David R. Canright

A very compact s-box for AES

A key step in the Advanced Encryption Standard (AES) algorithm is the “S-box.” Many implementations of AES have been proposed, for various goals, that effect the S-box in various ways. In particular, the most compact implementations to date of Satoh et al.[14] and Mentens et al.[6] perform the 8-bit Galois field inversion of the S-box using subfields of 4 bits and of 2 bits. Our work refines this approach to achieve a more compact S-box. We examined many choices of basis for each subfield, not only polynomial bases as in previous work, but also normal bases, giving 432 cases. The isomorphism bit matrices are fully optimized, improving on the “greedy algorithm.” Introducing some NOR gates gives further savings. The best case improves on [14] by 20%. This decreased size could help for area-limited hardware implementations, e.g., smart cards, and to allow more copies of the S-box for parallelism and/or pipelining of AES.

Fast software AES encryption

This paper presents new software speed records for AES-128 encryption for architectures at both ends of the performance spectrum. On the one side we target the low-end 8-bit AVR microcontrollers and 32-bit ARM microprocessors, while on the other side of the spectrum we consider the high-performing Cell broadband engine and NVIDIA graphics processing units (GPUs). Platform specific techniques are detailed, explaining how the software speed records on these architectures are obtained. Additionally, this paper presents the first AES decryption implementation for GPU architectures.

Buoyant Instability of a Viscous Film Over a Passive Fluid

The article of record as published may be located at http://dx.doi.org/10.1017/S0022112093002514

Thermocapillary Flow Near a Cold Wall

The thermocapillary feedback mechanism important at the edge of weld pools and other materials processes is examined through a model problem. A pool of liquid with a flat horizontal free surface is bounded on one side by a vertical solid wall, which is maintained at a cold temperature to unit depth, and at a warmer temperature below; far away the fluid is at the warmer temperature. Surface tension is a decreasing function of temperature, so that the surface thermal gradient drives flow toward the corner. When convection is vigorous, the flow compresses the thermal gradient which is driving the flow; this positive feedback results in small local length scales and high velocities near the corner. This problem is examined through a detailed scaling analysis and through numerical simulation for a range of parameters. The results show that for vigorous convection, the flow in the cold corner is locally determined.

A More Compact AES

We explore ways to reduce the number of bit operations required to implement AES. One way involves optimizing the composite field approach for entire rounds of AES. Another way is integrating the Galois multiplications of MixColumns with the linear transformations of the S-box. Combined with careful optimizations, these reduce the number of bit operations to encrypt one block by 9.0%, compared to earlier work that used the composite field only in the S-box. For decryption, the improvement is 13.5%. This work may be useful both as a starting point for a bit-sliced software implementation, where reducing operations increases speed, and also for hardware with limited resources.

Estimating the spatial extent of attractors of Iterated Function Systems

Abstract From any given Iterated Function System, a small set of balls that cover the fractal attractor can be simply determined. This gives a priori bounds on the region of space in which the attractor may be constructed.

Buoyancy effects of a growing, isolated dendrite

An axisymmetric dendrite of pure material solidifies downward into an undercooled melt. Surface energy and kinetic undercooling are negligible. The Ivantsov [Dokl. Akad. Nauk SSSR 58 (1947) 567] parabolic dendrite is modified by buoyant convection. We construct an approximate solution to the growth/convection problem in powers of a buoyancy parameter G. The solution depends on Prandtl number P and Stefan number S (undercooling). When P and/or S are large enough, buoyancy enhances growth and distorts the dendrite by sharpening the tip and widening the base. These results compare well with the experiments on succinonitrile (P = 23) of Huang and Glicksman [Acta Met. 29 (1981) 701] and the local theory of Ananth and Gill [J. Crystal Growth 91 (1988) 587] up to G ≈ 1000, but overpredict convective effects for larger G. When P and S are small enough, buoyancy slows growth and flattens the tip. Physical explanations are given for the differences in buoyant effects at different P. The results suggest that near-tip effects of buoyancy should be different in metallics than in organics.

Circulant matrices and affine equivalence of monomial rotation symmetric Boolean functions

The goal of this paper is two-fold. We first focus on the problem of deciding whether two monomial rotation symmetric (MRS) Boolean functions are affine equivalent via a permutation. Using a correspondence between such functions and circulant matrices, we give a simple necessary and sufficient condition. We connect this problem with the well known Adams conjecture from graph theory. As applications, we reprove easily several main results of Cusick et?al. on the number of equivalence classes under permutations for MRS in prime power dimensions, as well as give a count for the number of classes in p q number of variables, where p , q are prime numbers with? p < q < p 2 . Also, we find a connection between the generalized inverse of a circulant matrix and the invertibility of its generating polynomial over? F 2 , modulo a product of cyclotomic polynomials, thus generalizing a known result on nonsingular circulant matrices.

Acoustic interactions in arrays of spherical elastic shells

The acoustical performance of a submerged linear array of spherical transducers is examined by combining the T‐matrix method of solving for multiple acoustic interactions among separate bodies with a model for transducers as thin spherical elastic shells. This approach solves the fully coupled problem of the response of the array to internal forcing. The results show that the assumptions giving rise to the Chebyshev criteria for optimal arrays of point sources appear to apply well even for large spheres at low frequencies. However, at frequencies near or above the lowest resonant frequency, the directional pattern may be degraded, depending on the material of the shells.

Laced Boolean functions and subset sum problems in finite fields

In this paper, we investigate some algebraic and combinatorial properties of a special Boolean function on n variables, defined using weighted sums in the residue ring modulo the least prime p>=n. We also give further evidence relating to a question raised by Shparlinski regarding this function, by computing accurately the Boolean sensitivity, thus settling the question for prime number values p=n. Finally, we propose a generalization of these functions, which we call laced functions, and compute the weight of one such, for every value of n.