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Article
A Note on the Behaviour of the Number Field Sieve in the Medium Prime Case: Smoothness of Norms
As we examine the behaviour of the number field sieve (NFS) in the medium prime case, we notice various patterns that can be exploited to improve the running time of the sieving stage. The contributions of the...
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Chapter and Conference Paper
“Ooh Aah... Just a Little Bit” : A Small Amount of Side Channel Can Go a Long Way
We apply the Flush+Reload side-channel attack based on cache hits/misses to extract a small amount of data from OpenSSL ECDSA signature requests. We then apply a “standard” lattice technique to extract the privat...
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Chapter and Conference Paper
Constructing Tower Extensions of Finite Fields for Implementation of Pairing-Based Cryptography
A cryptographic pairing evaluates as an element of a finite extension field, and the evaluation itself involves a considerable amount of extension field arithmetic. It is recognised that organising the extensi...
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Chapter and Conference Paper
On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves
When performing a Tate pairing (or a derivative thereof) on an ordinary pairing-friendly elliptic curve, the computation can be looked at as having two stages, the Miller loop and the so-called final exponenti...
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Chapter and Conference Paper
Fast Hashing to G 2 on Pairing-Friendly Curves
Pairings on elliptic curves usually take as input a point in a subgroup G 1 of an elliptic curve group $E({\mathbb{F}}...
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Chapter and Conference Paper
On the Security of Pairing-Friendly Abelian Varieties over Non-prime Fields
Let A be an abelian variety defined over a non-prime finite field \({\mathbb F}_{q}\) that has embedding degree k with ...
