Shorter addition chain for smooth integers using decomposition method.
An efficient computation of scalar multiplication in elliptic curve cryptography can be achieved by reducing the original problem into a chain of additions and doublings. Finding the shortest addition chain is an NP-problem. To produce the nearest possible shortest chain, various methods were introd...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Taylor & Francis
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25154/1/Shorter%20addition%20chain%20for%20smooth%20integers%20using%20decomposition%20method.pdf http://psasir.upm.edu.my/id/eprint/25154/ http://www.tandf.co.uk/journals/default.asp |
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| Summary: | An efficient computation of scalar multiplication in elliptic curve cryptography can be achieved by reducing the original problem into a chain of additions and doublings. Finding the shortest addition chain is an NP-problem. To produce the nearest possible shortest chain, various methods were introduced and most of them depends on the representation of a positive integer n into a binary form. Our method works out the given n by twice decomposition, first into its prime powers and second, for each prime into a series of 2's from which a set of rules based on addition and doubling is defined. Since prime factorization is computationally a hard problem, this method is only suitable for smooth integers. As an alternative, the need to decompose n can be avoided by choosing n of the form p1 e1p2 e2⋯r er. This shall not compromise the security of ECC since its does not depend on prime factorization problem. The result shows a significant improvement over existing methods especially when n grows very large. |
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