Highly Area-Efficient Implementation of Modular Multiplication for Elliptic Curve Cryptography

2020 ◽  
Author(s):  
Md. Sazedur Rahman ◽  
Md. Selim Hossain
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Efficient Implementation ◽  
Modular Multiplication ◽  
Area Efficient

scholarly journals Efficient implementation of modular multiplication over 192-bit NIST prime for 8-bit AVR-based sensor node

2020 ◽  
Author(s):  
Dong-won Park ◽  
Seokhie Hong ◽  
Nam Su Chang ◽  
Sung Min Cho
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Sensor Node ◽  
Efficient Implementation ◽  
Memory Access ◽  
Modular Multiplication ◽  
Reduction Operation ◽  
Computational Overhead ◽  
Integer Representation ◽  
Constrained Devices

Abstract Modular multiplication is one of the most time-consuming operations that account for almost 80% of computational overhead in a scalar multiplication in elliptic curve cryptography. In this paper, we present a new speed record for modular multiplication over 192-bit NIST prime P-192 on 8-bit AVR ATmega microcontrollers. We propose a new integer representation named Range Shifted Representation (RSR) which enables an efficient merging of the reduction operation into the subtractive Karatsuba multiplication. This merging results in a dramatic optimization in the intermediate accumulation of modular multiplication by reducing a significant amount of unnecessary memory access as well as the number of addition operations. Our merged modular multiplication on RSR is designed to have two duplicated groups of 96-bit intermediate values during accumulation. Hence, only one accumulation of the group is required and the result can be used twice. Consequently, we significantly reduce the number of load/store instructions which are known to be one of the most time-consuming operations for modular multiplication on constrained devices. Our implementation requires only 2888 cycles for the modular multiplication of 192-bit integers and outperforms the previous best result for modular multiplication over P-192 by a factor of 17%. In addition, our modular multiplication is even faster than the Karatsuba multiplication (without reduction) which achieved a speed record for multiplication on AVR processor.

scholarly journals Area-Time Efficient Hardware Implementation of Modular Multiplication for Elliptic Curve Cryptography

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 73898-73906 ◽  
Author(s):  
MD. Mainul Islam ◽  
MD. Selim Hossain ◽  
MD. Shahjalal ◽  
MOH. Khalid Hasan ◽  
Yeong Min Jang
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Hardware Implementation ◽  
Modular Multiplication

scholarly journals Efficient implementation of elliptic curve cryptography in wireless sensors

2010 ◽  
Vol 4 (2) ◽  
pp. 169-187 ◽  
Author(s):  
Diego Aranha ◽  
Ricardo Dahab ◽  
Julio López ◽  
Leonardo Oliveira
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Wireless Sensors ◽  
Efficient Implementation
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