Bruen chains over fields of small order

Bruen chains over fields of small order

We extend the classi cation of the Bruen chains to all elds of order at most 49, by showing the non-existence of Bruen chains over the elds of order 41, 43, 47 and 49. c © 2004 Elsevier B.V. All rights reserved.

On maximal curves over finite fields of small order

BLT-sets over small fields

A BLT-set is a set X of q+l points of the generalized quadrangle Q(4, q), q odd, such that no point of Q(4, q) is collinear with more than 2 points of X. BLT-sets are closely related to flocks of the quadratic cone, elation generalised quadrangles and certain translation planes. In this paper we report on the results of computer searches for BLT-sets for odd q ::; 25. We complete the classifica...

Algebraic Varieties over Small Fields

— We study curves and their Jacobians over F̄p and Q̄, and discuss applications to rational connectivity over these fields. We introduce certain dynamical systems on P, induced by translates by torsion points on elliptic curves, and study fields related to these systems.

Theoretical Analysis of XL over Small Fields

XL was first introduced to solve determined or overdetermined systems of equations over a finite field as an “algebraic attack” against multivariate cryptosystems. There has been a steady stream of announcements of cryptanalysis of primitives by such attacks, including stream ciphers (e.g. Toyocrypt), PKC’s, and more controversially block ciphers (AES/Rijndael and Serpent). Prior discussions of...