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- Article name
- An alternative method for designing signature schemes satisfying criterion of post-quantum security
- Authors
- Moldovyan N. A., , nmold@mail.ru, St. Petersburg Federal Research Center of the RAS (SPC RAS), St. Petersburg, Russia
Kostina A. A., , anna1805@mail.ru, St. Petersburg Institute for Informatics and Automation the RAS, St. Petersburg, Russia
- Keywords
- information protection / cryptography / digital signature / post-quantum cryptoscheme / discrete logarithm problem / finite associative algebra / non-commutative algebra
- Year
- 2020 Issue 3 Pages 16 - 21
- Code EDN
- Code DOI
- Abstract
- In order to reduce the size of the public key and signature, a new method is proposed for constructing electronic digital signature schemes based on the hidden discrete logarithm problem, which satisfy the previously formulated post-quantum security criterion, which requires the elimination of periods associated with the value of the discrete logarithm in periodic functions specified by the public parameters of the cryptosystem. Based on the method, a digital signature scheme is developed, the basic primitive of which is an exponentiation operation in a hidden commutative group that has two-dimensional cyclicity. An eight-dimensional finite non-commutative associative algebra containing sufficiently large number of different groups with two-dimensional cyclicality is used as the algebraic carrier of the cryptosystem. The public key is three eight-dimensional vectors calculated depending on two vectors having prime order, which form the basis of the hidden commutative group. The digital signature is three 256-bit numbers.
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