# Digital Signature Algorithm

 related topics {math, number, function} {law, state, case} {system, computer, user}

The Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature Standard (DSS), specified in FIPS 186,[1] adopted in 1993. A minor revision was issued in 1996 as FIPS 186-1.[2] The standard was expanded further in 2000 as FIPS 186-2 and again in 2009 as FIPS 186-3.[3]

DSA is covered by U.S. Patent 5,231,668, filed July 26, 1991, and attributed to David W. Kravitz,[4] a former NSA employee. This patent was given to "The United States of America as represented by the Secretary of Commerce, Washington, D.C." and the NIST has made this patent available worldwide royalty-free.[5] Dr. Claus P. Schnorr claims that his U.S. Patent 4,995,082 covers DSA; this claim is disputed.[6]

## Contents

### Key generation

Key generation has two phases. The first phase is a choice of algorithm parameters which may be shared between different users of the system:

• Choose an approved cryptographic hash function H. In the original DSS, H was always SHA-1, but the stronger SHA-2 hash functions are approved for use in the current DSS. The hash output may be truncated to the size of a key pair.
• Decide on a key length L and N. This is the primary measure of the cryptographic strength of the key. The original DSS constrained L to be a multiple of 64 between 512 and 1024 (inclusive). NIST 800-57[7] recommends lengths of 2048 (or 3072) for keys with security lifetimes extending beyond 2010 (or 2030), using correspondingly longer N.[3] specifies L and N length pairs of (1024,160), (2048,224), (2048,256), and (3072,256).
• Choose an N-bit prime q. N must be less than or equal to the hash output length.
• Choose an L-bit prime modulus p such that p–1 is a multiple of q.
• Choose g, a number whose multiplicative order modulo p is q. This may be done by setting g = h(p–1)/q mod p for some arbitrary h (1 < h < p-1), and trying again with a different h if the result comes out as 1. Most choices of h will lead to a usable g; commonly h=2 is used.