Minimal vectors in linear codes

Ashikhmin, Alexei; Barg, Alexander

doi:10.1109/18.705584

Cited by 282 publications

(257 citation statements)

References 15 publications

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“…Interestingly, use of intersecting codes or minimal codewords has been suggested for oblivious transfer [BCS96] and for secret sharing [AB98,DY03,SL12], which is a tool widely used for Secure Multi-Party Computation [CDN12].…”

Section: Intersecting Codes and Minimal Codesmentioning

confidence: 99%

Towards Secure Two-Party Computation from the Wire-Tap Channel

Chabanne

Cohen

Patey

2014

Information Security and Cryptology -- ICISC 2013

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We introduce a new protocol for secure two-party computation of linear functions in the semi-honest model, based on coding techniques. We first establish a parallel between the second version of the wire-tap channel model and secure two-party computation. This leads us to our protocol, that combines linear coset coding and oblivious transfer techniques. Our construction requires the use of binary intersecting codes or q-ary minimal codes, which are also studied in this paper.

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Section: Intersecting Codes and Minimal Codesmentioning

confidence: 99%

Towards Secure Two-Party Computation from the Wire-Tap Channel

Chabanne

Cohen

Patey

2014

Information Security and Cryptology -- ICISC 2013

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“…The following properties can be found in [1]; we will use the second one later on. (iii) If c is a minimal codeword in C, then wt(c) ≤ n − k + 1.…”

Section: Definition 14 Let C Be a Q-ary Linear Code A Non-zero Codementioning

confidence: 99%

Minimal codewords in Reed–Muller codes

Schillewaert

Storme

Thas

2009

Des. Codes Cryptogr.

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Minimal codewords were introduced by Massey [8] for cryptographical purposes. They are used in particular secret sharing schemes, to model the access structures. We study minimal codewords of weight smaller than 3·2 m−r in binary Reed-Muller codes RM(r, m) and translate our problem into a geometrical one, using a classification result of Kasami, Tokura, and Azumi [5, 6] on Boolean functions. In this geometrical setting, we calculate numbers of non-minimal codewords. So we obtain the number of minimal codewords in the cases where we have information about the weight distribution of the code RM(r, m).The presented results improve previous results obtained theoretically by Borissov, Manev, and Nikova [3], and computer aided results of Borissov and Manev [2]. This paper is in fact an extended abstract. Full proofs can be found on the arXiv.

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“…• m(n, n − 2) = n, for n ≥ 6 since there is a [6,4] code C 6 with dual distance 3 and M (C 6 ) = 6, eg C 6 = R ⊥ 3 ⊕ R ⊥ 3 .…”

Section: Propositionmentioning

confidence: 99%

“…This concept was considered independently in code-based secret sharing schemes [4] and also in the study of the Voronoi domain of a code in the context of decoding [1]. Let M (C) denote the number of minimal codewords of a code C. We consider the following natural question.…”

Section: Introductionmentioning

confidence: 99%