Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications
Public-key cryptosystems are broadly employed to provide security for digital information. Improving the efficiency of public-key cryptosystem through speeding up calculation and using fewer resources are among themain goals of cryptography research. In this paper, we introduce new symbols extract...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2014
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| Subjects: | |
| Online Access: | http://eprints.usm.my/38934/ http://eprints.usm.my/38934/1/Efficient_Big_Integer_Multiplication_and_Squaring_Algorithms_for_Cryptographic_Applications.pdf |
| Summary: | Public-key cryptosystems are broadly employed to provide security for digital information. Improving the efficiency of public-key
cryptosystem through speeding up calculation and using fewer resources are among themain goals of cryptography research. In this
paper, we introduce new symbols extracted from binary representation of integers called Big-ones.We present a modified version
of the classicalmultiplication and squaring algorithms based on the Big-ones to improve the efficiency of big integermultiplication
and squaring in number theory based cryptosystems. Compared to the adopted classical and Karatsuba multiplication algorithms
for squaring, the proposed squaring algorithm is 2 to 3.7 and 7.9 to 2.5 times faster for squaring 32-bit and 8-Kbit numbers,
respectively. The proposed multiplication algorithm is also 2.3 to 3.9 and 7 to 2.4 times faster for multiplying 32-bit and 8-Kbit
numbers, respectively.The number theory based cryptosystems, which are operating in the range of 1-Kbit to 4-Kbit integers, are
directly benefited from the proposed method since multiplication and squaring are the main operations in most of these systems. |
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