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Open AccessArticle

A Finite Regime Analysis of Information Set Decoding Algorithms

1
Department of Information Engineering (DII), Università Politecnica delle Marche, 60131 Ancona, Italy
2
Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, 20133 Milano, Italy
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(10), 209; https://doi.org/10.3390/a12100209
Received: 20 June 2019 / Revised: 16 September 2019 / Accepted: 25 September 2019 / Published: 1 October 2019
(This article belongs to the Special Issue Coding Theory and Its Application)
Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology.
Keywords: asymmetric cryptosystems; code-based cryptosystems; information set decoding asymmetric cryptosystems; code-based cryptosystems; information set decoding
MDPI and ACS Style

Baldi, M.; Barenghi, A.; Chiaraluce, F.; Pelosi, G.; Santini, P. A Finite Regime Analysis of Information Set Decoding Algorithms. Algorithms 2019, 12, 209.

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