Physical Sciences and Mathematics Commons^™

Error-Correcting Codes For Authentication And Subliminal Channels, Reihaneh Safavi-Naini, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

The application of coding theory to security scenarios is studied. Authentication systems are introduced that are based on algebraic codes and provide high protection against an intruder's impersonation and substitution attacks. It is shown that a subliminal channel can be embedded into these systems and that there is a trade-off between the authentication capability, subliminal capacity and error protection capability.

Generalized Bhaskar Rao Designs With Elements From Cyclic Groups Of Even Order, Andrew Bowler, Kathleen Quinn, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

A necessary condition is given for the existence of some Generalised Bhaskar Rao designs (GBRDs) with odd block size over cyclic groups of even order. Some constructions are given for GBRDs over cyclic groups of even order with block size 3 and with block size 4.

AMS Subject Classification: 05B99

Key words and phrases: Balanced Incomplete Block Designs; Generalised Bhaskar Rao Designs

Latin Squares And Critical Sets Of Minimal Size, Joan Cooper, Diane Donovan, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

This paper discusses critical sets for latin squares. We give the cardinality of the minimal critical set for a family of latin squares and for latin squares of small order.

Some Orthogonal Designs And Complex Hadamard Matrices By Using Two Hadamard Matrices, Jennifer Seberry, Xian-Mo Zhang

Faculty of Informatics - Papers (Archive)

We prove that if there exist Hadamard matrices of order h and n divisible by 4 then there exist two disjoint W(¹/₄hn, ¹/₈hn), whose sum is a (1, -1) matrix and a complex Hadamard matrix of order ¹/₄hn, furthermore, if there exists an OD(m; s₁, s₂,··· ,s_l) for even m then there exists an OD(¹/₄hnm; ¹/₄hns₁, ¹/₄hns₂,···, ¹/₄hns_l).

A Generalised Testbed For Analysing Block And Stream Ciphers, Lawrence Brown, Josef Pieprzyk, R. Safavi-Naini, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

With the recent development of a number of new ciphers, especially block ciphers, there is a need for a set of tools to help analyse them, in order to obtain some comparative measure of their relative security, and to assist in identifying any shortcomings in their design. This project uses a number of tests to provide a better determination of a cipher's capabilities than previous attempts, and incorporates them into a framework to aid extension of the testbed, through both the addition of new ciphers, and new tests. The testbed will be used for a comparative analysis of some of …

Addendum To Further Results On Base Sequences, Disjoint Complementary Sequences, Od(4t; T, T, T, T) And The Excess Of Hadamard Matrices, Christos Koukouvinos, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

It is known that if there are base sequences of lengths m + p, m + p, m, m and y is a Yang number then there are T-sequences of length (2m + p)y.

Let G = {g : g = 2^a10^b26^c, a, b, c non negative integers}. We show that base sequences currently exist for p = 1 and m ∑{I, ... , 18,20,21,23,25, 29} U G. Yang numbers currently exist for y ∑ {3, 5, ... ,33,37,41,45,51,53,59,65,81, ... and 2g + 1 > 81, g ∑ G}. This means T-sequences exist for

0 …

Supplementary Difference Sets And Optimal Designs, Christos Koukouvinos, Stratis Kounias, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

D-optimal designs of order n = 2v ≡ 2 (mod 4), where q is a prime power and v = q² + q + 1 are constructed using two methods, one with supplementary difference sets and the other using projective planes more directly.

An infinite family of Hadamard matrices of order n = 4v with maximum excess

(n) = n√n - 3 where q is a prime power and v = q² + q + 1 is a prime, is also constructed.

Existence Of Sbibd(4k2, 2k2 + K, K2 + K) And Hadamard Matrices With Maximal Excess, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

It is shown that SBIBD( 4k², 2k² ± k, k² ± k) and Hadamard matrices with maximal excess exist for k = qs, q ∑{q : q ≡ 1 (mod 4) is a prime power}, s ∑ {I, ... ,33, 37, ... ,41,45, ... ,59} U {2g + 1,g the length of a Golay sequence}.

This leaves the following odd k < 250 undecided 47,71,77,79,103,107;127,131,133,139, 141,151,163,167,177,179,191,199,209, ... ,217,223,227, 231,233,237,239,243,249. There is also a proper n dimensional Hadamard matrix of order (4k²)ⁿ. Regular symmetric Hadamard matrices with constant diagonal are obtained for orders 4k² whenever complete regular 4-sets of regular matrices of order k2 exist.

Hadamard Matrices Of Order ? (8 Mod 16) With Maximal Excess, Christos Koukouvinos, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Kounias and Farmakis, in 'On the excess of Hadamard matrices', Discrete Math. 68 (1988) 59-69, showed that the maximal excess (or sum of the elements) of an Hadamard matrix of order h, o(h) for h = 4m(m -1) is given by

o(4m(m - 1))≤4(m - 1)²(2m + 1).

Kharaghani in 'An infinite class of Hadamard matrices of maximal excess' (to appear) showed this maximal excess can be attained if m is the order of a skew-Hadamard matrix. We give another proof of Kharaghani's result, by generalizing an example of Farmakis and Kounias, 'The excess of Hadamard matrices and …

Amicable Hadamard Matrices And Amicable Orthogonal Designs, Jennifer Seberry, Mieko Yamada

Faculty of Informatics - Papers (Archive)

New constructions for amicable orthogonal designs are given. These new designs then give new amicable Hadamard matrices and new skew-Hadamard matrices. In particular we show that if p is the order of normalized amicable Hadamard matrices there are normalized amicable Hadamard matrices of order (p - 1)^u + 1, u > 0 an odd integer.

Tables are given for the existence of amicable and skew-Hadamard matrices of orders 2^tq, t ≥ 2 an integer, q(odd)≤2000. This gives further evidence to support the conjecture that "for every odd integer q there exists an integer t (dependent on q) so …