There is no MacWilliams identity for convolutional codes

An example is provided of two convolutional codes that have the same transmission gain but whose dual codes do not. This shows that no analog of the MacWilliams identity for block codes can exist relating the transmission gains of a convolutional code and its dual

A comprehensive analysis of constant-time polynomial inversion for post-quantum cryptosystems

Post-quantum cryptosystems have currently seen a surge in interest thanks to the current standardization initiative by the U.S.A. National Institute of Standards and Technology (NIST). A common primitive in post-quantum cryptosystems, in particular in code-based ones, is the computation of the inverse of a binary polynomial in a binary polynomial ring. In this work, we analyze, realize in software, and benchmark a broad spectrum of binary polynomial inversion algorithms, targeting operand sizes which are relevant for the current second round candidates in the NIST standardization process. We evaluate advantages and shortcomings of the different inversion algorithms, including their capability to run in constant-time, thus preventing timing side-channel attacks

Submicron Systems Architecture: Semiannual Technical Report

No abstract available

Linear Recurring Sequences Over Finite Fields

This thesis deals with the problem of how the elements from a finite field F of characteristic p are distributed among the various linear recurrent sequences with a given fixed characteristic polynomial fε F[x]. The first main result is a method of extending the so-called "classical method" for solving linear recurrences in terms of the roots of f. The main difficulty is that f might have a root θ which occurs with multiplicity exceeding p-1; this is overcome by replacing the solutions θt, tθt, t2θt, ..., by the solutions θt, (t1)θt, (t2)θt, .... The other main result deals with the number N of times a given element a ε F appears in a period of the sequence, and for a≠0, the result is of the form N≡0 (mod pε where ε is an integer which depends upon f, but not upon the particular sequence in question. Several applications of the main results are given