A 0.821-ratio purely combinatorial algorithm for maximum k-vertex cover in bipartite graphs

We study the polynomial time approximation of the max k-vertex cover problem in bipartite graphs and propose a purely combinatorial algorithm that beats the only such known algorithm, namely the greedy approach. We present a computer-assisted analysis of our algorithm, establishing that the worst case approximation guarantee is bounded below by 0.821. © Springer-Verlag Berlin Heidelberg 2016

The complexity of the Pk partition problem and related problems in bipartite graphs

International audienceIn this paper, we continue the investigation made in [MT05] about the approximability of Pk partition problems, but focusing here on their complexity. Precisely, we aim at designing the frontier between polynomial and NP-complete versions of the Pk partition problem in bipartite graphs, according to both the constant k and the maximum degree of the input graph. We actually extend the obtained results to more general classes of problems, namely, the minimum k-path partition problem and the maximum Pk packing problem. Moreover, we propose some simple approximation algorithms for those problems

LNCS

This paper studies the concrete security of PRFs and MACs obtained by keying hash functions based on the sponge paradigm. One such hash function is KECCAK, selected as NIST’s new SHA-3 standard. In contrast to other approaches like HMAC, the exact security of keyed sponges is not well understood. Indeed, recent security analyses delivered concrete security bounds which are far from existing attacks. This paper aims to close this gap. We prove (nearly) exact bounds on the concrete PRF security of keyed sponges using a random permutation. These bounds are tight for the most relevant ranges of parameters, i.e., for messages of length (roughly) l ≤ min{2n/4, 2r} blocks, where n is the state size and r is the desired output length; and for l ≤ q queries (to the construction or the underlying permutation). Moreover, we also improve standard-model bounds. As an intermediate step of independent interest, we prove tight bounds on the PRF security of the truncated CBC-MAC construction, which operates as plain CBC-MAC, but only returns a prefix of the output

Impact of ANSI X9.24-1:2009 Key Check Value on ISO/IEC 9797-1:2011 MACs

Abstract. ANSI X9.24-1:2009 specifies the key check value, which is used to verify the integrity of the blockcipher key. This value is defined as the most significant bits of the ciphertext of the zero block, and is assumed to be publicly known data for verification. ISO/IEC 9797-1:2011 illustrates a total of ten CBC MACs, where one of these MACs, the basic CBC MAC, is widely known to be insecure. In this paper, we consider the remaining nine CBC MACs and derive the quantitative security impact of using the key check value. We first show attacks against five MACs by taking advantage of the knowledge of the key check value. We then prove that the analysis is tight, in a concrete security paradigm. For the remaining four MACs, we prove that the standard birthday bound still holds even with the presence of the key check value. As a result, we obtain a complete characterization of the impact of using ANSI X9.24-1 key check value with the ISO/IEC 9797-1 MACs

The Hardness of Code Equivalence over Fq\mathbf{F}_q and its Application to Code-based Cryptography

International audienceThe code equivalence problem is to decide whether two linear codes over F_q are equivalent, that is identical up to a linear isometry of the Hamming space. In this paper, we review the hardness of code equivalence over F_q due to some recent negative results and argue on the possible implications in code-based cryptography. In particular, we present an improved version of the three-pass identification scheme of Girault and discuss on a connection between code equivalence and the hidden subgroup problem

LESS is More: Code-Based Signatures without Syndromes

Devising efficient and secure signature schemes based on coding theory is still considered a challenge by the cryptographic community. In this paper, we construct a signature scheme by exploring a new approach to the area. To do this, we design a zero-knowledge identification scheme, which we then render static via standard means (e.g. Fiat-Shamir). We show that practical instances of our protocol have the potential to outperform the state of the art on code-based signatures, achieving small data sizes with a low computational complexity

Blockcipher-based MACs: Beyond the Birthday Bound without Message Length

We present blockcipher-based MACs (Message Authentication Codes) that have beyond the birthday bound security without message length in the sense of PRF (Pseudo-Random Function) security. Achieving such security is important in constructing MACs using blockciphers with short block sizes (e.g., 64 bit). Luykx et al. (FSE2016) proposed LightMAC, the first blockcipher-based MAC with such security and a variant of PMAC, where for each $n$-bit blockcipher call, an $m$-bit counter and an $(n-m)$-bit message block are input. By the presence of counters, LightMAC becomes a secure PRF up to $O(2^{n/2})$ tagging queries. Iwata and Minematsu (TOSC2016, Issue1) proposed F_t, a keyed hash function-based MAC, where a message is input to $t$ keyed hash functions (the hash function is performed $t$ times) and the $t$ outputs are input to the xor of $t$ keyed blockciphers. Using the LightMAC\u27s hash function, F_t becomes a secure PRF up to $O(2^{t n/(t+1)})$ tagging queries. However, for each message block of $(n-m)$ bits, it requires $t$ blockcipher calls. In this paper, we improve F_t so that a blockcipher is performed only once for each message block of $(n-m)$ bits. We prove that our MACs with $t \leq 7$ are secure PRFs up to $O(2^{t n/(t+1)})$ tagging queries. Hence, our MACs with $t \leq 7$ are more efficient than F_t while keeping the same level of PRF-security