Editing Digital Signature Algorithm (section)

====Parameter generation====
* Choose an approved [[cryptographic hash function]] <math>H</math> with output length <math>|H|</math> bits. In the original DSS, <math>H</math> was always [[SHA-1]], but the stronger [[SHA-2]] hash functions are approved for use in the current DSS.<ref name="FIPS-186-4"/><ref name="FIPS-180-4">{{cite web|url=http://csrc.nist.gov/publications/fips/fips180-4/fips-180-4.pdf|title=FIPS PUB 180-4: Secure Hash Standard (SHS), March 2012|website=csrc.nist.gov}}</ref> If <math>|H|</math> is greater than the modulus length <math>N</math>, only the leftmost <math>N</math> bits of the hash output are used.
* Choose a key length <math>L</math>. The original DSS constrained <math>L</math> to be a multiple of 64 between 512 and 1024 inclusive. NIST 800-57 recommends lengths of 2048 (or 3072) for keys with security lifetimes extending beyond 2010 (or 2030).<ref>{{cite web|url=http://csrc.nist.gov/publications/nistpubs/800-57/sp800-57-Part1-revised2_Mar08-2007.pdf |title=NIST Special Publication 800-57 |website=csrc.nist.gov |url-status=dead |archive-url=https://web.archive.org/web/20140606050814/http://csrc.nist.gov/publications/nistpubs/800-57/sp800-57-Part1-revised2_Mar08-2007.pdf |archive-date=2014-06-06 }}</ref>
* Choose the modulus length <math>N</math> such that <math>N < L</math> and <math>N \leq |H|</math>. FIPS&nbsp;186-4 specifies <math>L</math> and <math>N</math> to have one of the values: (1024, 160), (2048, 224), (2048, 256), or (3072, 256).<ref name="FIPS-186-4" />
* Choose an <math>N</math>-bit prime <math>q</math>.
* Choose an <math>L</math>-bit prime <math>p</math> such that <math>p - 1</math> is a multiple of <math>q</math>.
* Choose an integer <math>h</math> randomly from <math>\{ 2 \ldots p-2 \}</math>.
* Compute <math>g := h^{(p - 1)/q} \mod p</math>. In the rare case that <math>g=1</math> try again with a different <math>h</math>. Commonly <math>h=2</math> is used. This [[modular exponentiation]] can be computed efficiently even if the values are large.
The algorithm parameters are (<math>p</math>, <math>q</math>, <math>g</math>). These may be shared between different users of the system.