On the Linear Complexity and Multidimensional Distribution of Congruential Generators over Elliptic Curves

2005 ◽  
Vol 35 (1) ◽  
pp. 111-117 ◽  
Author(s):  
Florian Hess ◽  
Igor E. Shparlinski
Keyword(s):  
Elliptic Curves ◽  
Linear Complexity ◽  
Multidimensional Distribution

scholarly journals On the linear complexity of the Naor–Reingold sequence with elliptic curves

2010 ◽  
Vol 16 (5) ◽  
pp. 329-333 ◽  
Author(s):  
Marcos Cruz ◽  
Domingo Gómez ◽  
Daniel Sadornil
Keyword(s):  
Elliptic Curves ◽  
Linear Complexity

scholarly journals Pseudorandom Bit Sequence Generator for Stream Cipher Based on Elliptic Curves

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Jilna Payingat ◽  
Deepthi P. Pattathil
Keyword(s):  
Elliptic Curves ◽  
Linear Complexity ◽  
Complexity Analysis ◽  
Key Exchange ◽  
Pseudorandom Sequence ◽  
Time Sharing ◽  
Random Number Generators ◽  
Plain Text ◽  
Point Multiplication ◽  
Sequence Generator

This paper proposes a pseudorandom sequence generator for stream ciphers based on elliptic curves (EC). A detailed analysis of various EC based random number generators available in the literature is done and a new method is proposed such that it addresses the drawbacks of these schemes. Statistical analysis of the proposed method is carried out using the NIST (National Institute of Standards and Technology) test suite and it is seen that the sequence exhibits good randomness properties. The linear complexity analysis shows that the system has a linear complexity equal to the period of the sequence which is highly desirable. The statistical complexity and security against known plain text attack are also analysed. A comparison of the proposed method with other EC based schemes is done in terms of throughput, periodicity, and security, and the proposed method outperforms the methods in the literature. For resource constrained applications where a highly secure key exchange is essential, the proposed method provides a good option for encryption by time sharing the point multiplication unit for EC based key exchange. The algorithm and architecture for implementation are developed in such a way that the hardware consumed in addition to point multiplication unit is much less.

Elliptic Curves

1997 ◽  
Author(s):  
Henry McKean ◽  
Victor Moll
Keyword(s):  
Elliptic Curves

The Joint Universality for L-Functions of Elliptic Curves

2004 ◽  
Vol 9 (4) ◽  
pp. 331-348
Author(s):  
V. Garbaliauskienė
Keyword(s):  
Elliptic Curves ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

A joint universality theorem in the Voronin sense for L-functions of elliptic curves over the field of rational numbers is proved.

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