Analysis of the DES and the Design of the LOKI Encryption Scheme
by Lawrence Peter Brown
Abstract
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.
Availability
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