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

Code-based Identification and Signature Schemes

In an age of explosive growth of digital communications and electronic data storage, cryptography plays an integral role in our society. Some examples of daily use of cryptography are software updates, e-banking, electronic commerce, ATM cards, etc. The security of most currently used cryptosystems relies on the hardness of the factorization and discrete logarithm problems. However, in 1994 Peter Shor discovered polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. Therefore, it is of extreme importance to develop cryptosystems that remain secure even when the adversary has access to a quantum computer; such systems are called post-quantum cryptosystems. One promising candidate is based on codes; in this thesis we focus more specifically on code-based identification and signature schemes. Public key identification schemes are typically applied in cryptography to reach the goal of entity authentication. Their applications include authentication and access control services such as remote login, credit card purchases and many others. One of the most well-known systems of this kind is the zero-knowledge identification scheme introduced in Crypto 1993 by Stern. It is very fast compared to schemes based on number-theoretic problems since it involves only simple and efficiently executable operations. However, its main drawbacks are the high communication complexity and the large public key size, that makes it impractical for many applications. Our first contribution addresses these drawbacks by taking a step towards reducing communication complexity and public key size simultaneously. To this end, we propose a novel zero-knowledge five-pass identification scheme which improves on Stern's scheme. It reduces the communication complexity by a factor of 25 % compared to Stern's one. Moreover, we obtain a public key of size of 4 KB, whereas Stern's scheme requires 15 KB for the same level of security. To the best of our knowledge, there is no code-based identification scheme with better performance than our proposal using random codes. Our second contribution consists of extending one of the most important paradigms in cryptography, namely the one by Fiat and Shamir. In doing so, we enlarge the class of identification schemes to which the Fiat-Shamir transform can be applied. Additionally, we put forward a generic methodology for proving the security of signature schemes derived from this class of identification schemes. We exemplify our extended paradigm and derive a provably secure signature scheme based on our proposed five-pass identification scheme. In order to contribute to the development of post-quantum schemes with additional features, we present an improved code-based threshold ring signature scheme using our two previous results. Our proposal has a shorter signature length and a smaller public-key size compared to Aguilar et al.'s scheme, which is the reference in this area

Improved Successive Cancellation Flip Decoding of Polar Codes Based on Error Distribution

Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar codes has mediocre error-correction performance on short to moderate codeword lengths: the SC-Flip decoding algorithm is one of the solutions that have been proposed to overcome this issue. On the other hand, SC-Flip has a higher implementation complexity compared to SC due to the required log-likelihood ratio (LLR) selection and sorting process. Moreover, it requires a high number of iterations to reach good error-correction performance. In this work, we propose two techniques to improve the SC-Flip decoding algorithm for low-rate codes, based on the observation of channel-induced error distributions. The first one is a fixed index selection (FIS) scheme to avoid the substantial implementation cost of LLR selection and sorting with no cost on error-correction performance. The second is an enhanced index selection (EIS) criterion to improve the error-correction performance of SC-Flip decoding. A reduction of $24.6\%$ in the implementation cost of logic elements is estimated with the FIS approach, while simulation results show that EIS leads to an improvement on error-correction performance improvement up to $0.42$ dB at a target FER of $10^{-4}$.Comment: This version of the manuscript corrects an error in the previous ArXiv version, as well as the published version in IEEE Xplore under the same title, which has the DOI:10.1109/WCNCW.2018.8368991. The corrections include all the simulations of SC-Flip-based and SC-Oracle decoders, along with associated comments in-tex

Multispectral Palmprint Encoding and Recognition

Palmprints are emerging as a new entity in multi-modal biometrics for human identification and verification. Multispectral palmprint images captured in the visible and infrared spectrum not only contain the wrinkles and ridge structure of a palm, but also the underlying pattern of veins; making them a highly discriminating biometric identifier. In this paper, we propose a feature encoding scheme for robust and highly accurate representation and matching of multispectral palmprints. To facilitate compact storage of the feature, we design a binary hash table structure that allows for efficient matching in large databases. Comprehensive experiments for both identification and verification scenarios are performed on two public datasets -- one captured with a contact-based sensor (PolyU dataset), and the other with a contact-free sensor (CASIA dataset). Recognition results in various experimental setups show that the proposed method consistently outperforms existing state-of-the-art methods. Error rates achieved by our method (0.003% on PolyU and 0.2% on CASIA) are the lowest reported in literature on both dataset and clearly indicate the viability of palmprint as a reliable and promising biometric. All source codes are publicly available.Comment: Preliminary version of this manuscript was published in ICCV 2011. Z. Khan A. Mian and Y. Hu, "Contour Code: Robust and Efficient Multispectral Palmprint Encoding for Human Recognition", International Conference on Computer Vision, 2011. MATLAB Code available: https://sites.google.com/site/zohaibnet/Home/code