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

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

Projective Aspects of the AES Inversion

We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite field \GF (2^8), which is most naturally considered as a projective transformation. Such a viewpoint allows us to demonstrate certain properties of this AES nonlinear function. In particular, we make some comments about the group generated by such transformations, and we give a characterisation for the values in the AES {\em Difference} or XOR {\em Table} for the AES nonlinear function and comment on the geometry given by this XOR Table

A forensics software toolkit for DNA steganalysis.

Recent advances in genetic engineering have allowed the insertion of artificial DNA strands into the living cells of organisms. Several methods have been developed to insert information into a DNA sequence for the purpose of data storage, watermarking, or communication of secret messages. The ability to detect, extract, and decode messages from DNA is important for forensic data collection and for data security. We have developed a software toolkit that is able to detect the presence of a hidden message within a DNA sequence, extract that message, and then decode it. The toolkit is able to detect, extract, and decode messages that have been encoded with a variety of different coding schemes. The goal of this project is to enable our software toolkit to determine with which coding scheme a message has been encoded in DNA and then to decode it. The software package is able to decode messages that have been encoded with every variation of most of the coding schemes described in this document. The software toolkit has two different options for decoding that can be selected by the user. The first is a frequency analysis approach that is very commonly used in cryptanalysis. This approach is very fast, but is unable to decode messages shorter than 200 words accurately. The second option is using a Genetic Algorithm (GA) in combination with a Wisdom of Artificial Crowds (WoAC) technique. This approach is very time consuming, but can decode shorter messages with much higher accuracy