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 |
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Hindawi Publishing Corporation
2014
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| Online Access: | http://eprints.usm.my/38934/ http://eprints.usm.my/38934/1/Efficient_Big_Integer_Multiplication_and_Squaring_Algorithms_for_Cryptographic_Applications.pdf |
| _version_ | 1848878606573371392 |
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| author | Jahani, Shahram Samsudin, Azman Subramanian, Kumbakonam Govindarajan |
| author_facet | Jahani, Shahram Samsudin, Azman Subramanian, Kumbakonam Govindarajan |
| author_sort | Jahani, Shahram |
| building | USM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T17:34:01Z |
| format | Article |
| id | usm-38934 |
| institution | Universiti Sains Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T17:34:01Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | usm-389342018-02-14T07:06:08Z http://eprints.usm.my/38934/ Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications Jahani, Shahram Samsudin, Azman Subramanian, Kumbakonam Govindarajan QA75.5-76.95 Electronic computers. Computer science 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. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://eprints.usm.my/38934/1/Efficient_Big_Integer_Multiplication_and_Squaring_Algorithms_for_Cryptographic_Applications.pdf Jahani, Shahram and Samsudin, Azman and Subramanian, Kumbakonam Govindarajan (2014) Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications. Journal of Applied Mathematics, 2014 (107109). pp. 1-9. ISSN 1110-757X http://dx.doi.org/10.1155/2014/107109 |
| spellingShingle | QA75.5-76.95 Electronic computers. Computer science Jahani, Shahram Samsudin, Azman Subramanian, Kumbakonam Govindarajan Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications |
| title | Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications |
| title_full | Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications |
| title_fullStr | Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications |
| title_full_unstemmed | Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications |
| title_short | Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications |
| title_sort | efficient big integer multiplication and squaring algorithms for cryptographic applications |
| topic | QA75.5-76.95 Electronic computers. Computer science |
| url | http://eprints.usm.my/38934/ http://eprints.usm.my/38934/ http://eprints.usm.my/38934/1/Efficient_Big_Integer_Multiplication_and_Squaring_Algorithms_for_Cryptographic_Applications.pdf |