On the Minimal Embedding Field

Let C be a curve of genus g, defined over a finite field Fq, where q = pm 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 qk

• Type: Conference
• Year: 2007
• Where: PAIRING
• Authors: Laura Hitt
• Keywords: Cryptography, Discrete Logarithm, Discrete Logarithm Problem, Large Integer Coprime, PAIRING 2007