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The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions
Discrete logarithms SNFS
2014/3/10
In this paper, we study the discrete logarithm problem in finite fields related to pairing-based curves. We start with a precise analysis of the state-of-the-art algorithms for computing discrete loga...
Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions
public-key cryptography / Hyperelliptic Curves Genus 2 Order Computation
2012/6/14
The use of (hyper)elliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test wheth...
Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions
public-key cryptography / Hyperelliptic Curves Genus 2 Order Computation Ordinary Curves Pairing-Friendly Constructions Cocks-Pinch Method Brezing-Weng Method.
2012/3/22
The use of (hyper)elliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test wheth...
Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions
public-key cryptography / Hyperelliptic Curves Genus 2 Order Computation Ordinary Curves Pairing-Friendly Constructions Cocks-Pinch Method Brezing-Weng Method.
2012/3/21
The use of (hyper)elliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test wheth...