Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication
Cryptography via public key cryptosystems (PKC) has been widely used for providing services such as confality, authentication, integrity and non-repudiation. Other than security, computational efficiency is another major issue of concern. And for PKC, it is largely controlled by either modular expon...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Cogent OA
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/62242/ http://psasir.upm.edu.my/id/eprint/62242/1/Iterative%20sliding%20window%20method%20for%20shorter%20number.pdf |
| _version_ | 1848854592191725568 |
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| author | Noma, Adamu Muhammad Muhammed, Abdullah Ahmad Zukarnain, Zuriati Mohamed, Muhammad Afendee |
| author_facet | Noma, Adamu Muhammad Muhammed, Abdullah Ahmad Zukarnain, Zuriati Mohamed, Muhammad Afendee |
| author_sort | Noma, Adamu Muhammad |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Cryptography via public key cryptosystems (PKC) has been widely used for providing services such as confality, authentication, integrity and non-repudiation. Other than security, computational efficiency is another major issue of concern. And for PKC, it is largely controlled by either modular exponentiation or scalar multiplication operations such that found in RSA and elliptic curve cryptosystem (ECC), respectively. One approach to address this operational problem is via concept of addition chain (AC), in which the exhaustive single operation involving large integer is reduced into a sequence of operations consisting of simple multiplications or additions. Existing techniques manipulate the representation of integer into binary and m-ary prior performing the series of operations. This paper proposes an iterative variant of sliding window method (SWM) form of m-ary family, for shorter sequence of multiplications corresponding to the modular exponentiation. Thus, it is called an iterative SWM. Moreover, specific for ECC that imposes no extra resource for point negation, the paper proposes an iterative recoded SWM, operating on integers recoded using a modified non-adjacent form (NAF) for speeding up the scalar multiplication. The relative behaviour is also examined, of number of additions in scalar multiplications, with the integers hamming weight. The proposed iterative SWM methods reduce the number of operations by up to 6% than the standard SWM heuristic. They result to even shorter chains of operations than ones returned by many metaheuristic algorithms for the AC. |
| first_indexed | 2025-11-15T11:12:19Z |
| format | Article |
| id | upm-62242 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:12:19Z |
| publishDate | 2017 |
| publisher | Cogent OA |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-622422019-05-21T06:21:36Z http://psasir.upm.edu.my/id/eprint/62242/ Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication Noma, Adamu Muhammad Muhammed, Abdullah Ahmad Zukarnain, Zuriati Mohamed, Muhammad Afendee Cryptography via public key cryptosystems (PKC) has been widely used for providing services such as confality, authentication, integrity and non-repudiation. Other than security, computational efficiency is another major issue of concern. And for PKC, it is largely controlled by either modular exponentiation or scalar multiplication operations such that found in RSA and elliptic curve cryptosystem (ECC), respectively. One approach to address this operational problem is via concept of addition chain (AC), in which the exhaustive single operation involving large integer is reduced into a sequence of operations consisting of simple multiplications or additions. Existing techniques manipulate the representation of integer into binary and m-ary prior performing the series of operations. This paper proposes an iterative variant of sliding window method (SWM) form of m-ary family, for shorter sequence of multiplications corresponding to the modular exponentiation. Thus, it is called an iterative SWM. Moreover, specific for ECC that imposes no extra resource for point negation, the paper proposes an iterative recoded SWM, operating on integers recoded using a modified non-adjacent form (NAF) for speeding up the scalar multiplication. The relative behaviour is also examined, of number of additions in scalar multiplications, with the integers hamming weight. The proposed iterative SWM methods reduce the number of operations by up to 6% than the standard SWM heuristic. They result to even shorter chains of operations than ones returned by many metaheuristic algorithms for the AC. Cogent OA 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/62242/1/Iterative%20sliding%20window%20method%20for%20shorter%20number.pdf Noma, Adamu Muhammad and Muhammed, Abdullah and Ahmad Zukarnain, Zuriati and Mohamed, Muhammad Afendee (2017) Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication. Cogent Engineering, 4 (1). art. no. 1304499. pp. 1-13. ISSN 2331-1916 https://www.tandfonline.com/doi/full/10.1080/23311916.2017.1304499 10.1080/23311916.2017.1304499 |
| spellingShingle | Noma, Adamu Muhammad Muhammed, Abdullah Ahmad Zukarnain, Zuriati Mohamed, Muhammad Afendee Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication |
| title | Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication |
| title_full | Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication |
| title_fullStr | Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication |
| title_full_unstemmed | Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication |
| title_short | Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication |
| title_sort | iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication |
| url | http://psasir.upm.edu.my/id/eprint/62242/ http://psasir.upm.edu.my/id/eprint/62242/ http://psasir.upm.edu.my/id/eprint/62242/ http://psasir.upm.edu.my/id/eprint/62242/1/Iterative%20sliding%20window%20method%20for%20shorter%20number.pdf |