RSA(6) Games Manual RSA(6)
NAME
genrsa, pubout, asn1parse, cksum, sign, verify - RSA utilities
SYNOPSIS
genrsa [nbits] >rsa.key
pubout <rsa.key >rsa.pub
asn1parse <key
cksum <file >digest
sign key file >sigfile
verify key file <sigfile
DESCRIPTION
The genrsa utility generates an RSA private key, which essentially
involves the generation of two prime numbers. The generated private key,
along with other information, is written into the standard output and
encoded into PEM + ASN.1 format, containing the following data:
o The version (hardcoded to "0").
o The composite modulus, N.
o The public value, e.
o The private value, d.
o The private value, d.
o The first prime factor of N, p.
o The second prime factor of N, p.
o The first exponent, d % (p - 1).
o The second exponent, d % (q - 1).
o The coefficient, q^-1 mod p.
The pubout utility extracts the public key (N and e) out of the private
key. The extracted public key is written into standard output. The
private key is read from standard input.
The asn1parse utility parses a private or public key created with the
genrsa or pubout utilities.
The cksum utility hashes the contents read from standard input into a
digest using the SHA256 algorithm for cryptographic hash function. The
processed digest is written into standard output.
The sign utility signs the file file using the key key into a signature,
which consists of the RSA+OAEP encryption of the SHA256 hash of the
contents of the given file. The signature is written into standard
output.
The verify utility verifies the authenticity of file by verifying its
signature with the given key. The verification is done by comparing
whether the SHA256 hash of the contents of the given file is equal to the
RSA+OAEP decryption of the given signature. The signature is read from
standard input.
EXAMPLES
Generate a 1024-bit private key into key and extract the public key into
key.pub:
$ genrsa 1024 | tee rsa1024.key | pubout >rsa1024.pub
Check the structure of a previously-generated 1024-bit private key:
$ asn1parse <rsa1024.key
Create a signature for a given file using a previously-generated 1024-bit
private key:
$ sign rsa1024.key archive.zip > archive.sig
Verify the signature of a given file using a previously-generated
1024-bit private key:
$ verify rsa1024.key archive.zip < archive.sig
SEE ALSO
openssl(1)
The following books were used during the development of these utilities:
Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography,
CRC Press, 2021.
Donald E. Knuth, The Art of Computer Programming, Addison Wesley Longman,
2, 1998.
IMPLEMENTATION
RSA is a cipher scheme that uses an asymmetric key pair (one private, and
the other public) associated to a given bit length (at least 1024), and
generated after two random prime numbers (whose product has the given bit
length). The security of RSA is based on the problem of factoring large
numbers.
Prime number generation is, perhaps, the slowest factor on the key
generation, for it consists of generating random numbers and checking for
their primality. The primality test is performed using the Miller-Rabin
test.
The RSA cipher system, however, is deterministic and subject to Chosen-
Plaintext Attacks. OAEP is a padding scheme used with RSA to add
randomness to RSA's deterministic encryption.
The source code contains the following modules. Modules are written as a
.c source file and an optional .c header file. The header file is
present on shared modules; and absent on modules containing the program's
entry point (the main function).
The shared modules are as follows:
bignum Routines and structures for arbitrary-precision arithmetic.
keyio Routines for key I/O in the PEM+ASN.1 format.
oaep Routines for verifying and signing files using OAEP padding.
sha Routines and constants for SHA256 cryptographic hashing.
HISTORY
These RSA utilities are the product of a project for 2022 2nd semester's
course of Cyber Security of the Computer Science department of the
University of Brasilia, Brazil.
BUGS
The bignum.o module was written from scratch and is probably buggy; i
should have used an already existant arbitrary-precision arithmetic
library.
Generating keys can take long time, especially for 1024 bits or more.
OpenBSD 7.2 February 9, 2023 OpenBSD 7.2