CONTENTS - Emerald

041531 `The Cryptographic Mathematics of Enigma'
AR Miller, Cryptologia v XIX no 1 (Jan 95) pp 65{80
The author describes the Enigma and calculates the e ective key diversity of a
number of con gurations.
041532 `New c-ary perfect factors in the de Bruijn graph'
CJ Mitchell, Cirencester 93 pp 299{313
A perfect factor is a set of cycles whose elements are drawn from some set and such
that each n-tuple occurred exactly once | a generalisation of a de Bruijn sequence.
These are further generalised by the author to structures which contain each tuple
within a given segment of one of the sequences; some constructions are given, and this
provides some perfect factors of previously unknown size.
041533 `Aperiodic and Semi-Periodic Perfect Maps'
CJ Mitchell, IEEE Transactions on Information Theory v 41 no 1 (Jan 95) pp 88{95
The author constructs aperiodic and semi-periodic perfect maps for all possible
parameter sets, and thus shows that they exist even where periodic ones do not.
041534 `A study on the security of RDES-1 cryptosystem against linear
cryptanalysis'
Y Nakao, T Kaneko, K Koyama, R Terada, JW-ISC 95 pp 163{172
RDES-1 is avariant ofDES in which a probabilistic swapping function is added
onto the right half of the input to each round. It is shown to be more secure than DES
against linear cryptanalysis.
041535 `On a new factorisation algorithm for polynomials over nite elds'
H Niederreiter, R Gottfert, Mathematics of Computation v 64 no 209 (Jan 95) pp 347{
353
The rst author's polynomial factorisation algorithm was improved by the second
for the case of characteristic two. They now join forces to optimise it for arbitrary
positive characteristic.
041536 `Provable Security Against a Di erential Attack'
K Nyberg, LR Knudsen, Journal of Cryptology v 8 no 1 (1995) pp 27{37
The authors prove lower bounds on the di erentials of block cipher round functions
given by quadratic permutations, and exhibit one of the form x 2k +1 for which the
maximum probability is2 3,n ,where n is the block size. They also show bounds on
multiround probabilities. Finally, they suggest using x 3 in GF (2 33 ), with one output
coordinate discarded, as a round function. With six rounds, and 198 independent key
bits, this should have a maximum di erential probability of2 ,61 .
041537 `An upper bound on the number of functions satisfying the strict
avalanche criterion'
L O'Connor, Information Processing Letters v 52 no 6 (23/12/94) pp 325{327
The author de nes S(n; k) as the number of Boolean functions on n variables which
are 50% dependent onany subset of k variables. He provides closed form expressions
for S(n; 1) and S(n; 2), and an inequality between S(n; k) and the number of functions
satisfying a strict avalanche criterion of order k.
041538 `A Uni ed Markov Approach to Di erential and Linear Cryptanalysis'
L O'Connor, JD Golic, Asiacrypt 94 pp 328{338
This paper introduces Markov methods to linear cryptanalysis, as Lai, Massey and
Murphy did for di erential cryptanalysis. Based on results in random graph theory,
it is shown that if the round function of an iterated block cipher is a random function,
both Markov chains converge to the uniform distribution with high probability
under the assumption that the rounds are independent uniformly distributed random
variables.
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