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Full-Text Articles in Physical Sciences and Mathematics
Generation Of A Frequency Square Orthogonal To A 10 X 10 Latin Square, H C. Kirton, Jennifer Seberry
Generation Of A Frequency Square Orthogonal To A 10 X 10 Latin Square, H C. Kirton, Jennifer Seberry
Professor Jennifer Seberry
In general it is a difficult if not impossible task to find a latin square orthogonal to a given latin square. Because of a practical problem it was required to find a frequency square orthogonal to a given latin square. We describe a computer approach which was successful in finding a (4,23) frequency square orthogonal to a given 10 x 10 latin square.
A Few More Small Defining Sets For Sbibd(4t-1, 2t-1, T-1), Thomas Kunkle, Jennifer Seberry
A Few More Small Defining Sets For Sbibd(4t-1, 2t-1, T-1), Thomas Kunkle, Jennifer Seberry
Professor Jennifer Seberry
It has been conjectured by Dinesh Sarvate and Jennifer Seberry, that, when p is an odd prime or prime power congruent to 1 mod 4, a certain collection of p sets of p elements can be used to define uniquely an SBIBD(2p+ 1, p, 1/2(p-1)), and that, when p is a prime power congruent to 3 mod 4, then a certain collection of 1/2(p-1) sets can be used to define uniquely an SBIBD(p, 4(p - 1), 1/4(p - 3)). This would mean that, in certain cases, 2t - 1 rows are enough to complete uniquely the Hadamard matrix of order …
Pitfalls In Designing Substitution Boxes, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng
Pitfalls In Designing Substitution Boxes, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng
Professor Jennifer Seberry
Two significant recent advances in cryptanalysis, namely the differential attack put forward by Biham and Shamir [3] and the linear attack by Matsui [7, 8] have had devastating impact on data encryption algorithms. An eminent problem that researchers are facing is to design S-boxes or substitution boxes so that an encryption algorithm that employs the S-boxes is immune to the attacks. In this paper we present evidence indicating that there are many pitfalls on the road to achieve the goal. In particular, we show that certain types of S-boxes which are seemly very appealing do not exist. We also show …
A Construction For Generalized Hadamard Matrices, Jennifer Seberry
A Construction For Generalized Hadamard Matrices, Jennifer Seberry
Professor Jennifer Seberry
We prove that if pv and pr -1 are both prime powers then there is a generalized Hadamard matrix of order pr(pr -1) with elements from the elementary abelian group Zp x...x Zp. This result was motivated by results of Rajkundlia on BIBD's. This result is then used to produce pr -1 mutually orthogonal F-squares F(pr(pr -1); pr -1).
Some Remarks On Supplementary Difference Sets, Jennifer Seberry
Some Remarks On Supplementary Difference Sets, Jennifer Seberry
Professor Jennifer Seberry
Let S1,S2 ,... ,Sn be subsets of V, a finite abelian group of order v written in additive notation, containing k1 k2,... ,kn elements respectively. Write Ti for the totality of all differences between elements of Si (with repetitions), and T for the totality of elements of all the Ti. If T contains each non-zero element of V a fixed number of times, lambda say, then the sets S1, S2,... ,Sn will be called n - {v; k1, k2, .....,kn;lambda} supplementary difference sets. Throughout this paper this will be abbreviated as sds.
Database Authentication Revisited, Thomas Hardjono, Yuliang Zheng, Jennifer Seberry
Database Authentication Revisited, Thomas Hardjono, Yuliang Zheng, Jennifer Seberry
Professor Jennifer Seberry
Database authentication via cryptographic checksums represents an important approach to achieving an affordable safeguard of the integriry of data in publicly accessible database systems against illegal manipulations. This paper revisits the issue of database integrity and offers a new method of safeguarding the authenticity of data in database systems. The method is based on the recent development of pseudo-random function families and sibling intractable function families, rather than on the traditional use of cryptosystems. The database authentication scheme can be applied to records or fields. The advantage of the scheme lies in the fact that each record can be associated …
Orthogonal Designs, Anthony V. Geramita, Joan Murphy Geramita, Jennifer Seberry
Orthogonal Designs, Anthony V. Geramita, Joan Murphy Geramita, Jennifer Seberry
Professor Jennifer Seberry
Orthogonal designs of special type have been extensively studied, and it is the existence of these special types that has motivated our study of the general problem of the existence of orthogonal designs. This paper is organized in the following way. In the first section we give some easily obtainable necessary conditions for the existence of orthogonal designs of various order and type. In Section 2 we briefly survey the examples of such designs that we have found in the literature. In the third section we describe several methods for constructing orthogonal designs. In the fourth section we obtain some …
On Small Defining Sets For Some Sbibd(4t-1, 2t-1, T-1), Jennifer Seberry
On Small Defining Sets For Some Sbibd(4t-1, 2t-1, T-1), Jennifer Seberry
Professor Jennifer Seberry
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 …
Some Infinite Classes Of Hadamard Matrices, Jennifer Seberry
Some Infinite Classes Of Hadamard Matrices, Jennifer Seberry
Professor Jennifer Seberry
A recursive method of A. C. Mukhopadhay is used to obtain several new infinite classes of Hadamard matrices. Unfortunately none of these constructions give previously unknown Hadamard matrices of order <40,000.
On Supplementary Difference Sets, Jennifer Seberry
On Supplementary Difference Sets, Jennifer Seberry
Professor Jennifer Seberry
Given a finite abelian group V and subsets S1, S2, ... ,Sn of V, write Ti for the totality of all the possible differences between elements of Si (with repetitions counted multiply) and T for the totality of members of all the Ti. If T contains each non-zero element of V the same number of times, then the sets S1, S2,...,Sn will be called supplementary difference sets. We discuss some properties for such sets, give some existence theorems and observe their use in the construction of Hadamard matrices and balanced incomplete block designs.
On The Smith Normal Form Of Weighing Matrices, Christos Koukouvinos, C. Mitrouli, Jennifer Seberry
On The Smith Normal Form Of Weighing Matrices, Christos Koukouvinos, C. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
The Smith normal forms (SNF) of weighing matrices are studied. We show that for all orders n ≥ 35 the full spectrum of Smith normal forms (SNF) exists for weighing matrices W(n,9) ie there exists a W(n,9) with SNF 11/2(n-s)3s91/2(n-s), for s in a set, which is described, of consecutive integers.
On Hadamard Matrices Of Order 2t Pq:I, Jennifer Seberry
On Hadamard Matrices Of Order 2t Pq:I, Jennifer Seberry
Professor Jennifer Seberry
We prove a new result for orthogonal designs showing if all full orthogonal designs, OD (r; a, b, r - a - b), exist, where gcd(a, b, r - a - b) = 2t, then all full orthogonal designs, OD(s; c, d, s - c - d), exist, where gcd(c, d, s - c - d) = 2t+u, u ≥ 0. It is known that,for infinitely many numbers r = 2wp,such OD(r; a, b, r - a - b) exist. In particular we show OD(4; x, y, 4 - x - y), OD(24; x, y, 24 - x - y) …
A Computer Listing Of Hadamard Matrices, Jennifer Seberry
A Computer Listing Of Hadamard Matrices, Jennifer Seberry
Professor Jennifer Seberry
A computer has been used to list all known Hadamard matrices of order less than 40,000. If an Hadamard matrix is not known of order 4q (q odd) then the smallest t so that there is an Hadamard matrix of order 2tq is given. Hadamard matrices are not yet known for orders 268, 412, 428.
Orthogonal Designs In Powers Of Two, Peter J. Robinson, Jennifer Seberry
Orthogonal Designs In Powers Of Two, Peter J. Robinson, Jennifer Seberry
Professor Jennifer Seberry
Repeat designs are introduced and it is shown how they may be used to give very powerful constructions for orthogonal designs in powers of two. These results are used to show all full four variable and all three variable designs exist in 2t , t ≤ 9. We believe these constructions demonstrate the existence of all possible four variable designs with no zeros in every power of two but we have not been able to prove this.
Experience Of Using A Type Signature Password System For User Authentication In A Heavily Used Computing Environment, Mike Newberry, Jennifer Seberry
Experience Of Using A Type Signature Password System For User Authentication In A Heavily Used Computing Environment, Mike Newberry, Jennifer Seberry
Professor Jennifer Seberry
This paper describes a user authentication system based around the user's type signature, a statistical measure of the user's typing style. It was tested on two heavily loaded computers.
A Note On Orthogonal Designs In Order Eighty, Joan Cooper, Jennifer Seberry
A Note On Orthogonal Designs In Order Eighty, Joan Cooper, Jennifer Seberry
Professor Jennifer Seberry
This is a short note showing the existence of all twovariable designs in order 80 except possibly (13, 64) and (15, 62) which have not yet been construced. The designs are constructed using designs in order 8, 16, 20, and 40 and applying lemmas and theorems concerning orthogonal designs. Three-variable designs (a, b, n-a-b), which are useful in constructing Hadamard matrices, are also considered for n = 40 and 80.
On The Existence Of Hadamard Matrices, Jennifer Seberry
On The Existence Of Hadamard Matrices, Jennifer Seberry
Professor Jennifer Seberry
Given any natural number q > 3 we show there exists an integer t ≤ [2 log2 (q – 3)] such that an Hadamard matrix exists for every order 2sq where s > t. The Hadamard conjecture is that s = 2. This means that for each q there is a finite number of orders 2vq for which an Hadamard matrix is not known. This is the first time such a statement could be made for arbitrary q. In particular it is already known that an Hadamard matrix exists for each 2sq where if q = 2m – 1 then s ≥ …
Integer Matrices Obeying Generalized Incidence Equations, Jennifer Seberry
Integer Matrices Obeying Generalized Incidence Equations, Jennifer Seberry
Professor Jennifer Seberry
We consider integer matrices obeying certain generalizations of the incidence equations for (v, k, lambda)-configurations and show that given certain other constraints, a constant multiple of the incidence matrix of a (v, k, lambda)-configuration may be identified as the solution of the equation.
A Note On Small Defining Sets For Some Sbibd(4t-1, 2t-1, T-1), Dinesh Sarvate, Jennifer Seberry
A Note On Small Defining Sets For Some Sbibd(4t-1, 2t-1, T-1), Dinesh Sarvate, Jennifer Seberry
Professor Jennifer Seberry
We conjecture that p specified sets of p elements are enough to define an SBIBD(2p+ l,p,(p - 1)/2) when p ≡ 1(mod 4) is a prime or prime power. This means in these cases p rows are enough to uniquely define the Hadamard matrix of order 2p + 2. We show that the p specified sets can be used to first find the residual BIBD(p + 1,2p,p,(p + 1)/2,(p - 1)/2) for p prime or prime power. This can then be used to uniquely complete the SBIBD for p = 5,9,13 and 17. This is another case where a residual …
Cryptographic Boolean Functions Via Group Hadamard Matrices, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng
Cryptographic Boolean Functions Via Group Hadamard Matrices, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng
Professor Jennifer Seberry
For any integers n,m, 2n > m > n we construct a set of boolean functions on Vm, say {f1(z),...,fn(z)}, which has the following important cryptographic properties: (i) any nonzero linear combination of the functions is balanced; (ii) the nonlinearity of any nonzero linear combination of the functions is at least 2m-1 - 2n-1; (iii) any nonzero linear combination of the functions satisfies the strict avalanche criterion; (iv) the algebraic degree of any nonzero linear combination of the functions is m - n + 1; (v) F(z) = (f1(z),...,fn(z))runs through each vector in Vn precisely 2m-n times while z runs through Vm.
A New Construction For Williamson-Type Matrices, Jennifer Seberry
A New Construction For Williamson-Type Matrices, Jennifer Seberry
Professor Jennifer Seberry
It is shown that if q is a prime power then there are Williamson-type matrices of order (i) 1/2q2(q + 1) when q ≡ 1 (mod 4), (ii)1/4q2(q + 1) when q ≡ 3 (mod 4) and there are Williamson-type matrices of order l/4(q + 1). This gives Williamson-type matrices for the new orders 363, 1183, 1805, 2601, 3174, 5103. The construction can be combined with known results on orthogonal designs to give an Hadamard matrix of the new order 33396 = 4·8349.
A Note On Orthogonal Designs, J Hammer, D G. Sarvate, Jennifer Seberry
A Note On Orthogonal Designs, J Hammer, D G. Sarvate, Jennifer Seberry
Professor Jennifer Seberry
We extend a method of Kharaghani and obtain some new constructions for weighing matrices and orthogonal designs. In particular we show that if there exists an OD(s1,...,sr), where w = ∑si, of order n, then there exists an OD(s1w,s2w,...,8rw) of order n(n+k) for k ≥ 0 an integer. If there is an OD(t,t,t,t) in order n, then there exists an OD(12t,12t,12t,12t) in order 12n. If there exists an OD(s,s,s,s) in order 4s and an OD(t,t,t,t) in order 4t there exists an OD(12s²t,12s²t,12s²t,12s²t) in order 48s²t and an OD(20s²t,20s²t,20s²t20s²) in order 80s²t.
On Weighing Matrices, Christos Koukouvinos, Jennifer Seberry
On Weighing Matrices, Christos Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We give new sets of {0, 1, -1} sequences with zero autocorrelation function, new constructions for weighing matrices and review the weighing matrix conjecture for orders 4t, t є {1,...,25} establishing its veracity for orders 52, 68 and 76. We give the smallest known lengths for sequences with zero autocorrelation function and weights ≤ 100.
Ordered Partitions And Codes Generated By Circulant Matrices, R Razen, Jennifer Seberry, K Wehrhahn
Ordered Partitions And Codes Generated By Circulant Matrices, R Razen, Jennifer Seberry, K Wehrhahn
Professor Jennifer Seberry
We consider the set of ordered partitions of n into m parts acted upon by the cyclic permutation (I2 ... m). The resulting family of orbits P(n, m) is shown to have cardinality p(n, m) = (l/n) ∑d│m φ(d) (::.'!~) where φ is Euler's φ-function. P(n, m) is shown to be set-isomorphic to the family of orbits ℓ(n, m) of the set of all m-subsets of an n-set acted upon by the cyclic permutation (12 ... n). This isomorphism yields an efficient method for determining the complete weight enumerator of any code generated by a circulant matrix.
Some Orthogonal Designs And Complex Hadamard Matrices By Using Two Hadamard Matrices, Jennifer Seberry, Xian-Mo Zhang
Some Orthogonal Designs And Complex Hadamard Matrices By Using Two Hadamard Matrices, Jennifer Seberry, Xian-Mo Zhang
Professor Jennifer Seberry
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,··· ,sl) for even m then there exists an OD(1/4hnm; 1/4hns1, 1/4hns2,···, 1/4hnsl).
Bhaskar Rao Designs Over Small Groups, William D. Palmer, Jennifer Seberry
Bhaskar Rao Designs Over Small Groups, William D. Palmer, Jennifer Seberry
Professor Jennifer Seberry
We show that for each of the groups S3, D4, Q4, Z4 x Z2 and D6 the necessary conditions are sufficient for the existence of a generalized Bhaskar Rao design. That is, we show that: (i) a GBRD (v, 3, λ; S3) exists if and only if λ ≡ O (mod 6 ) and λv(v - 1) ≡ O(mod 24); (ii) if G is one of the groups D4, Q4, and Z4 x Z2, a GBRD (v, 3, λ; G) exists if and only if λ ≡ O(mod 8) and λv(v - 1) ≡ O(mod 6); (iii) a GBRD (v, …
On The (10,5,$\Lambda$)-Family Of Bhaskar Rao Designs, Ghulam R. Chaundhry, Jennifer Seberry
On The (10,5,$\Lambda$)-Family Of Bhaskar Rao Designs, Ghulam R. Chaundhry, Jennifer Seberry
Professor Jennifer Seberry
We prove a theorem for BRD(10,5,λ)s and give thirteen (13) inequivalent BRD(10,5,4)s
Some New Weighing Matrices Using Sequences With Zero Autocorrelation Function, Christos Koukouvinos, Jennifer Seberry
Some New Weighing Matrices Using Sequences With Zero Autocorrelation Function, Christos Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We verify the skew weighing matrix conjecture for orders 2t.13, t ≥ 5, and give new results for 2t.15 proving the conjecture for t ≥ 3.
A Skew-Hadamard Matrix Of Order 92, Jennifer Seberry
A Skew-Hadamard Matrix Of Order 92, Jennifer Seberry
Professor Jennifer Seberry
Previously the smallest order for which a skew-Hadamard matrix was not known was 92. We construct such a matrix below.
Some Remarks On Generalised Hadamard Matrices And Theorems Of Rajkundlia On Sbibds, Jennifer Seberry
Some Remarks On Generalised Hadamard Matrices And Theorems Of Rajkundlia On Sbibds, Jennifer Seberry
Professor Jennifer Seberry
Constructions are given for generalised Hadamard matrices and weighing matrices with entries from abelian groups. These are then used to construct families of SBIBDs giving alternate proofs to those of Rajkundlia.