Combinatorial Designs and Cryptography, Revisited (original) (raw)

Encryption methods based on combinatorial designs

1986

We explore the use of some combinatorial designs for possible use as secret codes. We are motivated to use designs as (1) combinatorial designs are often hard to find, (2) the algorithms for encryption ond decryption are of reasonable length, (3) combinatorial designs have very large numbers of designs in each equivalence class lending themselves readily to selection using a secret key. Disciplines Physical Sciences and Mathematics Publication Details Sarvate, DG and Seberry, J, Encryption methods based on combinatorial designs Ars Combinatoria, 21A, 1986, 237-246. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1019 Encryption Methods Bllsed on Combinlltorilll Designs Dinesh G. Sarvate and Jennifer Seberry Ba3:ser Department of COmputer Sciera , UnlYe"Hy of Sydney NSW,2006, Australia.

The combinatorics of cryptographic key establishment

One of the most important processes involved in securing a cryptographic system is establishing the keys on which the system will rely. In this article we review the significant contribution of combinatorial mathematics to the development of the theory of cryptographic key establishment. We will describe relevant applications, review current research and, where appropriate, identify areas where further research is required.

Some Applications of Bounds for Designs to the Cryptography

Lecture Notes in Computer Science, 1999

Recent years have seen numerous examples when designs play an important role in the study of such topics in cryptography as secrecy and authen- tication codes, secret sharing schemes, correlation-immune and resilient functions. In this paper we give applications of some methods and results from the design theory, especially bounding the optimal size of the designs and codes, to cryptography.

Constructions, Lower Bounds, and New Directions in Cryptography and Computational Complexity

In the first part of the thesis we show black-box separations in public and private-key cryptography. Our main result answers in the negative the question of whether we can base Identity Based Encryption (IBE) on Trapdoor Permutations. Furthermore, we make progress towards the black-box separation of IBE from the Decisional Diffie-Hellman assumption. We also show It is a great privilege to study Theory at the University of Toronto. I was also privileged to have an incredible advisor and PhD committee. I'm most thankful to Charles Rackoff for his invaluable research supervision, countless discussions, very close attention to my work, and insightful comments. In addition, Charlie is among the most open and liberal-minded individuals I have met in academia, which made this process more interesting. I'm also grateful to the other members of my committee Allan Borodin, Stephen Cook, and Toniann Pitassi for always been there with useful remarks, research suggestions, and encouragement. Many thanks to my external thesis reviewer Eric Allender for his detailed remarks and suggestions.

SPECIAL ISSUE ON INFORMATION THEORETIC SECURITY

THIS special issue of the IEEE TRANSACTIONS ON INFORMATION THEORY is devoted to the exciting research field of Information Theoretic Security. Cryptographic systems that are currently employed in practice are predominantly based on unproven mathematical assumptions such as the assumed infeasibility of factoring large integers and finding discrete logarithms over large finite fields.

Randomness and Secrecy - A Brief Introduction

J Ucs, 2006

We give a brief introduction to probabilistic encryptions. This serves as an example how randomness plays a pivotal role in cryptographic systems that satisfy advanced security concepts.

Combinatorial Optimization in Cryptography

The known attacks on different cryptosystems lead to a number of criteria that the implemented cryptographic algorithms (ciphers) must satisfy. The design of cryptographic systems needs to consider various characteristics simultaneously, which can be regarded as a multi-objective combinatorial optimization problem. Evolutionary computation present a range of problem-solving techniques based on the principles of biological evolution. Evolutionary algorithms can quickly offer satisfactory solution to combinatorial optimization problems. Evolutionary computation can be also used in evolving pseudorandom number generators which play important role as a countermeasure against side channel attacks. The purpose of this paper is to give a state-of-the-art overview of the evolutionary computation area in symmetric and asymmetric cryptography, as well as for the evolving pseudorandom number generators. In symmetric cryptosystem, one of the important components is the substitution box which can be successfully built by evolutionary algorithm. In asymmetric cryptosystem, evolutionary algorithms can be used to speed-up some discrete mathematic operations, like modular exponentiation.