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We give a comparison of the performance of the recently proposed torus-based public key cryptosystem CEILIDH, and XTR. Underpinning both systems is the mathematics of the two dimensional algebraic torus T6(Fp). However, while they both attain ...
DSA and ECDSA are well established standards for digital signature based on the discrete logarithm problem. In this paper we survey known properties, certification issues regarding the public parameters, and security proofs. ECDSA also includes a standard ...
We give estimates for the running-time of the function field sieve (FFS) to compute discrete logarithms in Fpn× for small p. Specifically, we obtain sharp probability estimates that allow us to select optimal parameters in cases of ...
This work studies linear elliptic problems under uncertainty. The major emphasis is on the deterministic treatment of such uncertainty. In particular, this work uses the Worst Scenario approach for the characterization of uncertainty on functional outputs ...
Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type algorithm for solving the discrete logarithm problem that works directly in these groups. Using a prototype implementation, we obtain ...
Physical systems encompassing a variety of strongly coupled scales pose major computational challenges in terms of analysis modeling and simulation. In this report we first discuss a multiscale modeling approach for the transport of particles such as DNA i ...
In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields F3n. Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special at ...
In 1984, C.H. Bennet and G. Brassard proposed a new protocol aimed to solve the problem of symmetric cryptographic key exchange. This protocol was called BB84 after the name of its authors. While a traditional method would rely on public key cryptography ( ...
Digital signature schemes often use domain parameters such as prime numbers or elliptic curves. They can be subject to security threats when they are not treated like public keys. In this paper we formalize the notion of "signature scheme with domain param ...
