Abstract
An upper bound is established for certain exponential sums with respect to multiplicative characters defined on the rational points of an elliptic curve over a prime field. The bound is applied to investigate the pseudo-randomness of a large family of binary sequences generated from elliptic curves by using discrete logarithm. That is, we use this estimate to show that the resulting sequences have the advantages of ‘small’ well-distribution measure and ‘small’ multiple correlation measure.
The work was supported in part by the National Natural Science Foundation of China (No. 60473028). Research of the first author was partially supported by the Natural Science Foundation of Fujian Province of China (No.A0540011), the Science and Technology Foundation of Fujian Educational Committee (No.JA04264) and the Science and Technology Foundation of Putian City (No.2005S04).
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Chen, Z., Li, S., Xiao, G. (2006). Construction of Pseudo-random Binary Sequences from Elliptic Curves by Using Discrete Logarithm. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_24
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DOI: https://doi.org/10.1007/11863854_24
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