The class numbers h + of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and that is why other methods have been developed, which approach the problem from different angles. In this thesis we extend a method of Schoof that was designed for real cyclotomic fields of… (More)
An arithmetic or with-carry analog of Blahut's theorem is presented. This relates the length of the smallest feedback with carry shift register to the number of nonzero classical Fourier coeecients of a periodic binary sequence.
Secure computation is a fundamental problem in modern cryptography in which multiple parties join to compute a function of their private inputs without revealing anything beyond the output of the function. A series of very strong results in the 1980's demonstrated that any polynomial-time function can be computed while guaranteeing essentially every desired… (More)
This dissertation covers two topics of interest for network applications: lookup protocols, a basic building block for distributed systems, and ring signatures, a powerful primitive for anonymous communication. In the first part of this work, we review lookup protocols, distributed algorithms that allow users to publish a document as well as to look up a… (More)
Ah, la recherche! Du temps perdu. Soit G le quotient du groupe libre a 26 g en era-teurs a; b; c; : : : ; z par les relations A = B, pour tout couple de mots (A; B) pouvant avoir la m^ eme prononciation en anglais. (Un groupe d eeni d'une mani ere analogue a et e consid er e dans Landsburg 1986].) Notre but est de d eterminer la structure du groupe G.… (More)
In Eurocrypt 2005, Wang et al. presented an exciting paper that showcased her method of breaking MD5 by attacking its collision resistance propery. However, Wang's paper does not give a thorough exposition of the attack and much of their techniques are shrouded in mystery. This paper attempts to explain Wang's attack on MD5 in greater detail by… (More)
Let F 0 = Q(√ −d), K 0 = Q(√ d), and L 0 = Q(√ d, i) with d a square-free positive integer such that 2 d. Let L j = L 0 (ζ 2 2+j) so that L 0 ⊂ L 1 ⊂ · · · ⊂ j L j is the cyclotomic Z 2-extension of L 0. We determine when fourth roots of certain elements of K 0 generate unramified extensions of L j. In particular, for elements of K 0 that are relatively… (More)
In this dissertation we determine new bounds and properties of codes in three different finite metric spaces, namely the ordered Hamming space, the binary Ham-ming space, and the Johnson space. The ordered Hamming space is a generalization of the Hamming space that arises in several different problems of coding theory and numerical integration. Structural… (More)