# Digital Signature Standard

**DSA** (Digital Signature Algorithm) - is the algorithm of digital signature public key, included in the standard DSS (Digital Signature Standard)operating in the United States. Intended for formation (calculations) and verify digital signatures.

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## Description of a digital signature algorithm

Let *p* is a prime numbe, *q* is a prime divisor of *p-1*, satisfying the conditions:

Select is an element field , with the order of *q*. To do this, select a random number and calculate . If =1, then select the number again.

Select a random number *a* in the interval and calculate the value . The number *a* is a "secret key", and set - *public key*.

## Algorithm to calculate the digital signature

Calculation algorithm of digital signature for a message *M* is of the form:

1. choose a random integer *r*, ;

3. calculate according to the algorithm SHA-1;

4. check condition : if it is not met, then select a new value *r*;

6. the signature for the message *M* is a pair .

## Algorithm to verify digital signatures

Algorithm to verify digital signatures consists of the following:

3. check the equality ; if it is true, then the signature is accepted; if it is false, then the signature is rejected.

## Bibliography

- Черемушкин А.В. Криптографические протоколы. Основные свойства и уязвимости. - М.: Издательский центр "Академия", 2009. — 272 с.