Physical Sciences and Mathematics Commons^™

Nonlinearity And Propagation Characteristics Of Balanced Boolean Functions, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng

Faculty of Informatics - Papers (Archive)

Three of the most important criteria for cryptographically strong Boolean functions are the balancedness, the nonlinearity and the propagation criterion. The main contribution of this paper is to reveal a number of interesting properties of balancedness and nonlinearity, and to study systematic methods for constructing Boolean functions satisfying some or all of the three criteria. We show that concatenating, splitting, modifying and multiplying (in the sense of Kronecker) sequences can yield balanced Boolean functions with a very high nonlinearity. In particular, we show that balanced Boolean functions obtained by modifying and multiplying sequences achieve a nonlinearity higher than that attainable …

Authentication Via Multi-Service Tickets In The Kuperee Server, Thomas Hardjono, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

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 …

Beacon Based Authentication, Azad Jiwa, Jennifer Seberry, Yuliang Zheng

Faculty of Informatics - Papers (Archive)

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 …

Channel-Optimized Vector Trellis Source Coding For The Awgn Channel, Philip Secker, Philip Ogunbona

Faculty of Informatics - Papers (Archive)

A channel-optimised (joint source and channel) trellis source coder is designed for the AWGN channel. The optimum decoder is a non-linear function of the real channel information. The extension to 2D vector alphabets coupled with modifications to the signal space are found to improve performance. Favourable comparisons are made against a trellis source coder/TCM system.

Methods Of Channel-Optimised Trellis Source Coding For The Awgn Channel, Philip Secker, Philip Ogunbona

Faculty of Informatics - Papers (Archive)

Improvements to channel-optimised trellis source coding for the AWGN channel are obtained by using, in various forms, real or ‘soft’ channel information. The proposed 1 bit/sample systems use a channel-optimised encoder matched to 1) a simple decision feedback detector, 2) an expanded codebook with 2-bit quantized information and 3) an optimum non-linear estimator decoder. The third system is further improved by considering vector alphabets and both constant and average energy constrained 2D signal constellations.

Near-Distance Software Engineering Education, F. O'Brien

Faculty of Informatics - Papers (Archive)

The University of Wollongong has been seeking ways by which it can attract capable students from the southern side of the States capital city, Sydney, Australia. The paper describes the concept of limiting the required daily travel to the University through an amalgam of technologies, and changes to the core teaching syllabus. Progress through 1994, and plans for full introduction in 1995, is described.

Improving The Strict Avalanche Characteristics Of Cryptographic Functions, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng

Faculty of Informatics - Papers (Archive)

This paper presents a simple yet effective method for transforming Boolean functions that do not satisfy the strict avalanche criterion (SAC) into ones that satisfy the criterion. Such a method has a wide range of applications in designing cryptographically strong functions, including substitution boxes (S-boxes) employed by common key block encryption algorithm.

Reusing Shares In Secret Sharing Schemes, Yuliang Zheng, Thomas Hardjono, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

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 Construction And Nonlinearity Of Correlation Immune Functions, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng

Faculty of Informatics - Papers (Archive)

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 …

Pitfalls In Designing Substitution Boxes, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng

Faculty of Informatics - Papers (Archive)

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 …

The Vprt - A Sequential Testing Procedure Dominating The Sprt, Noel A. Cressie, Peter Morgan

Faculty of Informatics - Papers (Archive)

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed …

The Excess Of Complex Hadamard Matrices, H. Kharaghani, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

A complex Hadamard matrix, C, of order n has elements 1, -1, i, - i and satisfies CC* = nI_n where C* denotes the conjugate transpose of C. Let C = [c_ij] be a complex Hadamard matrix of order n. S(C) = ∑ c_ij is called the sum of C. 0(C) = │S(C)│ is called the excess of C. We study the excess of complex Hadamard matrices. As an application many real Hadamard matrices of large and maximal excess are obtained.

Some Orthogonal Matrices Constructed By Strong Kronecker Multiplication, Jennifer Seberry, Xian-Mo Zhang

Faculty of Informatics - Papers (Archive)

Strong Kronecker multiplication of two matrices is useful for constructing new orthogonal matrices from those known. These results are particularly important as they allow small matrices to be combined to form larger matrices, but of smaller order than the straight-forward Kronecker product would permit.

On The Multiplication Theorems Of Hadamard Matrices Of Generalized Quaternion Type Using M-Structures, Jennifer Seberry, Mieko Yamada

Faculty of Informatics - Papers (Archive)

We show that M-structures can be extended to Hadamard matrices of generalized quaternion type and obtain multiplication type theorems which preserve the structure.

On G-Matrices, Christos Koukouvinos, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

G-matrices for the new orders 21, 23, 25 and 27 are constructed. Some constructions for Hadamard matrices and orthogonal designs using G-matrices are also presented.

On Weighing Matrices, Christos Koukouvinos, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

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.

Haval - A One-Way Hashing Algorithm With Variable Length Output, Yuliang Zheng, Josef Pieprzyk, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

A one-way hashing algorithm is a deterministic algorithm that compresses an arbitrary long message into a value of specified length. The output value represents the fingerprint or digest of the message. A cryptographically useful property of a one-way hashing algorithm is that it is infeasible to find two distinct messages that have the same fingerprint. This paper proposes a one-way hashing algorithm called HAVAL. HAVAL compresses a message of arbitrary length into a fingerprint of 128, 160, 192, 224 or 256 bits. In addition, HAVAL has a parameter that controls the number of passes a message block (of 1024 bits) …

Highly Nonlinear 0-1 Balanced Boolean Functions Satisfying Strict Avalanche Criterion, Jennifer Seberry, Xian-Mo Zhang

Faculty of Informatics - Papers (Archive)

Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 0- 1 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct

(i) 0-1 balanced boolean functions on V_2k+1 (k ≥ 1) having nonlinearity 2^2k - 2^k and satisfying SAC,

(ii) 0-1 balanced boolean functions on V_2k (k ≥ 2) having nonlinearity 2^2k-1 - 2^k and satisfying SAC.

We demonstrate that the above nonlinearities are very high not …

Improving Resistance To Differential Cryptanalysis And The Redesign Of Loki, Lawrence P. Brown, Matthew Kwan, Joseph Pieprzyk, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Differential Cryptanalysis is currently the most powerful tool available for analysing block ciphers, and new block ciphers need to be designed to resist it. It has been suggested that the use of S-boxes based on bent functions, with a fiat XOR profile, would be immune. However our studies of differential cryptanalysis, particularly applied to the LOKI cipher, have shown that this is not the case. In fact, this results in a relatively easily broken scheme. We show that an XOR profile with carefully placed zeroes is required. "We also show that in order to avoid some variant forms of differential …

Systematic Generation Of Cryptographically Robust S-Boxes, Jennifer Seberry, Xian-Mo Zhang, Yuliang Zheng

Faculty of Informatics - Papers (Archive)

Substitution boxes (S-boxes) are a crucial component of DES-like block ciphers. This research addresses problems with previous approaches towards constructing S-boxes, and proposes a new definition for the robustness of S-boxes to differential cryptanalysis, which is the most powerful cryptanalytic attack known to date. A novel method based on group Hadamard matrices is developed to systematically generate S-boxes that satisfy a number of critical cryptographic properties. Among the properties are the high nonlinearity, the strict avalanche characteristics, the balancedness, the robustness against differential cryptanalysis, and the immunity to linear cryptanalysis. An example is provided to illustrate the S-box generating method.

Constructions Of Balanced Ternary Designs Based On Generalized Bhaskar Rao Designs, Dinesh G. Sarvate, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

New series of balanced ternary designs and partially balanced ternary designs are obtained. Some of the designs in the series are non-isomorphic solutions for design parameters which were previously known or whose solution was obtained by trial and error, rather than by a systematic method.

Some New Weighing Matrices Using Sequences With Zero Autocorrelation Function, Christos Koukouvinos, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We verify the skew weighing matrix conjecture for orders 2^t.13, t ≥ 5, and give new results for 2^t.15 proving the conjecture for t ≥ 3.

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.

The Magnitude And Nature Of 'Noise' In World Sea-Level Records, Edward A. Bryant

Faculty of Science - Papers (Archive)

While average world sea-level is rising at a uniform rate of 1-1.5 mm yr-1, regional rates can vary by an order of magnitude. Over time scales of several years these rates can be 10-100 times greater because sea-level is affected at this scale by highly changeable meteorological and oceanographic variables. The inherent "noise" level in world sea-level records is 35 mm. Much of this is expressed as fluctuations on the order of 20-100 mm with a frequency of 3-5 years. This latter "noise" is highly coherent at tide gauges around the globe and appears unrelated to resonance or wave excitation …

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 …

Last Interglacial And Holocene Trends In Sea-Level Maxima Around Australia: Implications For Modern Rates, Edward A. Bryant

Faculty of Science - Papers (Archive)

This paper defines the spatial trend in sea-level around Australia at 3 timescales, namely at the time of the maximum of the last interglacial around 125000 yr BP, during the Holocene maximum between 5-6000 yr BP and over the last 20 years. Last interglacial elevations range from -2m around the Great Barrier Reef to +32m in northeast Tasmania. Trend surface analysis shows that over 77% of the noise in these sea-level elevations can be accounted for by a pattern evidencing tectonic uplift towards the southern edge of the continent. Assuming a eustatic sea-level at this time of +4 to 6m, …

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.