Handbook of Elliptic and Hyperelliptic Curve Cryptography

By H. Cohen, G. Frey, R. Avanzi, C. Doche, Tanja Lange, Kim Nguyen, Frederik Vercauteren. 2005

1,191 citations recorded by the source corpus.

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Verifiable ASICs (2016, methodology): “This operation takes as inputs a 255-bit scalar value v and an elliptic curve point Q, and computes the point R= [v]Q via a sequence of 255 double-and-add steps [21], one for each bit of v.”
Complex multiplication of abelian surfaces (2010, background): “The invariants i5, i6, i7 are much used in the computational literature (see [17, 97, 88] and up to constants also Spallek [79]).”
Full Accounting for Verifiable Outsourcing (2017, methodology): “This operation takes as inputs a 255-bit scalar value v and a curve point Q , and computes the point R = [v]Q via 255 double-and-add steps [11], one for each bit of v .”
Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects (2011, neutral): “The other reason is the application of hyperelliptic curves in cryptography, especially for the so-called CM methods (see [14]).”
Signing a Linear Subspace: Signature Schemes for Network Coding (2009, background): “…are believed to be infeasible are those for which G 1 , G 2 are (subgroups of) groups of rational points on elliptic curves or abelian varieties over finite fields; G T is (a subgroup of) a multiplicative group of a finite field; and e is (a variant of) the Weil pairing or Tate pairing [9].”