Biblio

The core operation of public-key cryptosystem e.g. elliptic curve cryptography (ECC) is the modular multiplication. It is the heavy computational block and the most costly cryptographic operation. Area-Efficient hardware architecture of 256-bit modified interleaved modular multiplication (IMM) is represented in this research. The novelty of this work is the device area minimization with keeping computational time as minimum as possible i.e., 2.09 μs for ECC with Koblitz Curve. In this research, IMM is implemented using a fewer number of resources such as 421 slices, 514 FF pairs, 522 registers, 1770 LUTs, and 1463 LUT-FF pairs. This hardware implementation provides a maximum frequency of 122.883 MHz and area-time (AT) product 0.879 and throughput rate 122.49 Mbps on Virtex-7 FPGA technology which is better than the other related recent works. The proposed design saves approximately 61.75% to 93.16% slice LUTs, 95.76% to 133.69% LUT-FF pairs, and 103.8% to 168.65% occupied slices on the Virtex-7 FPGA for the 256-bit prime field. This proposed hardware implementation design also keeps less AT product which is the most crucial parameter for ECC operation. To our best knowledge, this design provides better performance than the recently available designs for IMM for ECC operation.

Digital signature over elliptic curve is one of the most important applications of security because it is effective. Recently, it has been developed and defined in the various standard of security. The application of the digital signature are signer authentication, data integrity, and non-repudiation. Currently, the requirements to implement authentication process on a computer hardware with limited resource such as energy, memory and computing power are increasing. The developer should consider these factors along with security factor for the effective implement on the computer hardware with limited resource. In this paper, we propose the Schnorr signature scheme using Koblitz curve over a field of characteristic two. The advantage of Schnorr signature scheme is a good combination with Koblitz curve over a field of characteristic two, therefore its arithmetic can be performed in any computer. Moreover, we use Double-and-Add scalar multiplication to reduce time in the process of systems. In addition, this paper shows a result of time in the process of the system to compare the performance of the Schnorr signature scheme on Koblitz curve using Double-andAdd scalar multiplication with the Schnorr signature scheme on Koblitz curve using typical scalar multiplication. The result of this study is that both systems working correctly. However, the Schnorr signature scheme on Koblitz curve using Double-andAdd performs better in time efficiency than of Schnorr signature scheme on Koblitz curve using typical scalar multiplication.