Physical Sciences and Mathematics Commons^™

Practical Proven Secure Authentication With Arbitration, Yvo Desmedt, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Proven secure signature schemes and unconditionally secure authentication schemes with arbiter have been proposed. The former are not practical (too slow) and the latter cannot be reused. All these limitations are solved in this paper by presenting a resuable conditionally secure authentication scheme with arbiter. The scheme is unconditionally secure against denial by the sender of having sent a message (which signatures do not have) and conditionally secure against a receiver impersonating the sender or substituting a message and conditionally secure against a similar fraud by the arbiter.

Regular Sets Of Matrices And Applications, Jennifer Seberry, Xian-Mo Zhang

Faculty of Informatics - Papers (Archive)

Suppose A1,....,As are (1, -1) matrices of order m satisfying

A_iA_j=J, i,jє{1,...,s}

A^t_iA_j=A^t_jA_i=J, i≠j, i,jє{1,...,s}

∑(A_iA^t_i + A^T_iAi) = 2smI_m

JA_i = A_iJ = aJ, i є {1,....,s}, a constant

Call A₁,.....,A_s a regular s-set of matrices of order m if Eq. 1-3 are satisfied and a regular s-set of regular matrices if Eq. 4 is also satisfied, these matrices were first discovered by J. Seberry and A.L. Whiteman in "New Hadamard …

Immunizing Public Key Cryptosystems Against Chosen Ciphertext Attacks, Christos Koukouvinos, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

This paper presents three methods for strengthening public key cryptosystems in such a way that they become secure against adaptively chosen ciphertext attacks. In an adaptively chosen ciphertext attack, an attacker can query the deciphering algorithm with any ciphertexts, except for the exact object ciphertext to be cryptanalyzed. The first strengthening method is based on the use of one-way hash functions, the second on the use of universal hash functions, and the third on the use of digital signature schemes. Each method is illustrated by an example of a public key cryptosystem based on the intractability of computing discrete logarithms …

Semi Williamson Type Matrices And The W(2n, N) Conjecture, Jennifer Seberry, Xian-Mo Zhang

Faculty of Informatics - Papers (Archive)

Four (1, -1, 0)-matrices of order m, X = (Xij), Y = (Yij), Z = (Zij), U = (Uij) satisfying

(i) XX^T + yyT + ZZ^T + UU^T = 2mI_m ,

(ii) x²_ij + y²_ij + z²_ij + U²_ij = 2, i, j = 1, ... ,m,

(iii) X, Y, Z, U mutually amicable,

will be called semi Williamson type matrices of order m. In this paper we prove that if there exist Williamson type matrices of order n₁,...n_k. then there exist semi Williamson …

Selected Papers In Combinatorics - A Volume Dedicated To R.G. Stanton, Jennifer Seberry, Brendan Mckay, Scott Vanstone

Faculty of Informatics - Papers (Archive)

Professor Stanton has had a very illustrious career. His contributions to mathematics are varied and numerous. He has not only contributed to the mathematical literature as a prominent researcher but has fostered mathematics through his teaching and guidance of young people, his organizational skills and his publishing expertise. The following briefly addresses some of the areas where Ralph Stanton has made major contributions.

Product Of Four Hadamard Matrices, R. Craigen, Jennifer Seberry, Xian-Mo Zhang

Faculty of Informatics - Papers (Archive)

We prove that if there exist Hadamard matrices of order 4m, 4n, 4p, and 4q then there exists an Hadamard matrix of order 16mnpq. This improves and extends the known result of Agayan that there exists a Hadamard matrix of order 8mn if there exist Hadamard matrices of order 4m and 4n.

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 …

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 …