Computer Security and Cryptography

Our working group in cryptography is mostly interested in Elliptic Curve Cryptography (ECC) and Hyperelliptic Curve Cryptography (HCC). It is a special interest to us post-quantum cryptography, isogeny-based cryptography, etc.

We have organized many conferences including two NATO Advanced Study Institutes, special sessions of the American Mathematical Society meetings, and have regular annual gatherings.   We regularly organize conferences related to cryptography. For a list of conferences visit our conference page

Group members

Papers

• A. Elezi, T. Shaska, Reduction of binary forms via the hyperbolic centroid, Lobachevskii J. Math. 42 (2021), no. 1, 84–95.

• L. Beshaj, A. Elezi, T. Shaska, Isogenous components of Jacobian surfaces , Eur. J. Math. 6 (2020), no. 4, 1276–1302.

• G. Frey and T. Shaska, Curves, Jacobians, and Cryptography Contemporary Math. vol. 724, AMS (2019), pg. 279-345.

• L. Beshaj and T. Shaska, Heights on algebraic curves , NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 24, 2015.

• A. Elezi and T. Shaska, Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes,, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 24, 2015.

• L. Beshaj, T. Shaska, E. Zhupa, The case for superelliptic curves NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 24, 2015.

• L. Beshaj and T. Shaska, Decomposition of some Jacobian varieties of dimension 3 , Artificial Intelligence and Symbolic Computation, LNCS vol. 8884, 193-204.

• T. Shaska, Genus 2 curves with $(3,3)$-split Jacobian and large automorphism group. Algorithmic number theory (Sydney, 2002), 205--218, Lecture Notes in Comput. Sci., 2369, Springer, Berlin, 2002.

• T. Shaska and C. Shor, Codes over $F_{p^2}$ and $F_p \times F_p$, Hermitian lattices, and corresponding theta functions Advances in Coding Theory and Cryptology, vol 3. (2007), pg. 70-80.

• L. Beshaj and T. Shaska, The arithmetic of genus 2 curves , NATO ASI, Croatia 2010, ISO Press.