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Full-Text Articles in Physical Sciences and Mathematics
Relationships Between Boolean Functions And Symmetric Groups, Chengxin Qu, Jennifer Seberry, Josef Pieprzyk
Relationships Between Boolean Functions And Symmetric Groups, Chengxin Qu, Jennifer Seberry, Josef Pieprzyk
Professor Jennifer Seberry
We study the relations between boolean functions and symmetric groups. We consider elements of a symmetric group as variable transformations operators for boolean functions. Boolean function may be fixed or permuted by these operators. We give some properties relating the symmetric group Sn and boolean functions on Vn.
Bounds On The Maximum Determinant For (1,-1) Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Bounds On The Maximum Determinant For (1,-1) Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We suppose the Hadamard conjecture is true and an Hadamard matrix of order 4t, exists for all t ≥ 1. We use the results for the equivalent SBIBD(4t-1,2t-1,t-1) to establish the maximum determinant or a lower bound for the maximum determinant for all ±1 matrices. In particular we give numerical results for all orders ≤100.
Group Divisible Designs, Gbrdsds And Generalized Weighing Matrices, Dinesh G. Sarvate, Jennifer Seberry
Group Divisible Designs, Gbrdsds And Generalized Weighing Matrices, Dinesh G. Sarvate, Jennifer Seberry
Professor Jennifer Seberry
We give new constructions for regular group divisible designs, pairwise balanced designs, generalized Bhaskar Rao supplementary difference sets and generalized weighing matrices. In particular if p is a prime power and q divides p - 1 we show the following exist; (i) GDD (2(p2+p+1), 2(p2+p+1), rp2,2p2, λ1 = p2λ, λ2 = (p2-p)r, m=p2+p+1,n=2), r_+1,2; (ii) GDD(q(p+1), q(p+1), p(q-1), p(q-1),λ1=(q-1)(q-2), λ2=(p-1)(q-1)2/q,m=q,n=p+1); (iii) PBD(21,10;K),K={3,6,7} and PDB(78,38;K), K={6,9,45}; (iv) GW(vk,k2;EA(k)) whenever a (v,k,λ)-difference set exists and k is a prime power; (v) PBIBD(vk2,vk2,k2,k2;λ1=0,λ2=λ,λ3=k) whenever a (v,k,λ)-difference set exists and k is a prime power; (vi) we give a GW(21;9;Z3).
Infinite Families Of Orthogonal Designs : I, Christos Koukouvinos, Jennifer Seberry
Infinite Families Of Orthogonal Designs : I, Christos Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We generalise a method inspired by Kharaghani and Holzmann to obtain infinite families of 6-variables orthogonal designs, OD(8t;k,k,k,k,k,k), and OD(8t;,k,k,k,k,2k,2k), for the first time for odd t.
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We obtain explicit formulae for the values of the v - j minors, j = 0,1,2 of (1, -1) incidence matrices of SBIBD(v,k,λ). This allows us to obtain explicit information on the growth problem for families of matrices with moderate growth. An open problem remians to establish whether the (1, -1) CP incidence matrices of SBIBD(v,k,λ), can have growth greater than V for families other than Hadamard families.
Infinite Families Of Generalized Bhaskar Rao Designs, Jennifer Seberry
Infinite Families Of Generalized Bhaskar Rao Designs, Jennifer Seberry
Professor Jennifer Seberry
We show that GBRD(p,1/2(p-1), 1/8(p-1)(p-3);EA(1/2p-1)) exist for all prime powers p ≡ 3 (mod 4). We also show that GBRD(p,1/2(p - 1), 1/4(p - 1)(p - 3); EA(1/2(p - 1)) exist for all prime powers p ≡ 1 (mod 4). This allows us to give a new proof that a BIBD(f(ef + 1),(ef + 1)(ef2 + f -1),ef + f -1,f,f - 1) exists whenever p = ef + 1 is a prime power. This gives many new GBRDs including a GBRD(19,9,36;EA(9)), a GBRD(13,6,30;Z6) and a GBRD(17,8,6;EA(8)).
Beacon Based Authentication, Azad Jiwa, Jennifer Seberry, Yuliang Zheng
Beacon Based Authentication, Azad Jiwa, Jennifer Seberry, Yuliang Zheng
Professor Jennifer Seberry
Reliable authentication of communicating entities is essential for achieving security in a distributed computing environment. The design of such systems as Kerberos, SPX and more recently KryptoKnight and Kuperee, have largely been successful in addressing the problem. The common element with these implementations is the need for a trusted thirdparty authentication service. This essentially requires a great deal of trust to be invested in the authentication server which adds a level of complexity and reduces system flexibility. The use of a Beacon to promote trust between communicating parties was first suggested by M. Rabin in "Transactions protected by beacons," Journal …
Influence Of Entries In Critical Sets Of Room Squares, Ghulam Chaudhry, Jennifer Seberry
Influence Of Entries In Critical Sets Of Room Squares, Ghulam Chaudhry, Jennifer Seberry
Professor Jennifer Seberry
We consider structures which have rules for completion such as balanced incomplete block designs, Latin squares, Rooms squares, F-squares, Youden squares, regular graphs, colourings, finite geometries and difference sets. In particular we are concerned with the problem of unique completion of structures given partial information. If the partial structure can be uniquely completed then this partial structure together with the rules contains the same information as the final structure. In this paper, we study the information inherent in partial Room squares, where it is not possible to uniquely complete the square. We study the influence and power of parts of …
Growth In Gaussian Elimination For Weighing Matrices W(N,N-1), C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Growth In Gaussian Elimination For Weighing Matrices W(N,N-1), C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We consider the values for large minors of a skew-Hadamard matrix or conference matrix W of order n and find maximum n x n minor equals to (n-1)n/2, maximum (n-1) x (n-1) minor equals to (n-1)n/2-1, maximum (n-2) x (n-2) minor equals 2(n-1)n/2-2, and maximum (n-3) x (n-3) minor equals to 4(n-1)n/2-3. This leads us to conjecture that the growth factor for Gaussian elimination of compeletely pivoted skew-Hadamard or conference matrices and indeed any completely pivoted weighing matrix or order n and weight n-1 is n-1 and that the first and last few pivots are (1,2,2,3 or 4,.....,n-1 or n-1/2,n-1/2,n-1) …
Authentication Via Multi-Service Tickets In The Kuperee Server, Thomas Hardjono, Jennifer Seberry
Authentication Via Multi-Service Tickets In The Kuperee Server, Thomas Hardjono, Jennifer Seberry
Professor Jennifer Seberry
The subject of this paper is the authentication services as found in the Kuperee3 server. The authentication protocol is based on the Zheng-Seberry public key cryptosystem, and makes use of the distinct features of the cryptosystem. Although couched in the terminology of Kerberos, the protocol has subtle features, such as the binding together of two entities by a third entity, leading to the need of equal co-operation by the two entities in order to complete the authentication procedure. Another important feature is the use of a multi-service ticket to access multiple services offered by different servers. This removes the need …
An Almost Optimal Fail-Stop Signature Scheme, Willy Susilo, R. Safavi-Naini, M. Gysin, Jennifer Seberry
An Almost Optimal Fail-Stop Signature Scheme, Willy Susilo, R. Safavi-Naini, M. Gysin, Jennifer Seberry
Professor Jennifer Seberry
Security of ordinary digital signature schemes relies on a computational assumption. Fail-stop signature schemes provide security for a sender against a forger with unlimited computational power by enabling the sender to provide a proof of forger, if it occurs. In this paper, we give an efficient fail-stop signature scheme that uses two hard problems, discrete logarithm and factorisation , as the basis of receiver's security. We show that the scheme has provable security against adaptively chosen message attack and is the most efficient scheme with respect to the ratio of the message length to the signature length. The scheme provides …
On Construction And Nonlinearity Of Correlation Immune Functions, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng
On Construction And Nonlinearity Of Correlation Immune Functions, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng
Professor Jennifer Seberry
A Boolean function is said to be correlation immune if its output leaks no information about its input values. Such functions have many applications in computer security practices including the construction of key stream generators from a set of shift registers. Finding methods for easy construction of correlation immune functions has been an active research area since the introduction of the notion by Siegenthaler. In this paper we study balanced correlation immune functions using the theory of Hadamard matrices. First we present a simple method for directly constructing balanced correlation immune functions of any order. Then we prove that our …
Reusing Shares In Secret Sharing Schemes, Yuliang Zheng, Thomas Hardjono, Jennifer Seberry
Reusing Shares In Secret Sharing Schemes, Yuliang Zheng, Thomas Hardjono, Jennifer Seberry
Professor Jennifer Seberry
A (t, w) threshold scheme is a method for sharing a secret among w shareholders so that the collaboration of at least t shareholders is required in order to reconstruct the shared secret. This paper is concerned with the re-use of shares possessed by shareholders in threshold schemes. We propose a simple (t, w) threshold scheme based on the use of cryptographically strong pseudo-random functions and universal hash functions. A remarkable advantage of the scheme is that a shareholder can use a single string in the share of many different secrets; in particular, a shareholder need not be given a …
On Integer Matrices Obeying Certain Matrix Equations, Jennifer Seberry
On Integer Matrices Obeying Certain Matrix Equations, Jennifer Seberry
Professor Jennifer Seberry
We discuss integer matrices B of odd order v which satisfy Br = ± B, BBr = vI - J, BJ = O. Matrices of this kind which have zero diagonal and other elements ± 1 give rise to skew-Hadamard and n-type matrices; we show that the existence of a skew-Hadamard (n-type) matrix of order h implies the existence of skew-Hadamard (n-type) matrices of orders (h - 1)5 + 1 and (h - 1)7 + 1. Finally we show that, although there are matrices B with elements other than ± 1 and 0, the equations force considerable restrictions on the …
On The Distribution Of The Permanent Of Cyclic (0,1) Matrices, Evi Nemeth, Jennifer Seberry, Michael Shu
On The Distribution Of The Permanent Of Cyclic (0,1) Matrices, Evi Nemeth, Jennifer Seberry, Michael Shu
Professor Jennifer Seberry
Some results are obtained on the permanent of cyclic (0,1) matrices which support the conjecture that for such matrices of prime order p the number of distinct values the permanent attains is of order p. Writing e(r) for the number of distinct values the permanent of cyclic (0,1) matrices of order n can attain we found e(5) = 6, e(6) = 12, e(7) = 9, e(8) = 11, e(9) = 21, e(10) ≤ 44, and e(11) ≤ 30. It is easy to show e(p) ≤ 1/p(2p-2)+2, p prime, but these answers are considerably smaller. We obtain formulae for the permanent …
Maximal Ternary Codes And Plotkin's Bound, Conrad Mackenzie, Jennifer Seberry
Maximal Ternary Codes And Plotkin's Bound, Conrad Mackenzie, Jennifer Seberry
Professor Jennifer Seberry
The analogue of Plotkin's bound is developed for ternary codes with high distance relative to length. Generalized Hadamard matrices are used to obtain codes which meet these bounds. The ternary analogue of Levenshtein's construction is discussed and maximal codes constructed.
Supplementary Difference Sets And Optimal Designs, Christos Koukouvinos, Stratis Kounias, Jennifer Seberry
Supplementary Difference Sets And Optimal Designs, Christos Koukouvinos, Stratis Kounias, Jennifer Seberry
Professor Jennifer Seberry
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.
Minimal Critical Set Of A Room Square Of Order 7, Ghulam R. Chaudhry, Jennifer Seberry
Minimal Critical Set Of A Room Square Of Order 7, Ghulam R. Chaudhry, Jennifer Seberry
Professor Jennifer Seberry
A Room square R of order r is an r x r array each of whose cells may either be empty or contain an unordered pair of objects 0,1,2,...,r, subject to the following conditions: (i) each of the objects 0,1,2.....r occurs precisely once in each row of R and precisely once in each column of R, and (ii) every possible unordered pair of objects occurs precisely once in the whole array.
New Results With Near- Yang Sequences, Marc Gysin, Jennifer Seberry
New Results With Near- Yang Sequences, Marc Gysin, Jennifer Seberry
Professor Jennifer Seberry
We construct new TW -sequences, weighing matrices and orthogonal designs using near-Yang sequences. In particular we construct new OD(60(2m + 1) + 4t; 13(2m+ 1), 13(2m+ 1), 13(2m+ 1), 13(2m+ 1) and new W(60(2m+ 1) + 4t; 13s(2m+ 1))for all t ≥ O, m ≤ 30, s = 1,2,3,4.
A Generalised Testbed For Analysing Block And Stream Ciphers, Lawrence Brown, Josef Pieprzyk, R. Safavi-Naini, Jennifer Seberry
A Generalised Testbed For Analysing Block And Stream Ciphers, Lawrence Brown, Josef Pieprzyk, R. Safavi-Naini, Jennifer Seberry
Professor Jennifer Seberry
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 …
Applications Of Smartcards For Anonymous And Verifiable Databases, Thomas Hardjono, Jennifer Seberry
Applications Of Smartcards For Anonymous And Verifiable Databases, Thomas Hardjono, Jennifer Seberry
Professor Jennifer Seberry
In this paper we describe a practical solution towards anonymous and verifiable databases based on the use of smartcards and the recent Improved Leighton-Micali protocol for the distribution of keys. The scheme is addressed particularly to public data held in separate government databases with the aim of preventing unauthorized government institutions from gathering and merging private data concerning individuals from these separate containers. The solution can be realized through the recent Clipper Chip and smartcard technology, and its security relies on the strength of these technologies. The scheme is also extendible to mobile computing environments.
New Normal Sequences Of Length 25, Marc Gysin, Jennifer Seberry
New Normal Sequences Of Length 25, Marc Gysin, Jennifer Seberry
Professor Jennifer Seberry
An introduction to binary sequences, combinatorial designs and how they are related to communication theory and computer security is given. An exhaustive search algorithm for normal sequences is presented. This is the first time that the lengths n = 24 and n = 25 have been searched through completely. No sequences of length 24 are found. It turns out that all the normal sequences of length 25 can be derived from Turyn sequences. This construction is subject to a new theorem that is given here.
Electronic Funds Transfer Point Of Sale In Australia, Ralph Gyoery, Jennifer Seberry
Electronic Funds Transfer Point Of Sale In Australia, Ralph Gyoery, Jennifer Seberry
Professor Jennifer Seberry
The Australia wide eftpos systems was developed by the Australian Retail Banks to meet Australian conditions including a small population, which overwhehningly uses cash for transactions, a small number of banks capable of "exchange of value" settlements and enormous distances. This paper discusses the system that has evolved first involving only ATM's and banks, then extending to POS systems for retailers and non bank fmancial institutions.
On The Multiplication Theorems Of Hadamard Matrices Of Generalized Quaternion Type Using M-Structures, Jennifer Seberry, Mieko Yamada
On The Multiplication Theorems Of Hadamard Matrices Of Generalized Quaternion Type Using M-Structures, Jennifer Seberry, Mieko Yamada
Professor Jennifer Seberry
We show that M-structures can be extended to Hadamard matrices of generalized quaternion type and obtain multiplication type theorems which preserve the structure.
New Hadamard Matrices And Conference Matrices Obtained Via Mathon's Construction, Jennifer Seberry, Albert L. Whiteman
New Hadamard Matrices And Conference Matrices Obtained Via Mathon's Construction, Jennifer Seberry, Albert L. Whiteman
Professor Jennifer Seberry
We give a formulation, via (1, - 1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5·9²r+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6.9²r+1+ 2, 10.9²t+1 + 2, 8·49·9², t ≥ 0; q2(q + 3) + 2 where q ≡ 3 (mod 4) is a prime power and 1/2(q + 5) is the order of a skew-Hadamard matrix); (q + 1)q².9t, t ≥ …
Multiplication Of Sequences With Zero Autocorrelation, Christos Koukouvinos, Stratis Kounias, Jennifer Seberry, C. H. Yang, Joel Yang
Multiplication Of Sequences With Zero Autocorrelation, Christos Koukouvinos, Stratis Kounias, Jennifer Seberry, C. H. Yang, Joel Yang
Professor Jennifer Seberry
Near normal sequences of new lengths n = 4m + 1 = 49,53,57 are constructed. The relation between a special set of near normal sequences and Golay sequences is discussed. A reformulation of Yang's powerful theorems on T-sequences is also given. We give base sequences for lengths m + p, m + p, m, m for p = 1 and m є {19, ... ,30}. Some of these are new lengths, or new decompositions into four squares for n and constructed here for the first time.
Regular Sets Of Matrices And Applications, Jennifer Seberry, Xian-Mo Zhang
Regular Sets Of Matrices And Applications, Jennifer Seberry, Xian-Mo Zhang
Professor Jennifer Seberry
Suppose A1,....,As are (1, -1) matrices of order m satisfying AiAj=J, i,jє{1,...,s} AtiAj=AtjAi=J, i≠j, i,jє{1,...,s} ∑(AiAti + ATiAi) = 2smIm JAi = AiJ = aJ, i є {1,....,s}, a constant Call A1,.....,As 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 matrices and conference matrices obtained via Mathon's construction". Graphs and Combinatorics. 4(1988), 355-377. In this paper, we prove that (i) if there exist a regular s-set of order …
Relative Compromise Of Statistical Databases, M Miller, Jennifer Seberry
Relative Compromise Of Statistical Databases, M Miller, Jennifer Seberry
Professor Jennifer Seberry
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 …
Generalized Bhaskar Rao Designs With Elements From Cyclic Groups Of Even Order, Andrew Bowler, Kathleen Quinn, Jennifer Seberry
Generalized Bhaskar Rao Designs With Elements From Cyclic Groups Of Even Order, Andrew Bowler, Kathleen Quinn, Jennifer Seberry
Professor Jennifer Seberry
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
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Joseph Hammer, Jennifer Seberry
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Joseph Hammer, Jennifer Seberry
Professor Jennifer Seberry
When n2 elements are given they can be arranged in the form of a square, similarly when ng elements (g ≥ 3 an integer) are given they can be arranged in the form of a g-dimensional cube of side n (in short a g-cube). The position of the elements can be indicated by g suffixes.