Abstract
Elliptic Curve Cryptography (ECC) has established itself as the most preferred and secured cryptography algorithm for the secure data transfer and secure data storage in embedded system environment. Efficient implementation of point multiplication algorithm is crucial activity for designing area efficient, low footprint ECC cryptoprocessors. In this paper, an area efficient implementation of double point multiplication algorithm over binary elliptic curve is presented. Area analysis of double point multiplication algorithm based on differential addition chains method is carried out and area report is generated. Area optimization is achieved by using pipelined structure and by reutilizing idle resources from previous stages in processing unit. The proposed architecture for double point multiplication is implemented on Xilinx Virtex-4 FPGA device. Architecture is modeled in verilog-HDL and synthesized using Xilinx ISE 14.1 design software and is found to be more efficient in terms of area than the existing such architectures.
Highlights
Victor Miller and Neal Koblitz proposed the concept of elliptic curve cryptography in the mid of 1980‘s and was considered as a big step in public key cryptographic systems
The main advantage of Elliptic Curve Cryptography (ECC) over RSA is the usage of shorter key and it is aided with a drawback that the design for ECC when implemented in software performs at dead slow speed, whereas if the implementation is done in hardware, the process is much more efficient
ECC is the best choice for cryptographic hardware implementation
Summary
Victor Miller and Neal Koblitz proposed the concept of elliptic curve cryptography in the mid of 1980‘s and was considered as a big step in public key cryptographic systems. The main advantage of ECC over RSA is the usage of shorter key and it is aided with a drawback that the design for ECC when implemented in software performs at dead slow speed, whereas if the implementation is done in hardware, the process is much more efficient. ECC is the best choice for cryptographic hardware implementation Due to these many advantages of ECC, a number of hardware implementations have been proposed, and included in many standards such as IEEE 1363and NIST. An operation called point addition is defined on an elliptic curve. Using consecutive point additions, an operation called ―Elliptic curve point multiplication‖ is defined. The elliptic curve point doubling and point multiplication activities are shown in figure 2 and 3
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