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- Keyword
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- Construction (7)
- Orthogonal designs (6)
- Hadamard matrices (5)
- Sequences (5)
- AMS Subject Classification: Primary 05B15 (4)
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- AMS Subject Classification: Primary 05B20 (4)
- Autocorrelation (4)
- Orthogonal design (4)
- 15A15 (3)
- Algorithm (3)
- Amicable sets (3)
- Circulant matrices (3)
- Complete pivoting (3)
- Gaussian elimination (3)
- Goethals-Seidel array (3)
- Minors (3)
- SBIBD (3)
- Secondary 62K05. (2)
- 05B20 (2)
- 15A36. (2)
- 62K10 (2)
- Amicable set of matrices (2)
- Batch Verification (2)
- D-optimal designs (2)
- Digital Signatures (2)
- Generalized Bhaskar Rao design (2)
- Growth (2)
- Hadamard matrix (2)
- Key escrow (2)
- Secondary 62K05 (2)
Articles 1 - 30 of 62
Full-Text Articles in Physical Sciences and Mathematics
New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We give new sets of sequences with entries from {0, ±a, ±b, ±c} on the commuting variables a, b, c and zero autocorrelation function. Then we use these sequences to construct some new orthogonal de-signs. We show the necessary conditions for the existence of an OD(28; s1, s2, s3) plus the condition that (s1, s2, s3) ≠ (1,5,20) are sufficient conditions for the existence of an OD(28; s1, s2, s3). We also show the necessary conditions for the existence of an OD(28; s1, s2, s3) constructed using four circulant matrices are sufficient conditions for the existence of 4 — NPAF(s1, …
Orthogonal Designs Of Kharaghani Type: Ii, C. Koukouvinos, Jennifer Seberry
Orthogonal Designs Of Kharaghani Type: Ii, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
H. Kharaghani, in "Arrays for orthogonal designs", J. Combin. Designs, 8 (2000), 166-173, showed how to use amicable sets of matrices to construct orthogonal designs in orders divisible by eight. We show how amicable orthogonal designs can be used to make amicable sets and so obtain infinite families of orthogonal designs in six variables in orders divisible by eight.
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We use a new algorithm to find new sets of sequences with entries from {0, ±a, ±b, ±c, ±d}, on the commuting variables a, b, c, d, with zero autocorrelation function. Then we use these sequences to construct a series of new three and four variable orthogonal designs in order 36. We show that the necessary conditions plus (.s1, s2, s3, s4) not equal to 12816 18 816 221313 26721 36 816 4889 12825 191313 23 424 289 9 381015 8899 14425 22 916 are sufficient for the existence of an OD(36; s1, s2 s3, s4) constructed using four circulant …
Hadamard Ideals And Hadamard Matrices With Circulant Core, I. S. Kotsireas, C. Koukouvinos, Jennifer Seberry
Hadamard Ideals And Hadamard Matrices With Circulant Core, I. S. Kotsireas, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
Computational Algebra methods have been used successfully in various problems in many fields of Mathematics. Computational Algebra encompasses a set of powerful algorithms for studying ideals in polynomial rings and solving systems of nonlinear polynomial equations efficiently. The theory of Grobner bases is a cornerstone of Computational Algebra, since it provides us with a constructive way of computing a kind of a particular basis of an ideal which enjoys some important properties. In this paper we introduce the concept of Hadamard ideals in order to establish a new approach to the construction of Hadamard matrices with circulant core. Hadamard ideals …
On Amicable Orthogonal Designs Of Order 8, Y. Zhao, Y. Wang, Jennifer Seberry
On Amicable Orthogonal Designs Of Order 8, Y. Zhao, Y. Wang, Jennifer Seberry
Professor Jennifer Seberry
Some new amicable orthogonal designs of order 8 are found as part of a complete search of the equivalence classes for orthogonal designs OD(8; 1,1,1,1), OD(8; 1,1,1,4), OD(8; 1,1,2,2), OD(8; 1,1,1,2), OD (8; 1,1,2,4), OD(8; 1,1,1,3), OD(8; 1,1,2,3), OD(8; 1,1,1,5) and OD(8; 1,1,3,3).
A Cryptographic Solution For General Access Control, Y. Kong, Jennifer Seberry, J. R. Getta, Ping Yu
A Cryptographic Solution For General Access Control, Y. Kong, Jennifer Seberry, J. R. Getta, Ping Yu
Professor Jennifer Seberry
As one of the most popular information safeguarding mechanisms, access control is widely deployed in information systems. However, access control approach suffers from a tough problem, i.e. system administrators must be unconditionally trusted. Cryptographic substitutes have been developed to solve the above problem. In particular, hierarchical encryption, as an alternate solution of access control in a hierarchy, has been intensively studied. In this paper, we propose a cryptographic solution for general access control based on Chinese Remainder Theorem. Our solution has two categories: data based solution and key based solution. In contrast to the most recent hierarchical encryption system: Ray, …
Equitability In Retroactive Data Confiscation Versus Proactive Key Escrow, Y. Desmedt, M. Burmester, Jennifer Seberry
Equitability In Retroactive Data Confiscation Versus Proactive Key Escrow, Y. Desmedt, M. Burmester, Jennifer Seberry
Professor Jennifer Seberry
The British Regulations of Investigatory Powers (RIP) Act 2000 is one of the first modern bills for mandatory disclosure of protected data in a democratic country. In this paper we compare this bill from a technical point of view with the US key escrow proposal (EES) and its variants and then, more generally we compare the merits of key confiscation vs key escrow. A major problem with key escrow is that once a private key is recovered it can be used to decipher ciphertexts which were sent well before a war-rant was issued (or after its expiration). Several alternative key …
On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
In this paper we give a general theorem which can be used to multiply the length of amicable sequences keeping the amicability property and the type of the sequences. As a consequence we have that if there exist two, four or eight amicable sequences of length m and type (al, a2), (al, a2, a3, a4) or (al, a2, ... , a8) then there exist amicable sequences of length ℓ ≡ 0 (mod m) and of the same type. We also present a theorem that produces a set of 2v amicable sequences from a set of v (not necessary amicable) sequences …
Values Of Minors Of An Infinite Family Of D-Optimal Designs And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Values Of Minors Of An Infinite Family Of D-Optimal Designs 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 2v — j minors, j = 0, 1, 2 of D-optimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of either two SBIBD(2s2 + 2s + 1, s2, s2-s/2) or 2 — {2s2 + 2s + 1; s2, s2; s(s–1)} sds. This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growth greater than 2(2s2 + 2s + 1) but experimentation has not …
Crypto Topics And Applications Ii, Jennifer Seberry, C. Charnes, J. Pieprzyk, R. Safavi-Naini
Crypto Topics And Applications Ii, Jennifer Seberry, C. Charnes, J. Pieprzyk, R. Safavi-Naini
Professor Jennifer Seberry
In this chapter we continue our exposition of the crypto topics which was begun in the previous chapter. This chapter covers: Secret Sharing, Threshold Cryptography, Signature Schemes, and finally Quantum Key Distribution and Quantum Cryptography. As in the previous chapter, we have focused only on the essentials of each topic. We have included in the bibliography sufficient items which can be consulted for further details.
On A Use Of Golay Sequences For Asynchronous Ds Cdma Applications, Jennifer Seberry, Beata J. Wysocki, Tadeusz A. Wysocki
On A Use Of Golay Sequences For Asynchronous Ds Cdma Applications, Jennifer Seberry, Beata J. Wysocki, Tadeusz A. Wysocki
Professor Jennifer Seberry
Golay complementary sequences, often referred to as Golay pairs, are characterised by the property that the sum of their aperiodic autocorrelation functions equals to zero, except for the zero shift. Because of this property, Golay complementary sequences can be utilised to construct Hadamard matrices defining sets of orthogonal spreading sequences for DS CDMA systems of the lengths not necessary being a power of 2. In the paper, we present an evaluation, from the viewpoint of asynchronous DS CDMA applications, of some sets of spreading sequences derived from Golay complementary sequences. We then modify those sets of sequences to enhance their …
New D-Optimal Designs Of Order 110, R. J. Fletcher, Jennifer Seberry
New D-Optimal Designs Of Order 110, R. J. Fletcher, Jennifer Seberry
Professor Jennifer Seberry
We give two new D-optimal designs of order 110.
An Infinite Family Of Goethals-Seidel Arrays, M. Xia, Tianbing Xia, Jennifer Seberry
An Infinite Family Of Goethals-Seidel Arrays, M. Xia, Tianbing Xia, Jennifer Seberry
Professor Jennifer Seberry
In this paper we construct an infinite family of Goethals-Seidel arrays and prove the theorem: If q = 4n - 1 is a prime power = 3(mod 8), then there exists an Hadamard matrix of order 4n of Goethals-Seidel type
Inequivalence Of Nega-Cyclic ±1 Matrices, R. Ang, Jennifer Seberry, Tadeusz A. Wysocki
Inequivalence Of Nega-Cyclic ±1 Matrices, R. Ang, Jennifer Seberry, Tadeusz A. Wysocki
Professor Jennifer Seberry
We study nega-cyclic ±1 matrices. We obtain preliminary results which are then used to decrease the search space. We find that there are 2, 4, 9, 23, 63, and 187 ip-equivalence classes for lengths 3, 5, 7, 9, 11, and 13 respectively. The matrices we find are used in a variant given here of the Goethals-Seidel array to form Hadamard matrices, the aim being to later check them for suitability for CDMA schemes.
On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We find new full orthogonal designs in order 56 and show that of 1285 possible OD(56; s1, s2, s3, 56—s1—s2-s3) 163 are known, of 261 possible OD(56; s1, s2, 56—s1—s2) 179 are known. All possible OD(56; s1, 56 — s1) are known.
Crypto Topics And Applications I, Jennifer Seberry, C. Charnes, J. Pieprzyk, R. Safavi-Naini
Crypto Topics And Applications I, Jennifer Seberry, C. Charnes, J. Pieprzyk, R. Safavi-Naini
Professor Jennifer Seberry
In this chapter we discuss four related areas of cryptology, namely: Authentication, Hashing, Message Authentication Codes (MACs), and Digital Signatures. These topics represent currently active and growing research topics in cryptology. Due to space limitations, we concentrate only on the essential aspects of each topic. The bibliography is intended to supplement our survey. We have included sufficiently many items to provide the interested reader with an overall view of the current state of knowledge in the above areas.
Strongbox Secured Secret Sharing Schemes, Jennifer Seberry, A. Penfold Street
Strongbox Secured Secret Sharing Schemes, Jennifer Seberry, A. Penfold Street
Professor Jennifer Seberry
We present one way in which combinatorial designs can be used to give conditionally perfect secret sharing schemes. Schemes formed in this way have the advantage over classical secret sharing schemes of being easily adapted for use as compartmentalized or hierarchical access structures. We study the problem of completion of structures, given partial information, to obtain measures of how closely the behaviour of the secret sharing schemes approaches to ideal behaviour in practice. It may happen that part of a combinatorial design can never be reconstructed from a subset of a minimal defining set. That is, to find the blocks …
The Theory Of Quaternion Orthogonal Designs, Jennifer Seberry, K. Finlayson, S. Spense Adams, Tadeusz A. Wysocki, Tianbing Xia, Beata J. Wysocki
The Theory Of Quaternion Orthogonal Designs, Jennifer Seberry, K. Finlayson, S. Spense Adams, Tadeusz A. Wysocki, Tianbing Xia, Beata J. Wysocki
Professor Jennifer Seberry
Over the past several years, there has been a renewed interest in complex orthogonal designs for their application in space-time block coding. Motivated by the success of this application, this paper generalizes the definition of complex orthogonal designs by introducing orthogonal designs over the quaternion domain. This paper builds a theory of these novel quaternion orthogonal designs, offers examples, and provides several construction techniques. These theoretical results, along with the results of preliminary simulations, lay the foundation for developing applications of these designs as orthogonal space-time-polarization block codes.
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
Call four type 1(1,-1) matrices, x1,x2,x3,x4; of the same group of order m (odd) with the properties (i) (Xi-I)T = -(Xi-I), i=1,2,3, (ii)XT4 = X4 and the diagonal elements are positive, (iii) XiXj = XjXi and (iv) X1XT1 + X2XT2+X3XT3 +X4XT4 = 4mIm, best matrices. We use a computer to give, for the first time, all inequivalent best matrices of odd order m ≤31. Inequivalent best matrices of order m, m odd, can be used to find inequivalent skew-Hadamard matrices of order 4m. We use best matrices of order 1/4(s2+3) to construct new orthogonal designs, including new OD(2s2+6;1,1,2,2,s2,s2).
Hadamard Matrices, Orthogonal Designs And Construction Algorithms, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Hadamard Matrices, Orthogonal Designs And Construction Algorithms, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction. Next we move to algorithms to determine the equivalence of Hadamard matrices using the profile and projections of Hadamard matrices. A summary is then given which considers inequivalence of Hadamard matrices of orders up to 44. The final two sections give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.
A New Cryptanalytic Method Using The Distribution Characteristics Of Substitution Distances, B. Song, H. Wang, Jennifer Seberry
A New Cryptanalytic Method Using The Distribution Characteristics Of Substitution Distances, B. Song, H. Wang, Jennifer Seberry
Professor Jennifer Seberry
In this paper, we suggest a new method for cryptanalysis of the basic structures of the block ciphers having SP network structure. The concept of the substitution difference is introduced and the distribution characteristics of substitution distances in an S-box is developed. This gives clues for cryptanalysis of the cipher. We then examine if this method is applicable to cryptanalysis of Rijndael. We present the method for cryptanalysis of the first round of Rijndael including the initial Round-Key addition part in order to illustrate our new method.
On The Spectrum Of An F-Square, L. Fitina, Jennifer Seberry
On The Spectrum Of An F-Square, L. Fitina, Jennifer Seberry
Professor Jennifer Seberry
Given an F-square of some type F(n; αo, αl, ..., αv-1) what critical set sizes can we obtain for this type? Such a question was considered by Donovan and Howse (1999), in the case of Latin squares. In this note we solve this question for the type F(n;1,n – 1), and also obtain partial results for type F(n; 2,n – 2).
Orthogonal Designs From Negacyclic Matrices, K. Finlayson, Jennifer Seberry
Orthogonal Designs From Negacyclic Matrices, K. Finlayson, Jennifer Seberry
Professor Jennifer Seberry
We study the use of negacyclic matrices to form orthogonal designs and hence Hadamard matrices. We give results for all possible tuple for order 12, all but 3 for order 20 and all but 3 for order 28.
A New Method For Constructing T-Matrices, M. Xia, Tianbing Xia, Jennifer Seberry, G. Zuo
A New Method For Constructing T-Matrices, M. Xia, Tianbing Xia, Jennifer Seberry, G. Zuo
Professor Jennifer Seberry
For every prime power q = 3 (mod 8) we prove the existence of (q; x, 0, y, y)-partitions of GF(q) with q = x2 + 2y2 for some x, y, which are very useful for constructing SDS, T-matrices and Hadamard matrices. We discuss the transformations of (q; x, 0, y, y)-partitions and, by using the partitions, construct generalized cyclotomic classes which have properties similar to those of classical cyclotomic classes. Thus we provide a new construction for T-matrices of order q2.
On The Internal Structure Of Alpha-Mac, J. Huang, Jennifer Seberry, Willy Susilo
On The Internal Structure Of Alpha-Mac, J. Huang, Jennifer Seberry, Willy Susilo
Professor Jennifer Seberry
ALPHA-MAC is a MAC function which uses the building blocks of AES. This paper studies the internal structure of this new design. First, we provide a method to find second preimages based on the assumption that a key or an intermediate value is known. The proposed searching algorithm exploits the algebraic properties of the underlying block cipher and needs to solve eight groups of linear functions to find a second preimage. Second, we show that our idea can also be used to find internal collisions under the same assumption. We do not make any claims that those findings in any …
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.
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
The book, Orthogonal Designs: Quadratic Forms and Hadamard Matrices, Marcel Dekker, New York-Basel, 1979, by A. V. Geramita and Jennifer Seberry, has now been out of print for almost two decades. Many of the results on weighing matrices presented therein have been greatly improved. Here we review the theory, restate some results which are no longer available and expand on the existence of many new weighing matrices and orthogonal designs of order 2n where n is odd. We give a number of new constructions for orthogonal designs. Then using number theory, linear algebra and computer searches we find new weighing …
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 remains 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.
Combinatorial Structures For Design Of Wireless Sensor Networks, Dibyendu Chakrabarti, Jennifer Seberry
Combinatorial Structures For Design Of Wireless Sensor Networks, Dibyendu Chakrabarti, Jennifer Seberry
Professor Jennifer Seberry
Combinatorial designs are very effective tools for managing keys in an infrastructure where power and memory are two major constraints. None of the present day wireless technologies takes the advantage of combinatorial designs. In this paper, we have proposed a general framework using combinatorial designs which will enable the participating devices to communicate securely among themselves with little memory and power overhead. The scheme caters for different kinds of user requirements and allows the designer to choose different combinatorial designs for different parts or levels of the network. This general framework will find application in all wireless radio technologies, typically …
On The (10, 5, Λ)-Family Of Bhaskar Rao Designs, G. Chaudhry, Jennifer Seberry
On The (10, 5, Λ)-Family Of Bhaskar Rao Designs, G. Chaudhry, Jennifer Seberry
Professor Jennifer Seberry
We prove a theorem for BRD(10,5,Lambda)s and give thirteen (13) inequivalent BRD(10,5,4)s.