Computational and Algebraic Aspects of the Advanced Encryption Standard

Abstract. The new Advanced Encryption Standard (AES) has been recently selected by the US government to replace the old Data Encryption Standard (DES) for protecting sensitive official information. Due to its simplicity and elegant algebraic structure, the choice of the AES algorithm has motivated the study of a new approach to the analysis of block ciphers. While conventional methods of cryptanalysis (e.g. differential and linear cryptanalysis) are usually based on a “statistical ” approach, where an attacker attempts to construct statistical patterns through many interactions of the cipher, the so-called algebraic attacks exploit the intrinsic algebraic structure of a cipher. More specifically, the attacker expresses the encryption transformation as a set of multivariate polynomial equations and attempts to recover the encryption key by solving the system. In this paper we consider a number of algebraic aspects of the AES, and examine a few computational and algebraic techniques that could be used in the cryptanalysis of cipher. We show how one can express the cipher as a very large, though surprisingly simple, system of multivariate quadratic equations over the finite field F 2 8, and consider some approaches that can be used to solve this system

A Polynomial Description of the Rijndael Advanced Encryption Standard

The paper gives a polynomial description of the Rijndael Advanced Encryption Standard recently adopted by the National Institute of Standards and Technology. Special attention is given to the structure of the S-Box.Comment: 12 pages, LaTe

Experimental realization of a highly secure chaos communication under strong channel noise

A one-way coupled spatiotemporally chaotic map lattice is used to contruct cryptosystem. With the combinatorial applications of both chaotic computations and conventional algebraic operations, our system has optimal cryptographic properties much better than the separative applications of known chaotic and conventional methods. We have realized experiments to pratice duplex voice secure communications in realistic Wired Public Switched Telephone Network by applying our chaotic system and the system of Advanced Encryption Standard (AES), respectively, for cryptography. Our system can work stably against strong channel noise when AES fails to work.Comment: 15 pages, 5 figure

Group theory in cryptography

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

Formal Verification of Security Protocol Implementations: A Survey

Automated formal verification of security protocols has been mostly focused on analyzing high-level abstract models which, however, are significantly different from real protocol implementations written in programming languages. Recently, some researchers have started investigating techniques that bring automated formal proofs closer to real implementations. This paper surveys these attempts, focusing on approaches that target the application code that implements protocol logic, rather than the libraries that implement cryptography. According to these approaches, libraries are assumed to correctly implement some models. The aim is to derive formal proofs that, under this assumption, give assurance about the application code that implements the protocol logic. The two main approaches of model extraction and code generation are presented, along with the main techniques adopted for each approac

Algebraic properties of generalized Rijndael-like ciphers

We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field \GF (p^k) ($p\geq 2$ a prime number) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen the AES (Rijndael block cipher with specific block sizes) in case AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (2^k) is equal to the alternating group on the state space. In this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (p^k) ($p\geq 2$) is equal to the symmetric group or the alternating group on the state space.Comment: 22 pages; Prelim0