Parallel crypto-devices for GF(p) elliptic curve multiplication resistant against side channel attacks

All elliptic curve cryptographic schemes are based on scalar multiplication of points, and hence its faster computation signifies faster operation. This paper proposes two different parallelization techniques to speedup the GF(p) elliptic curve multiplication in affine coordinates and the corresponding architectures. The proposed implementations are capable of resisting different side channel attacks based on time and power analysis. The 160, 192, 224 and 256 bits implementations of both the architectures have been synthesized and simulated for both FPGA and 0.13@m CMOS ASIC. The final designs have been prototyped on a Xilinx Virtex-4 xc4vlx200-12ff1513 FPGA board and performance analyzes carried out. The experimental result and performance comparison show better throughput of the proposed implementations as compared to existing reported architectures.

[1]  Nigel P. Smart,et al.  Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series) , 2005 .

[2]  Blakely.  A Computer Algorithm for Calculating the Product AB Modulo M , 1983, IEEE Transactions on Computers.

[3]  Dipanwita Roy Chowdhury,et al.  A Robust GF(p) Parallel Arithmetic Unit for Public Key Cryptography , 2007 .

[4]  Tim Kerins,et al.  Fast Modular Division for Application in ECC on Reconfigurable Logic , 2003, FPL.

[5]  G. R. Blakley,et al.  A Computer Algorithm for Calculating the Product AB Modulo M , 1983, IEEE Trans. Computers.

[6]  Atsuko Miyaji,et al.  Secure Elliptic Curve Exponentiation against RPA, ZRA, DPA, and SPA , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[7]  Tsuyoshi Takagi,et al.  Zero-Value Register Attack on Elliptic Curve Cryptosystem , 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[8]  Jean-Sébastien Coron,et al.  Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems , 1999, CHES.

[9]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[10]  P. L. Montgomery.  Modular multiplication without trial division , 1985 .

[11]  Tsuyoshi Takagi,et al.  A Fast Parallel Elliptic Curve Multiplication Resistant against Side Channel Attacks , 2002, Public Key Cryptography.

[12]  Paul C. Kocher,et al.  Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems , 1996, CRYPTO.

[13]  Christophe Clavier,et al.  Universal Exponentiation Algorithm , 2001, CHES.

[14]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .

[15]  Francisco Rodríguez-Henríquez,et al.  Cryptographic Algorithms on Reconfigurable Hardware , 2010 .

[16]  Marc Joye,et al.  Low-cost solutions for preventing simple side-channel analysis: side-channel atomicity , 2004, IEEE Transactions on Computers.

[17]  Paul C. Kocher,et al.  Differential Power Analysis , 1999, CRYPTO.

[18]  Tim Kerins,et al.  An FPGA implementation of a GF(p) ALU for encryption processors , 2004, Microprocess. Microsystems.

[19]  Francisco Rodríguez-Henríquez,et al.  Cryptographic Algorithms on Reconfigurable Hardware (Signals and Communication Technology) , 2006 .

[20]  Bart Preneel,et al.  Power-Analysis Attacks on an FPGA - First Experimental Results , 2003, CHES.

[21]  Ingrid Verbauwhede,et al.  A fast dual-field modular arithmetic logic unit and its hardware implementation , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[22]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[23]  Alfred Menezes,et al.  Guide to Elliptic Curve Cryptography , 2004, Springer Professional Computing.

[24]  Marc Joye,et al.  Protections against Differential Analysis for Elliptic Curve Cryptography , 2001, CHES.

[25]  Louis Goubin,et al.  A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems , 2003, Public Key Cryptography.

[26]  Ingrid Verbauwhede,et al.  Balanced point operations for side-channel protection of elliptic curve cryptography , 2005 .

[27]  Christof Paar,et al.  A Scalable GF(p) Elliptic Curve Processor Architecture for Programmable Hardware , 2001, CHES.

[28]  Kenneth R. Sloan.  Comments on "A Computer Algorithm for Calculating the Product AB Modulo M" , 1985, IEEE Trans. Computers.

[29]  Berk Sunar,et al.  Low-Power Elliptic Curve Cryptography Using Scaled Modular Arithmetic , 2004, CHES.

[30]  Akashi Satoh,et al.  A Scalable Dual-Field Elliptic Curve Cryptographic Processor , 2003, IEEE Trans. Computers.

[31]  Joos Vandewalle,et al.  Hardware implementation of an elliptic curve processor over GF(p) , 2003, Proceedings IEEE International Conference on Application-Specific Systems, Architectures, and Processors. ASAP 2003.