Geodesic
Fast computation of cyclic convolutions and their applications in code-based asymmetric encryption schemes
Modelirovanie i analiz informacionnyh sistem, Tome 30 (2023) no. 4, pp. 354-365

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The development of fast algorithms for key generation, encryption and decryption not only increases the efficiency of related operations. Such fast algorithms, for example, for asymmetric cryptosystems on quasi-cyclic codes, make it possible to experimentally study the dependence of decoding failure rate on code parameters for small security levels and to extrapolate these results to large values of security levels. In this article, we explore efficient cyclic convolution algorithms, specifically designed, among other things, for use in encoding and decoding algorithms for quasi-cyclic LDPC and MDPC codes. Corresponding convolutions operate on binary vectors, which can be either sparse or dense. The proposed algorithms achieve high speed by compactly storing sparse vectors, using hardware-supported XOR instructions, and replacing modulo operations with specialized loop transformations. These fast algorithms have potential applications not only in cryptography, but also in other areas where convolutions are used.
Keywords: fast algorithms, encryption schemes.
Mots-clés : cyclic convolutions 
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     author = {A. N. Sushko and B. Y. Steinberg and K. V. Vedenev and A. A. Glukhikh and Y. V. Kosolapov},
     title = {Fast computation of cyclic convolutions and their applications in code-based asymmetric encryption schemes},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {354--365},
     publisher = {mathdoc},
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     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2023_30_4_a3/}
}
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A. N. Sushko; B. Y. Steinberg; K. V. Vedenev; A. A. Glukhikh; Y. V. Kosolapov. Fast computation of cyclic convolutions and their applications in code-based asymmetric encryption schemes. Modelirovanie i analiz informacionnyh sistem, Tome 30 (2023) no. 4, pp. 354-365. http://geodesic.mathdoc.fr/item/MAIS_2023_30_4_a3/