Signed Binary Representations Revisited

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3152, Issue , 2004, Pages 123-139

  Okeya, Katsuyuki ^a   Schmidt Samoa, Katja ^a   Spahn, Christian ^b   Takagi, Tsuyoshi ^b  

^a HITACHI LTD   (Japan)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Addition subtraction chains; Efficient computation; Elliptic curve cryptosystem; Exponentiation; Left to right; Mutual opposite form (MOF); Non adjacent form (NAF); Scalar multiplication; Signed binary

Indexed keywords

COMMUNICATION CHANNELS (INFORMATION THEORY); CRYPTOGRAPHY; GEOMETRY; GROUP THEORY; JAVA PROGRAMMING LANGUAGE;

EFFICIENT COMPUTATION; ELLIPTIC CURVE CRYPTOSYSTEM; EXPONENTIATIONS; LEFT-TO-RIGHT; MUTUAL OPPOSITE FORM; NON-ADJACENT FORM; SCALAR MULTIPLICATION; SIGNED BINARIES;

BINS;

EID: 35048856946     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-28628-8_8     Document Type: Article

References (24)

1. [Avi61] Aviziensis, A., Signed digit number representations for fast parallel arithmetic, IRE Trans. Electron. Comput., 10:389-400, (1961).
2. [BSS99] Blake, I., Seroussi, G., and Smart, N., Elliptic Curves in Cryptography, Cambridge University Press, 1999.
3. [BHLM01] Brown, M., Hankerson, D., Lopez, J., and Menezes, A., Software Implementation of the NIST Elliptic Curves Over Prime Fields, Topics in Cryptology - CT-RSA 2001, LNCS 2020, (2001), 250-265.
4. [Boo51] Booth, A., A signed binary multiplication technique, Journ. Mech. and Applied Math., 4(2), (1951), 236-240.
5. [CMO98] Cohen, H., Miyaji, A., and Ono, T., Efficient Elliptic Curve Exponentiation Using Mixed Coordinates, Advances in Cryptology - ASIACRYPT '98, LNCS1514, (1998), 51-65.
6. [EK94] Egecioglu, Ö, and Koc, C, Exponentiation using Canonical Recoding, Theoretical Computer Science, 129(2), (1994), 407-417.
7. [Gor98] Gordon, D., A survey of fast exponentiation methods, Journal of Algorithms, vol.27, (1998), 129-146.
8. [IEEE] IEEE P1363, Standard Specifications for Public-Key Cryptography, http://groupe.ieee.org/groups/1363/
9. [JM89] Jedwab, J., and Mitchell, C.J., Minimum Weight Modified Signed-digit Representations and Fast Exponentiation, Electronics Letters 25, (1989), 1171-1172.
10. [JY00] Joye, M., and Yen, S.-M., Optimal Left-to-Right Binary Signed-digit Exponent Recoding, IEEE Transactions on Computers 49(7), (2000), 740-748.
11. [Knu81] Knuth, D. E., The art of computer programmming, vol. 2, Seminumerical Algorithms, 2nd ed., Addison-Wesley, Reading, Mass. (1981).
12. [Kob87] Koblitz, N., Elliptic Curve Cryptosystems, Math. Comp. 48, (1987), 203-209.
13. [KT92] Koyama, K. and Tsuruoka, Y., Speeding Up Elliptic Curve Cryptosystems using a Signed Binary Windows Method, Advances in Cryptology -CRYPTO '92, LNCS740, (1992), 345-357.
14. [Mil86] Miller, V.S., Use of Elliptic Curves in Cryptography, Advances in Cryptology - CRYPTO '85, LNCS218, (1986), 417-426.
15. [MO90] Morain, P., Olivos, J., Speeding Up the Computations on an Elliptic Curve using Addition-Subtraction Chains, Informa. Theor. Appl., 24, (1990), pp.531-543.
16. [MOC97] Miyaji, A., Ono, T., and Cohen, H., Efficient Elliptic Curve Exponentiation, Information and Communication Security, ICICS 1997, LNCS 1334, (1997), 282-291.
17. [MOV96] Menezes, A., van Oorschot, P. and Vanstone, S., Handbook of Applied Cryptography, CRC Press, 1996.
18. [Möl02] Möller, B., Improved Techniques for Fast Exponentiation, The 5th International Conference on Information Security and Cryptology (ICISC 2002), LNCS 2587, (2003), 298-312.
19. [OCo99] O'Connor, L., An Analysis of Exponentiation Based on Formal Languages, Advances in Cryptology - EUROCRYPT '99, LNCS1592, (1999), 375-388.
20. [OSST04] Okeya, K., Schmidt-Samoa, K., Spahn, C., Takagi, T., Signed Binary Representations Revisited, Cryptology ePrint Archive (2004). http://eprint.iacr.org/
21. [Pro00] Prodinger, H., On Binary Representations of Integers with Digits {-1,0-1}, Integers: Electronic Journal of Combinatorial Number Theory 0, (2000)
22. [Rei60] Reitwiesner, G. W., Binary arithmetic, Advances in Computers, vol.1, (1960), 231-308.
23. [SolOO] Solinas, J.A., Efficient Arithmetic on Koblitz Curves, Designs, Codes and Cryptography, 19, (2000), 195-249.
24. [WMPW98] Win, E., Mister, S., Preneel, B., and Wiener, M., On the Performance of Signature Schemes Based on Elliptic Curves, Algorithmic Number Theory, ANTS-III, LNCS 1423, (1998), 252-266.