Analysis of the DES and the Design of the LOKI Encryption Scheme

by Lawrence Peter Brown

PhD Thesis,
School of Information Technology & Electrical Engineering,
(formerly the School of Computer Science)
UNSW@ADFA, Canberra, Australia


This thesis will analyse some existing encryption algorithms used to provide secrecy in communications and data storage, and will detail the development of a new private key algorithm. It starts with a brief survey of modern encyption algorithms and their uses. It then takes a closer look at the RSA public key algorithm, with particular reference to its practical implementation. It shows that whilst RSA has some very desirable properties for use in public networks in that keys need not be exchanged previously, limitations in implementation speeds mean that RSA alone is not sufficient. Consequently a hybrid scheme is required which combines a public key scheme for authentication and key exchange, with a private key scheme for privacy. At present the DES algorithm is the sole certified private key scheme. It has been extensively analysed for possible weaknesses since its adoption in 1977. It is generally agreed that whilst the structure is sound, its key size of 56-bits has become too small with the improvements in computational speed on modern computers. Whilst the DES algorithm is public, its design criteria are classified. This thesis examines the design of the DES data encryption algorithm and related schemes, particularly with reference to the fundamental avalanche and completeness properties. From this is developed some possible design criteria for such schemes. Using these criteria, along with insights based on generic substitution-permutation cipher construction, suggestions and support from the authors colleagues, and with some results on substitution box design by Pieprzyk and Seberry, a new group of private key schemes, the LOKI family, is designed and presented as the major achievement of this thesis.


The full text of my thesis is now available as a compressed postscript file (326 kb) (sans figures as these were added manually); or as a formatted ascii text (nroff output) file (459 kb) (sans figures and with mangled equations).

Dr Lawrie Brown / 14 May 97