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• W1639262935 abstract "Let E be an elliptic curve over a finite field Fq of q elements, with gcd(q,6)=1, given by an affine Weierstras equation. We use x(P) to denote the x-component of a point P=(x(P),y(P)) ∈ E. We estimate character sums of the form Σn=1Nχ(x(nP)x(nQ)) and Σn1,⋯,nk=1Nψ(Σj=1k cjx((Πi=1j ni)R)) on average over all Fq rational points P, Q, and R on E, where χ is a quadratic character, ψ is a nontrivial additive character in Fq, and (c1,..., ck) ∈ Fqk is a nonzero vector. These bounds confirm several recent conjectures of Jao, Jetchev, and Venkatesan, related to extracting random bits from various sequences of points on the elliptic curves." @default.
• W1639262935 created "2016-06-24" @default.
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• W1639262935 creator A5054840270 @default.
• W1639262935 date "2012-02-01" @default.
• W1639262935 modified "2023-09-26" @default.
• W1639262935 title "Pseudorandom Bits From Points on Elliptic Curves" @default.
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• W1639262935 doi "https://doi.org/10.1109/tit.2011.2170054" @default.
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