TEST_XP1) <unsigned integer>"
+.PD 0
+.IP """xp2"" (\fBOSSL_PKEY_PARAM_RSA_TEST_XP2\fR) <unsigned integer>" 4
+.IX Item """xp2"" (OSSL_PKEY_PARAM_RSA_TEST_XP2) <unsigned integer>"
+.IP """xq1"" (\fBOSSL_PKEY_PARAM_RSA_TEST_XQ1\fR) <unsigned integer>" 4
+.IX Item """xq1"" (OSSL_PKEY_PARAM_RSA_TEST_XQ1) <unsigned integer>"
+.IP """xq2"" (\fBOSSL_PKEY_PARAM_RSA_TEST_XQ2\fR) <unsigned integer>" 4
+.IX Item """xq2"" (OSSL_PKEY_PARAM_RSA_TEST_XQ2) <unsigned integer>"
+.PD
+These 4 fields are normally randomly generated. The prime factors "p1", "p2",
+"q1" and "q2" are determined from these values.
+.SS "RSA key parameters for FIPS module testing"
+.IX Subsection "RSA key parameters for FIPS module testing"
+The following intermediate values can be retrieved only if the values
+specified in "RSA key generation parameters for FIPS module testing" are set.
+These should not be accessed in a production environment.
+.IP """p1"" (\fBOSSL_PKEY_PARAM_RSA_TEST_P1\fR) <unsigned integer>" 4
+.IX Item """p1"" (OSSL_PKEY_PARAM_RSA_TEST_P1) <unsigned integer>"
+.PD 0
+.IP """p2"" (\fBOSSL_PKEY_PARAM_RSA_TEST_P2\fR) <unsigned integer>" 4
+.IX Item """p2"" (OSSL_PKEY_PARAM_RSA_TEST_P2) <unsigned integer>"
+.IP """q1"" (\fBOSSL_PKEY_PARAM_RSA_TEST_Q1\fR) <unsigned integer>" 4
+.IX Item """q1"" (OSSL_PKEY_PARAM_RSA_TEST_Q1) <unsigned integer>"
+.IP """q2"" (\fBOSSL_PKEY_PARAM_RSA_TEST_Q2\fR) <unsigned integer>" 4
+.IX Item """q2"" (OSSL_PKEY_PARAM_RSA_TEST_Q2) <unsigned integer>"
+.PD
+The auxiliary probable primes.
+.SS "RSA key validation"
+.IX Subsection "RSA key validation"
+For RSA keys, \fBEVP_PKEY_param_check\fR\|(3) and \fBEVP_PKEY_param_check_quick\fR\|(3)
+both return 1 unconditionally.
+.PP
+For RSA keys, \fBEVP_PKEY_public_check\fR\|(3) conforms to the SP800\-56Br1 \fIpublic key
+check\fR when the OpenSSL FIPS provider is used. The OpenSSL default provider
+performs similar tests but relaxes the keysize restrictions for backwards
+compatibility.
+.PP
+For RSA keys, \fBEVP_PKEY_public_check_quick\fR\|(3) is the same as
+\&\fBEVP_PKEY_public_check\fR\|(3).
+.PP
+For RSA keys, \fBEVP_PKEY_private_check\fR\|(3) conforms to the SP800\-56Br1
+\&\fIprivate key test\fR.
+.PP
+For RSA keys, \fBEVP_PKEY_pairwise_check\fR\|(3) conforms to the
+SP800\-56Br1 \fIKeyPair Validation check\fR for the OpenSSL FIPS provider. The
+OpenSSL default provider allows testing of the validity of multi\-primes.
+.SH "CONFORMING TO"
+.IX Header "CONFORMING TO"
+.IP FIPS186\-4 4
+.IX Item "FIPS186-4"
+Section B.3.6  Generation of Probable Primes with Conditions Based on
+Auxiliary Probable Primes
+.IP "RFC 8017, excluding RSA\-PSS and RSA\-OAEP" 4
+.IX Item "RFC 8017, excluding RSA-PSS and RSA-OAEP"
+.SH EXAMPLES
+.IX Header "EXAMPLES"
+An \fBEVP_PKEY\fR context can be obtained by calling:
+.PP
+.Vb 2
+\&    EVP_PKEY_CTX *pctx =
+\&        EVP_PKEY_CTX_new_from_name(NULL, "RSA", NULL);
+.Ve
+.PP
+An \fBRSA\fR key can be generated simply like this:
+.PP
+.Vb 1
+\&    pkey = EVP_RSA_gen(4096);
+.Ve
+.PP
+or like this:
+.PP
+.Vb 3
+\&    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);
+.Ve
+.PP
+An \fBRSA\fR key can be generated with key generation parameters:
+.PP
+.Vb 5
+\&    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);
+.Ve
+.SH "SEE ALSO"
+.IX Header "SEE ALSO"
+\&\fBEVP_RSA_gen\fR\|(3), \fBEVP_KEYMGMT\fR\|(3), \fBEVP_PKEY\fR\|(3), \fBprovider\-keymgmt\fR\|(7)
+.SH COPYRIGHT
+.IX Header "COPYRIGHT"
+Copyright 2020\-2024 The OpenSSL Project Authors. All Rights Reserved.
+.PP
+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
+<https://www.openssl.org/source/license.html>.