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- W1483451858 abstract "Let C be a curve of genus g, defined over a finite field ${mathbb F}_q$ , where q = p m for a prime p. Let N be a large integer coprime to p, dividing the order of the Jacobian variety associated to C. Pairings can transport the discrete logarithm problem (DLP) from the curve to a finite field where there are more efficient methods for solving the discrete logarithm. The embedding degree is defined to be the smallest positive integer k such that N divides q k − 1. We show that the minimal embedding field is not necessarily ${mathbb F}_{q^k}$ , as is traditionally understood, but rather is ${mathbb F}_{p^{{mathrm{ord}}_N p}}={mathbb F}_{q^{{mathrm{ord}}_Np/m}}$ , which can be a field of significantly smaller size. This fact reveals that attacks on the DLP can be dramatically faster than otherwise expected, so a parameter separate from the embedding degree k needs to be used to indicate security." @default.
- W1483451858 created "2016-06-24" @default.
- W1483451858 creator A5052776640 @default.
- W1483451858 date "2007-09-11" @default.
- W1483451858 modified "2023-10-17" @default.
- W1483451858 title "On the Minimal Embedding Field" @default.
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- W1483451858 doi "https://doi.org/10.1007/978-3-540-73489-5_16" @default.
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