Muralidhara, V. N. ; Sen, Sandeep (2007) A result on the distribution of quadratic residues with applications to elliptic curve cryptography INDOCRYPT 2007, 8th International Conference on Cryptology in India .

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Abstract
In this paper, we prove that for any polynomial function f of fixed degree without multiple roots, the probability that all the (f(x + 1), f(x + 2), ..., f(x +κ)) are quadratic nonresidue is ≈ 1/2^{κ}. In particular for f(x) = x^{3} + ax + b corresponding to the elliptic curve y^{2} = x^{3 }+ ax + b, it implies that the quadratic residues (f(x + 1), f(x + 2), . . . in a finite field are sufficiently randomly distributed. Using this result we describe an efficient implementation of ElGamal Cryptosystem. that requires efficient computation of a mapping between plaintexts and the points on the elliptic curve.
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Deposited On:  08 May 2012 08:35 
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