Jennifer Seberry

Bio: Jennifer Seberry is an academic researcher from University of Wollongong. The author has contributed to research in topics: Hadamard transform & Hadamard matrix. The author has an hindex of 37, co-authored 419 publications receiving 6556 citations. Previous affiliations of Jennifer Seberry include Australian Defence Force Academy & University of Nebraska–Lincoln.

Hadamard matrices, Sequences, and Block Designs

Abstract: One hundred years ago, in 1893, Jacques Hadamard [31] found square matrices of orders 12 and 20, with entries ±1, which had all their rows (and columns) pairwise orthogonal. These matrices, X = (Xij), satisfied the equality of the following inequality, |detX|2 ≤ ∏ ∑ |xij|2, and so had maximal determinant among matrices with entries ±1. Hadamard actually asked the question of finding the maximal determinant of matrices with entries on the unit disc, but his name has become associated with the question concerning real matrices. Disciplines Physical Sciences and Mathematics Publication Details Jennifer Seberry and Mieko Yamada, Hadamard matrices, Sequences, and Block Designs, Contemporary Design Theory – A Collection of Surveys, (D. J. Stinson and J. Dinitz, Eds.)), John Wiley and Sons, (1992), 431-560. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1070 11 "-. Hadamard Matrices, Sequences, and Block Designs Jennifer Seberry and Mieko Yamada 1 IN1RODUCTION 2 HADAMARD MATRICES 3 THE SmONGEST HADAMARD CONSmUCTION THEOREMS 4 ORTIIOGONAL DESIGNS AND AsYMPTOTIC EXISTENCE 5 SEQUENCES 6 AMICABLE HADAMARD MAmICES AND AOD 7 CoNSmUCTIONS FOR SKEW HADAMARD MAmICES 8 M -SmucTUREs 9 WILLIAMSON AND WILUAMSON-TYPE MAmICES 10 SBIBD AND THE EXCESS OF HADAMARD MATRICES 11 CoMPLEX HADAMARD MATRICES APPENDIX REFERENCES

Fundamentals of Computer Security

Abstract: From the Publisher: The book studies modern concepts of Computer Security. It is selfcontained in the sense that it introduces the basic mathematical background necessary to follow computer security concepts. Next we examine modern developments in Cryptography starting from private-key and public-key encryption, going through hashing, digital signatures, authentication, secret sharing, group-oriented cryptography, pseudorandomness, key establishment protocols, zero-knowledge protocols, identification and finishing with an introduction to modern e-business systems based on digital cash. Intrusion detection and access control provide examples of security systems implemented as a part of operating system. Database and network security is also discussed.

HAVAL - A One-Way Hashing Algorithm with Variable Length of Output

Abstract: A one-way hashing algorithm is a deterministic algorithm that compresses an arbitrary long message into a value of specified length. The output value represents the fingerprint or digest of the message. A cryptographically useful property of a one-way hashing algorithm is that it is infeasible to find two distinct messages that have the same fingerprint. This paper proposes a one-way hashing algorithm called HAVAL. HAVAL compresses a message of arbitrary length into a fingerprint of 128, 160, 192, 224 or 256 bits. In addition, HAVAL has a parameter that controls the number of passes a message block (of 1024 bits) is processed. A message block can be processed in 3, 4 or 5 passes. By combining output length with pass, we can provide fifteen (15) choices for practical applications where different levels of security are required. The algorithm is very efficient and particularly suited for 32-bit computers which predominate the current workstation market. Experiments show that HAVAL is 60% faster than MD5 when 3 passes are required, 15% faster than MD5 when 4 passes are required, and as fast as MD5 when full 5 passes are required. It is conjectured that finding two collision messages requires the order of 2n/2 operations, where n is the number of bits in a fingerprint. Disciplines Physical Sciences and Mathematics Publication Details Yuliang Zheng, Josef Pieprzyk and Jennifer Seberry, HAVAL A one-way hashing algorithm with variable length output, ( Jennifer Seberry and Yuliang Zheng, (Eds.)), Advances in Cryptography Auscrypt'92, Conference held at the Gold Coast, Australia, December 1992, 718, Lecture Notes in Computer Science, Springer-Verlag, Berlin--Heidelberg--New York, (1993), 83-104. This conference paper is available at Research Online: http://ro.uow.edu.au/infopapers/1080

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Handbook of Applied Cryptography

Abstract: From the Publisher: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Space-time block codes from orthogonal designs

Abstract: We introduce space-time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum-likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum-likelihood decoding algorithm which is based only on linear processing at the receiver. Space-time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm. The classical mathematical framework of orthogonal designs is applied to construct space-time block codes. It is shown that space-time block codes constructed in this way only exist for few sporadic values of n. Subsequently, a generalization of orthogonal designs is shown to provide space-time block codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For an arbitrary complex constellation such as PSK and QAM, space-time block codes are designed that achieve 1/2 of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three, and four transmit antennas, space-time block codes are designed that achieve, respectively, all, 3/4, and 3/4 of maximum possible transmission rate using arbitrary complex constellations. The best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well.

Public-key cryptosystems based on composite degree residuosity classes

Abstract: This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to public-key cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.

Random oracles are practical: a paradigm for designing efficient protocols

Abstract: We argue that the random oracle model—where all parties have access to a public random oracle—provides a bridge between cryptographic theory and cryptographic practice. In the paradigm we suggest, a practical protocol P is produced by first devising and proving correct a protocol PR for the random oracle model, and then replacing oracle accesses by the computation of an “appropriately chosen” function h. This paradigm yields protocols much more efficient than standard ones while retaining many of the advantages of provable security. We illustrate these gains for problems including encryption, signatures, and zero-knowledge proofs.