Application of Quasigroups in Cryptography and Data Communications

In the past decade, quasigroup theory has proven to be a fruitfull field for production of new cryptographic primitives and error-corecting codes. Examples include several finalists in the flagship competitions for new symmetric ciphers, as well as several assimetric proposals and cryptcodes. Since the importance of cryptography and coding theory for secure and reliable data communication can only grow within our modern society, investigating further the power of quasigroups in these fields is highly promising research direction. Our team of researchers has defined several research objectives, which can be devided into four main groups: 1. Design of new cryptosystems or their building blocks based on quasigroups - we plan to make a classification of small quasigroups based on new criteria, as well as to identify new optimal 8–bit S-boxes produced by small quasigroups. The results will be used to design new stream and block ciphers. 2. Cryptanalysis of some cryptosystems based on quasigroups - we will modify and improve the existing automated tools for differential cryptanalysis, so that they can be used for prove the resistance to differential cryptanalysis of several existing ciphers based on quasigroups. This will increase the confidence in these ciphers. 3. Codes based on quasigroups - we will designs new and improve the existing error correcting codes based on combinatorial structures and quasigroups. 4. Algebraic curves over finite fields with their cryptographic applications - using some known and new tools, we will investigate the rational points on algebraic curves over finite fields, and explore the possibilities of applying the results in cryptography

On the Security of Y-00 under Fast Correlation and Other Attacks on the Key

The potential weakness of the Y-00 direct encryption protocol when the encryption box ENC in Y-00 is not chosen properly is demonstrated in a fast correlation attack by S. Donnet et al in Phys. Lett. A 35, 6 (2006) 406-410. In this paper, we show how this weakness can be eliminated with a proper design of ENC. In particular, we present a Y-00 configuration that is more secure than AES under known-plaintext attack. It is also shown that under any ciphertext-only attack, full information-theoretic security on the Y-00 seed key is obtained for any ENC when proper deliberate signal randomization is employed

Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.Comment: Submitted to IEEE Transactions on Information Theor