High-Performance Pipelined Architecture of Point Multiplication on Koblitz Curves

This work has proposed a 4-stage pipelined architecture to achieve an optimized throughput over area ratio for point multiplication (PM) computation in binary huff curves (BHC) cryptography. The original mathematical formulation of BHC is revisited with an objective to reduce the required area. Consequently, a simplified formulation of BHC is obtained with 43% reduction in the hardware resources. As far as the throughput is concerned, it is improved first by reducing the critical path and second by minimizing the number of clock cycles (CCs) required to compute one PM. The critical path is reduced through the placement of pipeline registers, whereas the number of required CCs are minimized through an efficient scheduling of computations. These two factors i.e., the area reduction and throughput optimizations, have resulted in maximizing the throughput over area ratio. The proposed pipelined architecture is implemented over [Formula: see text] field, using standard NIST curve parameters. The architecture is modeled in Verilog and synthesized using Xilinx (ISE 14.7) design tool on Virtex 7 FPGA. The implementation results show that 17% improvement in clock frequency, 13% reduction in the time required to compute one PM and 2.6% improvement in throughput/area are achieved when compared with the most recent state of the art solutions.

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The Construction of ElGamal over Koblitz Curve

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.931-932.1441 ◽

2014 ◽

Vol 931-932 ◽

pp. 1441-1446 ◽

Cited By ~ 1

Author(s):

Krissanee Kamthawee ◽

Bhichate Chiewthanakul

Keyword(s):

Elliptic Curve ◽

Elliptic Curves ◽

Discrete Logarithm ◽

Scalar Multiplication ◽

Computer Hardware ◽

Point Multiplication ◽

Koblitz Curves ◽

Elliptic Curve Cryptosystems ◽

Elgamal Cryptosystem ◽

Primary Advantage

Recently elliptic curve cryptosystems are widely accepted for security applications key generation, signature and verification. Cryptographic mechanisms based on elliptic curves depend on arithmetic involving the points of the curve. it is possible to use smaller primes, or smaller finite fields, with elliptic curves and achieve a level of security comparable to that for much larger integers. Koblitz curves, also known as anomalous binary curves, are elliptic curves defined over F2. The primary advantage of these curves is that point multiplication algorithms can be devised that do not use any point doublings. The ElGamal cryptosystem, which is based on the Discrete Logarithm problem can be implemented in any group. In this paper, we propose the ElGamal over Koblitz Curve Scheme by applying the arithmetic on Koblitz curve to the ElGamal cryptosystem. The advantage of this scheme is that point multiplication algorithms can be speeded up the scalar multiplication in the affine coodinate of the curves using Frobenius map. It has characteristic two, therefore it’s arithmetic can be designed in any computer hardware. Moreover, it has more efficient to employ the TNAF method for scalar multiplication on Koblitz curves to decrease the number of nonzero digits. It’s security relies on the inability of a forger, who does not know a private key, to compute elliptic curve discrete logarithm.

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