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Title: On lower bounds for information set decoding over 𝔽q and on the effect of partial knowledge

Authors: Robert Niebuhr; Edoardo Persichetti; Pierre-Louis Cayrel; Stanislav Bulygin; Johannes Buchmann

Addresses: Artilleriestrasse 11, Darmstadt 64285, Merck KGaA, Germany ' Dakota State University, College of Arts and Sciences, 820 N Washington Ave, Madison, SD 57042, USA ' Laboratoire Hubert Curien, Université Jean Monnet, UMR CNRS 5516, Bâtiment F 18 Rue du Professeur Benoît Lauras, Saint-Etienne 42000, France ' Germany ' Technische Universität Darmstadt, Fachbereich Informatik Kryptographie und Computeralgebra, Hochschulstrasse 10, Darmstadt 64289, Germany

Abstract: Code-based cryptosystems are promising candidates for post-quantum cryptography since they are fast, require only basic arithmetic because their security is well understood. The increasing number of cryptographic schemes based on codes over fields other than 𝔽2 presents, however, security issues that are not relevant in the case of binary codes; the security of such constructions, therefore, requires separate assessment. Information set decoding (ISD) is one of the most important generic attacks against code-based cryptosystems. We give lower bounds for ISD over 𝔽q, thereby anticipating future software and hardware improvements. Our results allow to compute conservative parameters for cryptographic applications. While most security proofs assume that an attacker does not have any additional information about the secret, we show that in certain scenarios an attacker can gain partial knowledge of the secret. We present how this knowledge can be used to improve the efficiency of an attack and give new bounds for the complexity of such an attack. In this paper, we analyse two types of partial knowledge including concrete scenarios and give an idea how to prevent the leakage of such knowledge to an attacker.

Keywords: codes; post-quantum cryptography; information set decoding; ISD; lower bounds; partial knowledge; cryptosystems; security; attacks.

DOI: 10.1504/IJICOT.2017.081458

International Journal of Information and Coding Theory, 2017 Vol.4 No.1, pp.47 - 78

Received: 11 Jun 2016
Accepted: 01 Aug 2016

Published online: 02 Jan 2017 *

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