Cryptographic techniques

The public key cryptosystem published by Diffie and Hellman in 1976 is still of great interest today. Of the public key systems that have been proposed the RSA scheme of Rivest, Shamir and Adelman is of most current interest. We shall briefly describe this system (more can be found in references 2 and 7) and then describe a method to obtain suitable primes for use in the scheme

Recent advances in the construction of Hadamard matrices

In the past few years exciting new discoveries have been made in constructing Hadamard matrices. These discoveries have been centred in two ideas: (i) the construction of Baumert-Hall arrays by utilizing a construction of L. R. Welch, and (ii) finding suitable matrices to put into these arrays. We discuss these results, many of which are due to Richard J. Turyn or the author

A subliminal channel in codes for authentication without secrecy

G.J. Simmons has advanced the concept of using authentication in an open channel to actually convey information. We review the use of the knapsack problem for public codes and explore the use of Shamir\u27s method for a signature only knapsack to convey messages

Design and security issues in strongbox systems for the internet

This paper presents and discusses some design and security issues surrounding electronic strongboxes as an electronic counterpart of physical strongboxes typically found in large traditional financial institutions. The concept of electronic strongboxes is briefly discussed, comparing against physical strongboxes. A basic system for electronic strongboxes is then provided and the functional and security requirements of the system\u27s components is presented

Multiplication of ternary complementary pairs

We present a computer-search method for concatenating or multiplying binary or ternary complementary pairs. All multiplications by a particular number m are considered. The computer-search method is new and leads to a large set of new results. The results and equivalences are discussed and some applications and numerical consequences are shown

When the necessary conditions are not sufficient: sequences with zero autocorrelation function

Recently K. T. Arasu (personal communication) and Yoseph Strassler, in his PhD thesis, The Classification of Circulant Weighing Matrices of Weight 9, Bar-Ilan University, Ramat-Gan, 1997, have intensively studied circulant weighing matrices, or single sequences, with weight 9. They show many cases are non-existent. Here we give details of a search for two sequences with zero periodic autocorrelation and types (1,9), (1,16) and (4,9). We find some new cases but also many cases where the known necessary conditions are not sufficient. We instance a number of occasions when the known necessary conditions are not sufficient for the existence of weighing matrices and orthogonal de-signs constructed using sequences with zero autocorrelation function leading to intriguing new questions

Orthogonal Designs from Negacyclic Matrices

We study the use of negacyclic matrices to form orthogonal designs and hence Hadamard matrices. We give results for all possible tuple for order 12, all but 3 for order 20 and all but 3 for order 28