Paper 2016/914
Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields
Gora Adj and Isaac Canales-Martínez and Nareli Cruz-Cortés and Alfred Menezes and Thomaz Oliveira and Luis Rivera-Zamarripa and Francisco Rodríguez-Henríquez
Abstract
Since 2013 there have been several developments in algorithms for computing discrete logarithms in small-characteristic finite fields, culminating in a quasi-polynomial algorithm. In this paper, we report on our successful computation of discrete logarithms in the cryptographically-interesting characteristic-three finite field ${\mathbb F}_{3^{6 \cdot 509}}$ using these new algorithms; prior to 2013, it was believed that this field enjoyed a security level of 128 bits. We also show that a recent idea of Guillevic can be used to compute discrete logarithms in the cryptographically-interesting finite field ${\mathbb F}_{3^{6 \cdot 709}}$ using essentially the same resources as we expended on the ${\mathbb F}_{3^{6 \cdot 509}}$ computation. Finally, we argue that discrete logarithms in the finite field ${\mathbb F}_{3^{6 \cdot 1429}}$ can feasibly be computed today; this is significant because this cryptographically-interesting field was previously believed to enjoy a security level of 192 bits.
Metadata
- Available format(s)
- Publication info
- Preprint. MINOR revision.
- Keywords
- discrete logarithm problembilinear pairingscryptanalysisimplementation
- Contact author(s)
- francisco @ cs cinvestav mx
- History
- 2016-09-22: received
- Short URL
- https://ia.cr/2016/914
- License
-
CC BY