Sheelagh Lloyd

Counting functions satisfying a higher order strict avalanche criterion

The strict avalanche criterion was introduced by Webster and Tavares [3] in order to combine the ideas of completeness and the avalanche effect. A cryptographic transformation is complete if each output bit depends on all the input bits, and it exhibits the avalanche effect if an average of one half of the output bits change whenever a single input bit is complemented. To fulfil the strict avalanche criterion, each output bit should change with probability one half whenever a single input bit is complemented. This means, in particular, that there is no good lower order (fewer bits) approximation to the function. This is clearly a desirable cryptographic property since such an approximation would enable a corresponding reduction in the amount of work needed for an exhaustive search.

Counting binary functions with certain cryptographic properties

This paper investigates the connections between three properties of a binary function. These properties are important in cryptography and are the Strict Avalanche Criterion, balance, and correlation immunity. We derive necessary and sufficient conditions for a function to possess various combinations of these properties, and count the number of such functions.

A note on the nonexistence of Barker sequences

A Barker sequence is a sequence with elements ±1 such that all out-of-phase aperiodic autocorrelation coefficients are 0, 1 or -1. It is known that if a Barker sequence of length s > 13 exists then s = 4N2 for some odd integer N ≥ 55, and it has long been conjectured that no such sequence exists. We review some previous attempts to improve the bound on N which, unfortunately, contain errors. We show that a recent theorem of Eliahou et al. [5] rules out all but six values of N less than 5000, the smallest of which is 689.

Balance, uncorrelatedness and the strict avalanche criterion

Abstract A number of criteria have been proposed in the literature for cryptographic transformations. We explore here the connections between three of these: balance, uncorrelatedness and the strict avalanche criterion. Our main result is that there are no balanced, uncorrelated functions which satisfy the strict avalanche criterion of order n − 2.

Properties of binary functions

In this paper, we shall investigate the connections between three properties of a binary function: the Strict Avalanche Criterion, balance and correlation immunity. The strict avalanche criterion was introduced by Webster and Tavares [7] in order to combine the ideas of completeness and the avalanche effect. A cryptographic transformation is said to be complete if each output bit depends on each input bit, and it exhibits the avalanche effect if an average of one half of the output bits change whenever a single input bit is changed. Forre [1] extended this notion by defining higher order Strict Avalanche Criteria. A function is balanced if, when all input vectors are equally likely, then all output vectors are equally likely. This is an important property for many types of cryptographic functions. The idea of correlation immunity is also extremely important, especially in the field of stream ciphers, where combining functions which are not correlation immune are vulnerable to ciphertext only attacks (see, for example [4]). The concept of mth order correlation immunity was introduced by Siegenthaler [5] as a measure of resistance against such an attack.

Barker arrays II: odd number of elements

A Barker array is a two-dimensional array with elements

Position-sensing apparatus

\pm 1

Initial track recovery in position-sensing systems that use windowing patterns

such that all out-of-phase aperiodic autocorrelation coefficients are

Finding the Position of a Subarray in a Pseudo-random Array

0,1

Appareil de detection de position

, or