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- Article name
- Typical verification equations in algebraic digital signature algorithms with a hidden group
- Authors
- Moldovyan D. N., , mdn.spectr@mail.ru, St. Petersburg Electrotechnical Univeristy "LETI", St. Petersburg, Russia
- Keywords
- information security / digital signature / post-quantum cryptography / finite associative algebra / non-commutative algebra / hidden group
- Year
- 2022 Issue 1 Pages 31 - 37
- Code EDN
- Code DOI
- 10.52190/2073-2600_2022_1_31
- Abstract
- Typical forms of the verification equation of the digital signature algorithms with a hidden group, which use finite non-commutative associative algebras as an algebraic support are proposed. The principal feature of the algorithms of this type is that the signature includes a certain vector S as one of its elements, which enters several times in the verification equation. The multiple entry of the vector S in the verification equation determines the security of the algorithms to the forging signature attacks that use the vector S as a fitting parameter. However the multiple entry requires the use of a special method for calculating the vector S, when using the secret key. The specific form of the verification equation determines the formulas for calculation of the public-key elements. It is shown that the calculation of the signature can be performed in several different ways, but in all cases the signature randomization mechanism includes exponentiations of the elements of the hidden group to the degrees with random values.
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