Parallel Itoh-Tsujii multiplicative inversion algorithm for a special class of trinomials

Designs, Codes, and Cryptography

Volumn 45, Issue 1, 2007, Pages 19-37

  Rodríguez Henríquez, Francisco ^a   Morales Luna, Guillermo ^a   Saqib, Nazar A ^b   Cruz Cortés, Nareli ^c  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

^b NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

^c INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

Cryptography; FPGA design; Multiplicative inversion; Polynomial basis

Indexed keywords

ALGORITHMS; COMPUTER HARDWARE; CRYPTOGRAPHY; FIELD PROGRAMMABLE GATE ARRAYS (FPGA); POLYNOMIALS;

ITOH-TSUJII ALGORITHM; MULTIPLICATIVE INVERSION; POLYNOMIAL BASIS; TRINOMIALS;

INVERSE PROBLEMS;

EID: 34548500763     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-007-9073-6     Document Type: Article

References (21)

1. m ) using normal basis. Inf Comput 78: 171-177
2. m ). IEEE Trans Comput 38(10): 1383-1386
3. m ) using normal basis. IEEE Trans Comput 50(5): 394-398
4. Hasan MA (2001) Efficient computation of multiplicative inverses for cryptographic applications. In: Proceedings of the 15th IEEE symposium on computer arithmetic, Vail, Colorado, USA
5. m ). IEE Electron Lett 33(3): 196-197
6. n ). In: Proceedings of the Cryptographic hardware and embedded systems-CHES 2002, 4th international workshop, redwood shores, vol 2523, CA, USA, pp 484-499
7. m ). In: Proceedings of the international symposium on information technology (ITCC 2005), vol 1, Las Vegas, Nevada, USA, pp 574-579
8. Guajardo J and Paar C (2002). Itoh-tsujii inversion in standard basis and its application in cryptography and codes. Des Codes Cryptogr 25: 207-216
9. Knuth DE (1997). The art of computer programming. Addison-Wesley, Reading, MA
10. m ) for all trinomials. Cryptology ePrint Archive, Report 2006/133, http://eprint.iacr.org/.
11. m ). In: Stinson, STD (eds) Workshop on selected areas in cryptography (SAC 2000), vol LNCS 2012., pp 118-129. Springer, Berlin
12. Wu H (1999) Low complexity bit-parallel finite field arithmetic using polynomial basis. in: Proceedings of the cryptographic hardware and embedded systems-CHES 1999, first international workshop. ser. Lecture notes in computer science, vol 1717. Springer, Berlin, pp 280-291
13. IEEE standards documents (2004) IEEE P1363: standard specifications for public key cryptography. Draft Version D18. IEEE, http://grouper.ieee.org/ groups/1363/
14. Fong K, Hankerson D, López J and Menezes A (2004). Field inversion and point halving revisited. IEEE Trans Comput 53(8): 1047-1059
15. Fong K, Hankerson D, López J and Menezes A (2004). Field inversion and point halving revisited. IEEE Trans Comput 53(8): 1047-1059
16. Menezes AJ, Oorschot PC and Vanstone SA (1996). Handbook of applied cryptography. CRC Press, Boca Raton, FL
17. Rodríguez-Henríquez F, Morales-Luna G, Saqib NA, Cruz-Cortés N (2007) A parallel version of the Itoh-Tsujii multiplicative inversion algorithm. In: Proceedings of International Workshop on Applied Reconfigurable Computing (ARC2007), Lecture notes in computer science, Mangaratiba, Brazil, March 2007, Vol 4419. Springer, pp. 226-237
18. m ). Elsevier J Microprocessors Microsyst 28(8): 329-339
19. Goodman J and Chandrakasan AP (2001). An energy-efficient reconfigurable public-key cryptography processor. IEEE J Solid-State Circuits 36(11): 1808-1820
20. Bednara M, Daldrup M, Shokrollahi J, Teich J, von zur Gathen J (2002) Reconfigurable implementation of elliptic curve crypto algorithms. In: Proceedings of the 9th reconfigurable architectures workshop (RAW-02), Fort Lauderdale, FL, USA
21. Lutz J (2003) High performance elliptic curve cryptographic co-processor. Master's thesis, University of Waterloo