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Recently, several algorithms using number field sieves have been given to factor a number n in heuristic expected time Ln[1/3; c], wherefor n → ∞. In this paper we present an algorithm to solve the discrete logarithm problem for GF (p) with heuristic expected running time Lp[1/3; 3 2/3 ]. For numbers of a special form, there is an asymptotically slower but more practical version of the algorithm.

In several crypt,ographic systems, a fixed elcment g of a group (generally z / q z) is repeatedly raised to many different powers. In this paper we present a practical method of speeding u p such systems. using precomputed values to reduce the number of multiplications needed. In practice this provides a substantial improvement over the level of performance that can be obtained using addition chains, and allows the computation of g" for n < N in O(1og Nlloglog N) group multiplications. We also show how these methods can he parallelized. t o c o m p u t e powers in O(1og log iV) group multiplications with o(1og iV/ log log .V) processors.

Objective To identify the lifetime prevalence of non-consensual sexual experiences in men, the relationship between such experiences as a child and as an adult, associated psychological and behavioural problems, and help received. Design Cross sectional survey. Setting England. Subjects 2474 men (mean age 46 years) attending one of 18 general practices. Main outcome measures Experiences of non-consensual and consensual sex before and after the age of 16 years-that is, as a child and adult respectively-psychological problems experienced for more than 2 weeks at any one time, use of alcohol (CAGE questionnaire), self harm, and help received. Results 2474 of 3142 men (79%) agreed to participate; 71/2468 (standardised rate 2.89%, 95% confidence interval 2.21% to 3.56%) reported non-consensual sexual experiences as adults, 128/2423 (5.35%, 4.39% to 6.31%) reported non-consensual sexual experiences as children, and 185/2406 (7.66%, 6.54% to 8.77%) reported consensual sexual experiences as children that are illegal under English law. Independent predictors of non-consensual sex as adults were reporting male sexual partners (odds ratio 6.0, 2.6 to 13.5), non-consensual sex in childhood (4.2, 2.1 to 8.6), age (0.98, 0.96 to 0.99), and sex of interviewer (2.0, 1.2 to 3.5). Non-consensual sexual experiences were associated with a greater prevalence of psychological problems, alcohol misuse, and self harm. These sexual experiences were also significant predictors of help received from mental health professionals. Conclusion Almost 3% of men in England report non-consensual sexual experiences as adults. Medical professionals need to be aware of the range of psychological difficulties in men who have had such experiences. They also need to be aware of the relationship between sexual experiences in childhood and adulthood in men.

A (v, k, t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering's size, and the minimum size of such a covering is denoted by C(v, k, t). This paper gives three new methods for constructing good coverings: a greedy algorithm similar to Conway and Sloane's algorithm for lexicographic codes [6], and two methods that synthesize new coverings from preexisting ones. Using these new methods, together with results in the literature, we build tables of upper bounds on C(v, k, t) for v ≤ 32, k ≤ 16, and t ≤ 8.

In the 47 years since fluctuation analysis was introduced by Luria and Delbrück, it has been widely used to calculate mutation rates. Up to now, in spite of the importance of such calculations, the probability distribution of the number of mutants that will appear in a fluctuation experiment has been known only under the restrictive, and possibly unrealistic, assumptions: (1) that the mutation rate is exactly proportional to the growth rate and (2) that all mutants grow at a rate that is a constant multiple of the growth rate of the original cells. In this paper, we approach the distribution of the number of mutants from a new point of view that will enable researchers to calculate the distribution to be expected using assumptions that they believe to be closer to biological reality. The new idea is to classify mutations according to the number of observable mutants that derive from the mutation when the culture is selectively plated. This approach also simplifies the calculations in situations where two, or many, kinds of mutation may occur in a single culture.

Let pc(d) be the critical probability for percolation in Zd. It is shown that limd→∞ 2dpc(d) = 1. The proof uses the properties of a random subgraph of an m‐ary d‐dimensional cube. If each edge in this cube is included with probability greater than 1/2d(1−3/m), then, for large d, the cube will have a connected component of size cmd for some c > 0. This generalizes a result of Ajtai, Komlós and Szemerédi.

Numerous cryptosystems have been designed to be secure under the assumption that the computation of discrete logarithms is infeasible. This paper reports on an aggressive attempt to discover the size of fields of characteristic two for which the computation of discrete logarithms is feasible. We discover several things that were previously overlooked in the implementation of Coppersmith's algorithm, some positive, and some negative. As a result of this work we have shown that fields as large as GF (2 503 ) can definitely be attacked.