Stream/block ciphers, difference equations and algebraic attacks

In this paper we introduce a general class of stream and block ciphers that are defined by means of systems of (ordinary) explicit difference equations over a finite field. We call this class "difference ciphers". Many important ciphers such as systems of LFSRs, Trivium/Bivium and Keeloq are difference ciphers. To the purpose of studying their underlying explicit difference systems, we introduce key notions as state transition endomorphisms and show conditions for their invertibility. Reducible and periodic systems are also considered. We then propose general algebraic attacks to difference ciphers which are experimented by means of Bivium and Keeloq.Comment: 22 page

Trivium vs. Trivium Toy

We present the characteristic and minimal polynomials of the linear algorithms Trivium and Trivium Toy. We show the different cycles and mini-mum lengths obtained. The existence of initial states determining short cycles is verified. Finally, linear Trivium Toy is shown to be as cryptologically secure as the linear Trivium algorithm.III Workshop de Seguridad Informática (WSI)Red de Universidades con Carreras de Informática (RedUNCI

Trivium vs. Trivium Toy

We present the characteristic and minimal polynomials of the linear algorithms Trivium and Trivium Toy. We show the different cycles and mini-mum lengths obtained. The existence of initial states determining short cycles is verified. Finally, linear Trivium Toy is shown to be as cryptologically secure as the linear Trivium algorithm.III Workshop de Seguridad Informática (WSI)Red de Universidades con Carreras de Informática (RedUNCI

Trivium vs. Trivium Toy

We present the characteristic and minimal polynomials of the linear algorithms Trivium and Trivium Toy. We show the different cycles and mini-mum lengths obtained. The existence of initial states determining short cycles is verified. Finally, linear Trivium Toy is shown to be as cryptologically secure as the linear Trivium algorithm.III Workshop de Seguridad Informática (WSI)Red de Universidades con Carreras de Informática (RedUNCI

Trivial Transciphering With Trivium and TFHE

We examine the use of Trivium and Kreyvium as transciphering mechanisms for use with the TFHE FHE scheme. Originally these two ciphers were investigated for FHE transciphering only in the context of the BGV/BFV FHE schemes; this is despite Trivium and Kreyvium being particarly suited to TFHE. Recent work by Dobraunig et al. gave some initial experimental results using TFHE. We show that these two symmetric ciphers have excellent performance when homomorphically evaluated using TFHE. Indeed we improve upon the results of Dobraunig et al. by at least two orders of magnitude in terms of latency. This shows that, for TFHE at least, one can transcipher using a standardized symmetric cipher (Trivium), without the need for special FHE-friendly ciphers being employed. For applications wanting extra security, but without the benefit of relying on a standardized cipher, our work shows that Kreyvium is a good candidate

Biology of the Common Starfish as a Source of Study in the High School Biology Classroom and Laboratory

Many high school biology teachers find it necessary to use supplementary materials in presenting the starfish biology to the students. This report deals with such items as: the anatomy and physiology of the starfish; diagrams which can be used to present the material; methods for preparing laboratory specimens of the organism; outlines for laboratory exercises using the starfish; and a glossary of terms associated with. the biology of this animal. It is desired that the information presented in this report will be of value to secondary biology teachers in introducing the biology of the starfish to the high school student. Also, that some teachers who are not satisfied with the materials they currently employ may be assisted by the information or references presented.Natural Scienc