摘要
We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the 'truly' random sequences. The method indicates that it is possible to construct 'good' pseudorandom sequences over elliptic curves widely used in public key cryptography.
We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the 'truly' random sequences. The method indicates that it is possible to construct 'good' pseudorandom sequences over elliptic curves widely used in public key cryptography.
基金
Supported by the National Natural Science Foundation of China (61063041)
the Program for New Century Excellent Talents in Fujian Province University (JK2010047)
the Open Funds of State Key Laboratory of Information Security (01-01-1)