TY - JOUR
T1 - Pseudorandom bits from points on elliptic curves
AU - Farashahi, Reza Rezaeian
AU - Shparlinski, Igor E.
PY - 2012/2
Y1 - 2012/2
N2 - Let be an elliptic curve over a finite field of elements, with gcd(q, 6)= 1, given by an affine Weierstraß equation. We use x(P) to denote the x-component of a point P = (x(P), y(P)) ε E. We estimate character sums of the form NΣ n=1X(x(nP)x(nQ)) and NΣ n1,...,nk=1Π ( kΣj=1cjx(( jΠ i=1ni)R)) on average over all F qrational points P,Q, and R on E, where X is a quadratic character, φ is a nontrivial additive character in Fq, and (c 1,...,ck) ε F k qis 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.
AB - Let be an elliptic curve over a finite field of elements, with gcd(q, 6)= 1, given by an affine Weierstraß equation. We use x(P) to denote the x-component of a point P = (x(P), y(P)) ε E. We estimate character sums of the form NΣ n=1X(x(nP)x(nQ)) and NΣ n1,...,nk=1Π ( kΣj=1cjx(( jΠ i=1ni)R)) on average over all F qrational points P,Q, and R on E, where X is a quadratic character, φ is a nontrivial additive character in Fq, and (c 1,...,ck) ε F k qis 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.
UR - http://www.scopus.com/inward/record.url?scp=84856813869&partnerID=8YFLogxK
U2 - 10.1109/TIT.2011.2170054
DO - 10.1109/TIT.2011.2170054
M3 - Article
AN - SCOPUS:84856813869
VL - 58
SP - 1242
EP - 1247
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 2
M1 - 6043877
ER -