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- W2949476124 abstract "We describe a method to perform scalar multiplication on two classes of ordinary elliptic curves, namely E:y^2=x^3+Ax in prime characteristic p=1mod4, and E:y^2=x^3+B in prime characteristic p=1mod3. On these curves, the 4-th and 6-th roots of unity act as (computationally efficient) endomorphisms. In order to optimise the scalar multiplication, we consider a width-w-NAF (Non-Adjacent Form) digit expansion of positive integers to the complex base of @t, where @t is a zero of the characteristic polynomial x^2-tx+p of the Frobenius endomorphism associated to the curve. We provide a precomputationless algorithm by means of a convenient factorisation of the unit group of residue classes modulo @t in the endomorphism ring, whereby we construct a digit set consisting of powers of subgroup generators, which are chosen as efficient endomorphisms of the curve." @default.
- W2949476124 created "2019-06-27" @default.
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- W2949476124 date "2013-01-01" @default.
- W2949476124 modified "2023-10-16" @default.
- W2949476124 title "Symmetric Digit Sets for Elliptic Curve Scalar Multiplication without Precomputation." @default.
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