Constructive and destructive facets of Weil descent on elliptic curves

By P. Gaudry, Florian Hess, Nigel P. Smart. Journal of Cryptology, 2002

364 citations recorded by the source corpus.

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The Elliptic Curve Digital Signature Algorithm (ECDSA) (2001, background): “[32] refined these ideas to provide some evidence that when m has a small divisor l, e.”
The use of elliptic curves in cryptography (2007, background): “to one with running time O(q 2g g+1 +2 ) as q → ∞ [19].”
Guide to Elliptic Curve Cryptography (2004, background): “The GHS attack was presented by Gaudry, Hess and Smart [167] (see also Hess [196]).”
Public Key Cryptography (2014, neutral): “• Certain elliptic curves over Fq where q = p is a prime power and k is highly composite (see [11]).”
Short Signatures from the Weil Pairing (2001, neutral): “Note that we restrict these instantiations to those where l is prime, to avoid Weil-descent attacks [9,10].”
A public-key infrastructure for key distribution in TinyOS based on elliptic curve cryptography (2004, methodology): “Of recent interest to cryptographers are such curves over Fp and F2p , where p is prime, as neither appears vulnerable to subexponential attack [27].”