Geodesic
Public key cryptosystems on Boolean functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 54-57.

Voir la notice de l'article provenant de la source Math-Net.Ru

The objective of this conference paper is to present in Russian a brief review of contents of the recent article by authors (see Prikladnaya Diskrenaya Matematika, 2018, no. 40, pp. 23–33) where a cryptographic system including both public-key encryption and digital signature schemes has been constructed with the help of non-typical for such cryptosystems mathematical means, namely the invertible systems of Boolean functions which are in turn produced from bijective vector Boolean functions by applying the permutation and negation operations to their arguments and coordinates. Besides the cryptosystem definition, the article contains the descriptions of cryptanalysis problems for both encryption and signature schemes in the cryptosystem, their solutions with known plaintext attacks, a general scheme for constructing such attacks on the base of linearization set method for solving a nonlinear system of Boolean equations, specific attacks constructed according to this scheme for all possible types of a private key, and asymptotic estimates for computational complexity of these attacks. All the mentioned results, excluding the specific attacks in plural particular cases, are described in this review.
Keywords: vector Boolean functions, invertibility, asymmetric substitution cryptosystem
Mots-clés : cryptanalysis. 
@article{PDMA_2018_11_a16,
     author = {G. P. Agibalov and I. A. Pankratova},
     title = {Public key cryptosystems on {Boolean} functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {54--57},
     publisher = {mathdoc},
     number = {11},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2018_11_a16/}
}
TY  - JOUR
AU  - G. P. Agibalov
AU  - I. A. Pankratova
TI  - Public key cryptosystems on Boolean functions
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2018
SP  - 54
EP  - 57
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2018_11_a16/
LA  - ru
ID  - PDMA_2018_11_a16
ER  - 
%0 Journal Article
%A G. P. Agibalov
%A I. A. Pankratova
%T Public key cryptosystems on Boolean functions
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2018
%P 54-57
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2018_11_a16/
%G ru
%F PDMA_2018_11_a16
G. P. Agibalov; I. A. Pankratova. Public key cryptosystems on Boolean functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 54-57. http://geodesic.mathdoc.fr/item/PDMA_2018_11_a16/

[1] Agibalov G. P., Pankratova I. A., “Asymmetric cryptosystems on Boolean functions”, Prikladnaya diskretnaya matematika, 2018, no. 40, 23–33

[2] Agibalov G. P., “Substitution block ciphers with functional keys”, Prikladnaya diskretnaya matematika, 2017, no. 38, 57–65 | MR

[3] Agibalov G. P., “Metody resheniya sistem polinomialnykh uravnenii nad konechnym polem”, Vestnik Tomskogo gosudarstvennogo universiteta. Prilozhenie, 2006, no. 17, 4–9

[4] Agibalov G. P., “Logicheskie uravneniya v kriptoanalize generatorov klyuchevogo potoka”, Vestnik Tomskogo gosudarstvennogo universiteta. Prilozhenie, 2003, no. 6, 31–41