We provide conditions for which the round functions of an -bit Rijndael-like block cipher generate the alternating group on the set {0, 1} . These conditions show that the class of Rijndael-like ciphers whose round functions generate the alternating group on their message space is large, and includes both the actual Rijndael and the block cipher used by the compression function of the WHIRLPOOL hash function. The result indicates that there is no trapdoor design for a Rijndael-like cipher based on the imprimitivity of the group action of its proper round functions which is difficult to detect.

Abstract.While it is known previously that the cycle lengths of individual components of the AES round function are very small, we demonstrate here that the cycle length of the S-box combined with the ShiftRow and MixColumn transformation is at least 10205 . This result is obtained by providing new invariances of the complete AES round function without the key addition. Furthermore, we consider self-duality properties of the AES round function and derive a property analogous to the complementation property of the DES round function. These results confirm the assessments given in other publications that the AES components have several unexpected structural properties.

We show that the round functions of the KASUMI block cipher for odd and even round type generate the alternating group on the message space. Moreover, under the assumption of independent round keys, we prove that also the KASUMI two-round functions and the KASUMI encryption functions generate the alternating group.

This chapter analyzes how valuable the assumption of systematic environment imbalance is for performing roughand-ready intuitive estimates, which people regularly do when inferring the quantitative value of an object (e.g., its frequency, size, value, or quality). The chapter outlines how systematic environment imbalance can be quantified using the framework of power laws. It investigates to what extent power-law characteristics and other statistical properties of real-world environments can be allies of two simple estimation heuristics, QuickEst and the mapping heuristic. The analyses, which involve comparing the estimation performances of the heuristics relative to more complex strategies, demonstrate that QuickEst could be particularly suited for deriving roughand-ready estimates in skewed distributions with highly University Press Scholarship Online Oxford Scholarship Online How Estimation Can Benefit From an Imbalanced World