Algebraic Analysis of LEX

LEX is a stream cipher that progressed to Phase 3 of the eSTREAM stream cipher project. In this paper, we show that the security of LEX against algebraic attacks relies on a small equation system not being solvable faster than exhaustive search. We use the byte leakage in LEX to construct a system of 21 equa- tions in 17 variables. This is very close to the require- ment for an efficient attack, i.e. a system containing 16 variables. The system requires only 36 bytes of keystream, which is very low.

Algebraic analysis of small scale LEX-BES

This paper examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this paper, experiments were conducted to find solution of the equation system describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the author knows, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.

Algebraic analysis of small Scale LEX-BES

This work examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this article, experiments were conducted to find solutions of equation systems describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the authors know, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.

The rise of birds and mammals: are microevolutionary processes sufficient for macroevolution?

It is a basis of darwinian evolution that the microevolutionary mechanisms that can be studied in the present are sufficient to account for macroevolution. However, this idea needs to be tested explicitly, as highlighted here by the example of the superceding of dinosaurs and pterosaurs by birds and placental mammals that occurred near the Cretaceous/Tertiary boundary approximately 65 million years ago. A major problem for testing the sufficiency of microevolutionary processes is that independent ideas (such as the existence of an extraterrestrial impact, and the extinction of dinosaurs) were linked without the evidence for each idea being evaluated separately. Here, we suggest and discuss five testable models for the times and divergences of modern mammals and birds. Determination of the model that best represents these events will enable the role of microevolutionary mechanisms to be evaluated. The question of the sufficiency of microevolutionary processes for macroevolution is solvable, and available evidence supports an important role for biological processes in the initial decline of dinosaurs and pterosaurs.

Monte Carlo analysis of a puzzle game

When a puzzle game is created, its design parameters must be chosen to allow solvable and interesting challenges to be created for the player. We investigate the use of random sampling as a computationally inexpensive means of automated game analysis, to evaluate the BoxOff family of puzzle games. This analysis reveals useful insights into the game, such as the surprising fact that almost 100% of randomly generated challenges have a solution, but less than 10% will be solved using strictly random play, validating the inventor’s design choices. We show the 1D game to be trivial and the 3D game to be viable.

Decision-theoretic designs for dose-finding clinical trials with multiple outcomes

A decision-theoretic framework is proposed for designing sequential dose-finding trials with multiple outcomes. The optimal strategy is solvable theoretically via backward induction. However, for dose-finding studies involving k doses, the computational complexity is the same as the bandit problem with k-dependent arms, which is computationally prohibitive. We therefore provide two computationally compromised strategies, which is of practical interest as the computational complexity is greatly reduced: one is closely related to the continual reassessment method (CRM), and the other improves CRM and approximates to the optimal strategy better. In particular, we present the framework for phase I/II trials with multiple outcomes. Applications to a pediatric HIV trial and a cancer chemotherapy trial are given to illustrate the proposed approach. Simulation results for the two trials show that the computationally compromised strategy can perform well and appear to be ethical for allocating patients. The proposed framework can provide better approximation to the optimal strategy if more extensive computing is available.