Article
On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves
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Abstract
Given a prime p, an elliptic curve E/F p over the finite field F p of p ∞ elements and a binary linear recurrence sequence (u(n)) n=1 of order r, we study the distribution of the sequence of points r−1 X u(n + j)Pj, n = 1, . . . , N, j=0 on average over all possible choices of F p-rational points P1, . . . , Pr on E. For a sufficiently large N we improve and generalise a previous result in this direction due to E. El Mahassni.
Keywords
Pseudorandom numbers, subset sum problem, knapsack, exponential sums.
Citation
Blackburn, S. R., Ostafe, A., & Shparlinski, I. E. (2011). On the distribution of the subset sum pseudorandom number generator on elliptic curves. Uniform Distribution Theory, 6(1), 127–142.
S. R. Blackburn, A. Ostafe and I. E. Shparlinski, “On the distribution of the subset sum pseudorandom number generator on elliptic curves,” Uniform Distribution Theory, vol. 6, no. 1, pp. 127–142, 2011.
Blackburn SR, Ostafe A, Shparlinski IE. On the distribution of the subset sum pseudorandom number generator on elliptic curves. Uniform Distribution Theory. 2011;6(1):127–142.
Blackburn, S. R., Ostafe, A. and Shparlinski, I. E. (2011), ‘On the distribution of the subset sum pseudorandom number generator on elliptic curves’, Uniform Distribution Theory, 6(1), pp. 127–142.
Blackburn, Simon R., et al. “On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves.” Uniform Distribution Theory, vol. 6, no. 1, 2011, pp. 127–142.
Blackburn, Simon R., Alina Ostafe, and Igor E. Shparlinski. “On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves.” Uniform Distribution Theory 6, no. 1 (2011): 127–142.
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Published by: Engineering Journals
