The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid gr...
This paper proposes different low-cost coprocessors for public key authentication on 8-bit smart cards. Elliptic curve cryptography is used for its efficiency per bit of key and ...
Guerric Meurice de Dormale, Renaud Ambroise, David...
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...
This paper presents a scalable hardware implementation of both commonly used public key cryptosystems, RSA and Elliptic Curve Cryptosystem (ECC) on the same platform. The introduce...
We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlan...