Shashank Singh

Challenges with Assessing the Impact of NFS Advances on the Security of Pairing-Based Cryptography

In the past two years there have been several advances in Number Field Sieve (NFS) algorithms for computing discrete logarithms in finite fields \({\mathbb F}_{p^n}\) where p is prime and \(n > 1\) is a small integer. This article presents a concise overview of these algorithms and discusses some of the challenges with assessing their impact on keylengths for pairing-based cryptosystems.

A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm

In a recent work, Kim and Barbulescu had extended the tower number field sieve algorithm to obtain improved asymptotic complexities in the medium prime case for the discrete logarithm problem on

A new method for decomposition in the Jacobian of small genus hyperelliptic curves

\mathbb {F}_{p^{n}}

New Complexity Trade-Offs for the Multiple Number Field Sieve Algorithm in Non-Prime Fields

where n is not a prime power. Their method does not work when n is a composite prime power. For this case, we obtain new asymptotic complexities, e.g.,

A New Method for Decomposition in the Jacobian of Small Genus Hyperelliptic Curves.

L_{p^{n}}1/3,64/9^{1/3}

b(x^d)

resp.