41 research outputs found

    Group theory in cryptography

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    This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor typographical changes. To appear in Proceedings of Groups St Andrews 2009 in Bath, U

    Aperiodic logarithmic signatures

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    In this paper we propose a method to construct logarithmic signatures which are not amalgamated transversal and further do not even have a periodic block. The latter property was crucial for the successful attack on the system MST3 by Blackburn et al. [1]. The idea for our construction is based on the theory in Szab\'o's book about group factorizations [12]

    Cryptanalysis of the MST_3 Public Key Cryptosystem

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    In this paper we describe a cryptanalysis of MST_3, a public key cryptosystem based on non-commutative groups recently proposed by Lempken, Magliveras, van Trung and Wei

    Efficient implementation of a CCA2-secure variant of McEliece using generalized Srivastava codes

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    International audienceIn this paper we present efficient implementations of McEliece variants using quasi-dyadic codes. We provide secure parameters for a classical McEliece encryption scheme based on quasi-dyadic generalized Srivastava codes, and successively convert our scheme to a CCA2-secure protocol in the random oracle model applying the Fujisaki-Okamoto transform. In contrast with all other CCA2-secure code-based cryptosystems that work in the random oracle model, our conversion does not require a constant weight encoding function. We present results for both 128-bit and 80-bit security level, and for the latter we also feature an implementation for an embedded device

    DAGS:Key encapsulation using dyadic GS codes

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    Code-based cryptography is one of the main areas of interest for NIST's Post-Quantum Cryptography Standardization call. In this paper, we introduce DAGS, a Key Encapsulation Mechanism (KEM) based on quasi-dyadic generalized Srivastava codes. The scheme is proved to be IND-CCA secure in both random oracle model and quantum random oracle model. We believe that DAGS will offer competitive performance, especially when compared with other existing code-based schemes, and represent a valid candidate for post-quantum standardization.</p

    Algebraic Attack against Variants of McEliece with Goppa Polynomial of a Special Form

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    International audienceIn this paper, we present a new algebraic attack against some special cases of Wild McEliece Incognito, a generalization of the original McEliece cryptosystem. This attack does not threaten the original McEliece cryptosystem. We prove that recovering the secret key for such schemes is equivalent to solving a system of polynomial equations whose solutions have the structure of a usual vector space. Consequently, to recover a basis of this vector space, we can greatly reduce the number of variables in the corresponding algebraic system. From these solutions, we can then deduce the basis of a GRS code. Finally, the last step of the cryptanalysis of those schemes corresponds to attacking a McEliece scheme instantiated with particular GRS codes (with a polynomial relation between the support and the multipliers) which can be done in polynomial-time thanks to a variant of the Sidelnikov-Shestakov attack. For Wild McEliece & Incognito, we also show that solving the corresponding algebraic system is notably easier in the case of a non-prime base eld Fq. To support our theoretical results, we have been able to practically break several parameters de ned over a non-prime base field q in {9; 16; 25; 27; 32}, t < 7, extension degrees m in {2,3}, security level up to 2^129 against information set decoding in few minutes or hours

    Compact McEliece keys based on Quasi-Dyadic Srivastava codes

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    The McEliece cryptosystem is one of the few systems to be considered secure against Quantum attacks. The original scheme is built upon Goppa codes and produces very large keys, hence latest research has focused mainly on trying to reduce the public key size. Previous proposals tried to replace the class of Goppa codes with other families of codes, but this revealed to be an insecure choice. In this paper we introduce a construction based on Generalized Srivastava codes, a large class which include Goppa codes as a special case, that allows relatively short public keys without being vulnerable to known structural attacks

    A Digital Signature Scheme Based on MST

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    As special types of factorization of finite groups, logarithmic signature and cover have been used as the main components of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1, MST2, and MST3. Recently, Svaba et. al proposed a revised MST3 encryption scheme with greater security. Meanwhile, they put forward an idea of constructing signature schemes on the basis of logarithmic signatures and random covers. In this paper, we firstly design a secure digital signature scheme based on logarithmic signatures and random covers. In order to complete the task, we devise a new encryption scheme based on MST3 cryptosystems
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