A New Double Point Multiplication Algorithm and Its Application to Binary Elliptic Curves with Endomorphisms
We present a new double point multiplication algorithm based on differential addition chains. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We discuss deploying our scheme in a hardware implementation of single point mul...
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| Vydáno v: | IEEE transactions on computers Ročník 63; číslo 10; s. 2614 - 2619 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.10.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9340, 1557-9956 |
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| Abstract | We present a new double point multiplication algorithm based on differential addition chains. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We discuss deploying our scheme in a hardware implementation of single point multiplication on binary elliptic curves with efficiently computable endomorphisms. Based on operation counts, we expect to gain accelerations of 30% and 18% for computing single point multiplication with and without availability of parallel multipliers, respectively, and these results are verified in our implementations. |
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| AbstractList | We present a new double point multiplication algorithm based on differential addition chains. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We discuss deploying our scheme in a hardware implementation of single point multiplication on binary elliptic curves with efficiently computable endomorphisms. Based on operation counts, we expect to gain accelerations of 30% and 18% for computing single point multiplication with and without availability of parallel multipliers, respectively, and these results are verified in our implementations. |
| Author | Karabina, Koray Azarderakhsh, Reza |
| Author_xml | – sequence: 1 givenname: Reza surname: Azarderakhsh fullname: Azarderakhsh, Reza email: rxaeec@rit.edu organization: Dept. of Comput. Eng., Rochester Inst. of Technol., Rochester, NY, USA – sequence: 2 givenname: Koray surname: Karabina fullname: Karabina, Koray email: kkarabina@fau.edu organization: Dept. of Math. Sci., Florida Atlantic Univ., Boca Raton, FL, USA |
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| References | ref12 stam (ref13) 2003 menezes (ref3) 1996 montgomery (ref5) 1992 ref23 ref14 ref20 ref11 ref22 ref10 ref21 ref2 ref1 ref16 ref19 ref18 bernstein (ref8) 2006 m ller (ref4) 2001; 2259 hess (ref17) 2004; 7 ref9 ref6 knuth (ref15) 1997; 2 stam (ref7) 2003 |
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| SubjectTerms | Algorithm design and analysis Algorithms Availability Channels Counting differential addition chains double point multiplication Elliptic curve cryptography Elliptic curve cryptosystems Elliptic curves endomorphism Gain Hardware Multiplication Multipliers Resistance |
| Title | A New Double Point Multiplication Algorithm and Its Application to Binary Elliptic Curves with Endomorphisms |
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