Physical Sciences and Mathematics Commons^™

On Small Defining Sets For Some Sbibd(4t-1, 2t-1, T-1), Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We conjecture that 2t - 1 specified sets of 2t - 1 elements are enough to define an SBIBD(4t - 1, 2t - 1, t - 1) when 4t - 1 is a prime or product of twin primes (corrigendum 6:62,1992). This means that in these cases 2t - 1 rows are enough to uniquely define the Hadamard matrix of order 4t.

We show that the 2t -1 specified sets can be used to first find the residual BIBD(2t,4t - 2, 2t - 1, t, t - 1) for 4t - 1 prime. This can then be uniquely used to …

Resolvable Designs Applicable To Cryptographic Authentication Schemes, Keith M. Martin, Jennifer Seberry, Peter Wild

Faculty of Informatics - Papers (Archive)

We consider certain resolvable designs which have application to doubly perfect cartesian authentication schemes. These generalise structures determined by sets of mutually orthogonal latin squares and are related to semi-latin squares and other designs which find application in the design of experiments.

Constructing Hadamard Matrices From Orthogonal Designs, Christos Koukouvinos, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

The Hadamard conjecture is that Hadamard matrices exist for all orders 1,2, 4t where t ≥ 1 is an integer. We have obtained the following results which strongly support the conjecture:

(i) Given any natural number q, there exists an Hadamard matrix of order 2^sq for every s ≥ [2log₂(q - 3].

(ii) Given any natural number q, there exists a regular symmetric Hadamard matrix with constant diagonal of order 2^2s q2 for s as before.

A significant step towards proving the Hadamard conjecture would be proving "Given any natural number q and constant C …

A Cubic Rsa Code Equivalent To Factorization, John Loxton, David S.P. Khoo, Gregory J. Bird, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

The RSA public-key encryption system of Rivest, Shamir, and Adelman can be broken if the modulus, R say, can be factorized. However, it is still not known if this system can be broken without factorizing R. A version of the RSA scheme is presented with encryption exponent ℓ ≡ 3 (mod 6). For this modified version, the equivalence of decryption and factorization of R can be demonstrated.

‘”Suggestions For Presentation Of A Twenty-Minute Talk”’, Dinesh Sarvate, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

How to present a research talk which will be remembered for a long(!) time for its presentation and clarity is a question which every newcomer would like to ask. Yes, one may also have a slight itch to prove that one is working on a very hard problem and his/her solution is straight from "the BOOK". We would like to suggest some points to ponder on the presentation only (these points may also help reduce itching).

Hadamard Matrices, Sequences, And Block Designs, Jennifer Seberry, Mieko Yamada

Faculty of Informatics - Papers (Archive)

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 = (X_ij), satisfied the equality of the following inequality,

|detX|² ≤ ∏ ∑ |x_ij|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.

On Small Defining Sets For Some Sbibd(4t - 1, 2t - 1, T - 1), Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We conjecture that 2t - 1 specified sets of 2t - 1 elements are enough to define an SBIBD(4t - 1,2t - 1, t - 1) when 4t - 1 is a prime or product of twin primes. This means that in these cases 2t - 1 rows are enough to uniquely define the Hadamard matrix of order 4t. We show that the 2t - 1 specified sets can be used to first find the residual BIBD(2t, 4t - 2, 2t - 1, t, t - 1) for 4t - 1 prime. This can then be uniquely used to complete …

Catastrophic Wave Erosion On The Southeastern Coast Of Australia: Impact Of The Lanai Tsunamis Ca. 105 Ka?, R. W. Young, Edward A. Bryant

Faculty of Science - Papers (Archive)

Sand barriers along the coast of southern New South Wales, dating from the last interglacial, have been almost completely destroyed, most probably by a catastrophic tsunami. Evidence for catastrophic wave erosion can also be traced to heights of at least 15 m above present sea level on coastal abrasion ramps. These erosional features lie above the range of effective erosion by contemporary storm waves, and cannot be attributed to either eustatic fluctuations or local uplift. Chronological evidence for the timing of the destruction of the last interglacial barriers suggests that tsunami generated by the submarine slide off Lanai in the …

Evidence Of Tsunami Sedimentation On The Southeastern Coast Of Australia, Edward A. Bryant, R. W. Young, David M. Price

Faculty of Science - Papers (Archive)

In the coastal region, the highest magnitude storms cannot always be invoked to account for large-scale, anomalous sediment features. Any coastline in the Pacific Ocean region can be affected by tsunamis, including Australia which historically lacks evidence of such events. Geologically, tsunamis along the New South Wales coast have deposited a suite of Holocene features that consist of anomalous boulder masses, either chaotically tossed onto rock platforms and backshores or jammed into crevices; highly bimodal mixtures of sand and boulders; and dump deposits consisting of well sorted coarse debris. In addition many coastal aboriginal middens were disturbed by such events. …

Catastrophic Wave Erosion On The Southeastern Coast Of Australia: Impact Of The Lanai Tsunamis Ca. 105 Ka?: Reply, R. W. Young, Edward A. Bryant

Faculty of Science - Papers (Archive)

No abstract provided.

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 …

A Spatial Analysis Of Variance Applied To Soil-Water Infiltration, C Gotway, Noel A. Cressie

Faculty of Informatics - Papers (Archive)

A spatial analysis of variance uses the spatial dependence among the observations to modify the usual interference procedures associated with a statistical linear model. When spatial correlation is present, the usual tests for presence of treatment effects may no longer be valid, and erroneous conclusions may result from assuming that the usual F ratios are F distributed. This is demonstrated using a spatial analysis of soil-water infiltration data. Emphasis is placed on modeling the spatial dependence structure with geostatistical techniques, and this spatial dependence structure is then used to test hypotheses about fixed effects using a nested linear model. -Authors

Search Key Substitution In The Encipherment Of B-Trees, Thomas Hardjono, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

This paper suggests an improvement to the scheme by Bayer and Metzger for the encipherment of B-Trees. Search keys are "disguised" instead of encrypted, and together with the data pointers and tree pointers which remain encrypted, prevents the opponent or attacker from recreating the correct shape of the B-Tree. Combinatorial block designs are used as a method to substitute the search keys contained within the nodes of the B-Tree. The substitution provides advantages in terms of the number of decryptions necessary to traverse the B-Tree, while the use of block designs are advantageous in terms of the small amount of …

Loki - A Cryptographic Primitive For Authentication And Secrecy Applications, Lawrence Brown, Josef Pieprzyk, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

This paper provides an overview of the LOKI encryption primitive which may be used to encrypt and decrypt a 64-bit block of data using a 64-bit key. It has been developed as a result of work analysing the existing DEA-1, with the aim of designing a new family of encryption primitives [Brow88], [BrSe89], [BrSe90], [PiFi88], [Piep89b], [Piep89a], [PiSe89]. Its overall structure has a broad resemblence to DEA-1 (see Fig. 1), however the detailed structure has been designed to remove operations which impede analysis or hinder efficient implementation, but which do not add to the cryptographic security of the algorithm. The …

Some Remarks On Authentication Systems, Martin Hg Anthony, Keith M. Martin, Jennifer Seberry, Peter Wild

Faculty of Informatics - Papers (Archive)

Brickell, Simmons and others have discussed doubly perfect authentication systems in which an opponent's chance of deceiving the receiver is a minimum for a given number of encoding rules. Brickell has shown that in some instances to achieve this minimum the system needs to have splitting. Such a system uses a larger message space. Motivated by Brickell's ideas we consider authentication systems with splitting and the problems of reducing the message space.

On The Design Of Permutation P In Des Type Cryptosystems, Lawrence Brown, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

This paper reviews some possible design criteria for the permutation P in a DES style cryptosystem. These permutations provide the diffusion component in a substitution-permutation network. Some empirical rules which seem to account for the derivation of the permutation used in the DES are first presented. Then it is noted that these permutations may be regarded as latin-squares which link the outputs of S-boxes to their inputs at the next stage. A subset of these which perform well in a dependency analysis are then presented and suggested for use in future schemes.

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

Faculty of Informatics - Papers (Archive)

We obtain new base sequences, that is four sequences of lengths m + p, m + p, m, m, with p odd, which have zero auto correlation function which can be used with Yang numbers and four disjoint complementary sequences (and matrices) with zero non-periodic (periodic) auto correlation function to form longer sequences. We give an alternate construction for T-sequences of length (4n + 3)(2m + p) where n is the length of a Yang nice sequence. These results are then used in the Goethals-Seidel or (Seberry) Wallis-Whiteman construction to determine eight possible decompositions into squares of (4n + 3) …

On The Products Of Hadamard Matrices, Williamson Matrices And Other Orthogonal Matrices Using M-Structures, Jennifer Seberry, Mieko Yamada

Faculty of Informatics - Papers (Archive)

The new concept of M-structures is used to unify and generalize a number of concepts in Hadamard matrices including Williamson matrices, Goethals-Seidel matrices, Wallis-Whiteman matrices and generalized quaternion matrices. The concept is used to find many new symmetric Williamson-type matrices, both in sets of four and eight, and many new Hadamard matrices. We give as corollaries "that the existence of Hadamard matrices of orders 4g and 4h implies the existence of an Hadamard matrix of older 8gh" and "the existence of Williamson type matrices of orders u and v implies the existence of Williamson type matrices of order 2uv". This …

Key Scheduling Des Type Cryptosystems, Lawrence Brown, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

This paper reviews some possible design criteria for the key schedule in a DES style cryptosystem. The key schedule involves a Key Rotation component. and the permutation PC2. Together these provide for a diffusion of dependency of ciphertext bits on key bits. Some empirical rules which seem to account for the derivation of the key schedule used in the DES are first presented. A number of trials were run with various key schedules. and some further design rules were derived. An alternative form of key schedule was then tested. This used either a null PC2, or one in which permutations …

Relative Compromise Of Statistical Databases, M Miller, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Statistical databases are databases in which only statistical type of queries are allowed. The results of the statistical queries are intended for statistical use only. However, it has been shown that using only statistical queries it is often possible to infer an individuals's value of a protected field (e.g, using various types of trackers). In such a case we say that the database has been (positively) compromised. Various types of compromise have been studied but until now attention has centred on the inference of exact information from permitted queries. In this paper we introduce a new type of compromise, the …

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

Faculty of Informatics - Papers (Archive)

We show that an SBIBD(4k², 2k² + k, k² + k) is equivalent to a regular Hadamard matrix of order 4k² which is equivalent to an Hadamard matrix of order 4k² with maximal excess. We find many new SBIBD(4k², 2k² + k, k² + k) including those for even k when there is an Hadamard matrix of order 2k (in particular all 2k ≤ 210) and k є {1, 3, 5,...,29,33,...,41,45,51,53,61,...69,75,81,83,89,95,99,625,3^2m,25. 3^2m, m ≥ 0}.