This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Achieving NTRU with Montgomery Multiplication
April 2003 (vol. 52 no. 4)
pp. 440-448

Abstract—In this paper, we propose a new unified architecture that utilizes the Montgomery Multiplication algorithm to perform a modular multiplication for both integers and binary polynomials and NTRU's polynomial multiplications. The unified design is capable of supporting a majority of public-key cryptosystems such as NTRU, RSA, Diffie-Hellman key exchange, and Elliptic Curve schemes, among others. Furthermore, the architecture is highly efficient in terms of area and speed.

[1] R.L. Rivest,A. Shamir, and L.A. Adleman,"A Method for Obtaining Digital Signatures and Public Key Cryptosystems," Comm. ACM, vol. 21, pp. 120-126, 1978.
[2] N. Koblitz, “Elliptic Curve Cryptosystems,” Math. Computation, vol. 48, pp. 203-209, 1987.
[3] A.J. Menezes, Elliptic Curve Public Key Cryptosystems. Boston: Kluwer Academic, 1993.
[4] J. Hoffstein, J. Pipher, and J.H. Silverman, “NTRU: A Ring Based Public Key Cryptosystem,” Proc. Algorithmic Number Theory: Third Int'l Symp. (ANTS 3), J.P. Buhler, ed., pp. 267-288, June 1998.
[5] P.L. Montgomery, “Modular Multiplication without Trial Division,” Math. Computation, vol. 44, pp. 519-521, Apr. 1985.
[6] Ç.K. Koç and T. Acar, “Montgomery Multplication in$\big. GF(2^k)\bigr.$,” Design, Codes, and Cryptography, vol. 14, no. 1, pp. 57-69, 1998.
[7] E. Savas, A.F. Tenca, and Ç.K. Koç, “A Scalable and Unified Multiplier Architecture for Finite Fields$\big. GF(p)\bigr.$and$\big. GF(2^m)\bigr.$,” Proc. Workshop Cryptographic Hardware and Embedded Systems (CHES 2000), Ç.K. Koçand C. Paar, eds., pp. 277-292, 2000.
[8] G. Gaubatz, “Versatile Montgomery Multiplier Architectures,” master's thesis, Electrical and Computer Eng. Dept., Worcester Polytechnic Inst., Worcester, Mass., Apr. 2002.
[9] J. Hoffstein and J.H. Silverman, “Optimizations for NTRU,” Proc. Public Key Cryptography and Computational Number Theory, Sept. 2000.
[10] C.K. Koc, T. Acar, and B. Kaliski, “Analyzing and Comparing Montgomery Multiplication Algorithms,” IEEE Micro, vol. 16, no. 3, pp. 26-33, June 1996.
[11] M. Graphics, “ADK HTML Data Book TSMC 0.35 Micron FAST,” 2001.
[12] W. Diffie and M.E. Hellman, New Directions in Cryptography IEEE Trans. Information Theory, vol. 22, pp. 644-654, 1976.

Index Terms:
Cryptography, NTRU, unified architectures, Montgomery multipliers, Montgomery multiplication, finite fields.
Citation:
Colleen O'Rourke, Berk Sunar, "Achieving NTRU with Montgomery Multiplication," IEEE Transactions on Computers, vol. 52, no. 4, pp. 440-448, April 2003, doi:10.1109/TC.2003.1190585
Usage of this product signifies your acceptance of the Terms of Use.