Parallel modular exponentiation using load balancing without precomputation

The modular exponentiation operation of the current algorithms for asymmetric cryptography is the most expensive part in terms of computational cost. The RSA algorithm, for example, uses the modular exponentiation algorithm in encryption and decryption procedure. Thus, the overall performance of those asymmetric cryptosystems depends heavily on the performance of the specific algorithm used for modular exponentiation. This work proposes new parallel algorithms to perform this arithmetical operation and determines the optimal number of processors that yields the greatest speedup. The optimal number is obtained by balancing the processing load evenly among the processors. Practical implementations are also performed to evaluate the theoretical proposals.

[1]  Chae Hoon Lim,et al.  More Flexible Exponentiation with Precomputation , 1994, CRYPTO.

[2]  Nadia Nedjah,et al.  Efficient Parallel Modular Exponentiation Algorithm , 2002, ADVIS.

[3]  Nadia Nedjah,et al.  High-Performance Hardware of the Sliding-Window Method for Parallel Computation of Modular Exponentiations , 2009, International Journal of Parallel Programming.

[4]  Nadia Nedjah,et al.  Parallel computation of modular exponentiation for fast cryptography , 2007, Int. J. High Perform. Syst. Archit..

[5]  Joos Vandewalle,et al.  Comparison of Three Modular Reduction Functions , 1993, CRYPTO.

[6]  Joachim von zur Gathen Processor-Efficient Exponentiation in Finite Fields , 1992, Inf. Process. Lett..

[7]  E. Brickell,et al.  Fast Exponentiation with Precomputation: Algorithms and Lower Bounds , 1993 .

[8]  Ernest F. Brickell,et al.  Fast Exponentiation with Precomputation (Extended Abstract) , 1992, EUROCRYPT.

[9]  Ernest A. Brickell A survey of hardware implementations of RSA (abstract) , 1989, CRYPTO 1989.

[10]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[11]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[12]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[13]  Joachim von zur Gathen Computing Powers in Parallel , 1987, SIAM J. Comput..

[14]  Yookun Cho,et al.  Efficient parallel exponentiation in GF(2n) using normal basis representations , 2001, SPAA '01.

[15]  Joachim von zur Gathen Parallel algorithms for algebraic problems , 1983, STOC '83.

[16]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[17]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .