8-bit AVR Processor Research Articles

Fast Implementation of NIST P-256 Elliptic Curve Cryptography on 8-Bit AVR Processor

In this paper, we present a highly optimized implementation of elliptic curve cryptography (ECC) over NIST P-256 curve for an 8-bit AVR microcontroller. For improving the performance of ECC implementation, we focus on optimizing field arithmetics. In particular, we optimize the modular multiplication and squaring method exploiting the state-of-the-art optimization technique, namely range shifted representation (RSR). With optimized field arithmetics, we significantly improve the performance of scalar multiplication and set the speed record for execution time of variable base scalar multiplication over NIST P-256 curve. When compared with previous works, we achieve a performance gain of 17.3% over the best previous result on the same platform. Moreover, the execution time of our result is even faster than that over the NIST P-192 curve of the well-known TinyECC library. Our result shows that RSR can be applied to all field arithmetics and evaluate the impact of the adoption of RSR over the performance of scalar multiplication. Additionally, our implementation provides a high degree of regularity to withstand side-channel attacks.

Lightweight Implementations of NIST P-256 and SM2 ECC on 8-bit Resource-Constraint Embedded Device

Elliptic Curve Cryptography (ECC) now is one of the most important approach to instantiate asymmetric encryption and signature schemes, which has been extensively exploited to protect the security of cyber-physical systems. With the advent of the Internet of Things (IoT), a great deal of constrained devices may require software implementations of ECC operations. Under this circumstances, the SM2, a set of public key cryptographic algorithms based on elliptic curves published by Chinese Commercial Cryptography Administration Office, was standardized at ISO in 2017 to enhance the cyber-security. However, few research works on the implementation of SM2 for constrained devices have been conducted. In this work, we fill this gap and propose our efficient, secure, and compact implementation of scalar multiplication on a 256-bit elliptic curve recommended by the SM2, as well as a comparison implementation of scalar multiplication on the same bit-length elliptic curve recommended by NIST. We re-design some existent techniques to fit the low-end IoT platform, namely 8-bit AVR processors, and our implementations evaluated on the desired platform show that the SM2 algorithms have competitive efficiency and security with NIST, which would work well to secure the IoT world.

Montgomery multiplication and squaring for Optimal Prime Fields

Optimal Prime Fields (OPFs) are considered to be one of the best choices for lightweight elliptic curve cryptography implementations on resource-constraint embedded processors. In this paper, we revisit the efficient modular arithmetic over the special prime fields, and present improved implementations of modular multiplication and squaring for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) and Coarsely Integrated Sliding Block Doubling (OPF-CISBD) methods. The OPF-CIOC and OPF-CISBD methods follow the general ideas of (consecutive) operand caching and sliding block doubling techniques, respectively. The methods have been carefully optimized and redesigned for Montgomery multiplication and squaring in an integrated fashion. We then evaluate the practical performance of proposed methods on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC and OPF-CISBD methods outperform the previous best known results in ACNS'14 by a factor of 8% and 32%. Furthermore, our methods are implemented in a regular way which helps to reduce the leakage of side-channel information.

Karatsuba-Block-Comb technique for elliptic curve cryptography over binary fields

Efficient implementation of elliptic curve cryptography on resource-constrained microcontroller is considered to be one of the hot and challenging research topics because of the limited computing power and storages of target platforms and high computational costs of elliptic curve cryptography. In this paper, we focus on enhancing the performance of scalar multiplication over GF2m by suggesting a new technique for speeding up the performance of multiplication, called Karatsuba-Block-Comb KBC multiplication. KBC method combines both the advantages of Karatsuba algorithm and Block-Comb method. This technique replaces the part of expensive Block-Comb binary field multiplications with several cheap additions by following Karatsuba rule. In case of squaring, we describe an optimized squaring algorithm with 8-bit look-up table that is significantly faster than previous works with 4-bit look-up table. Both of the proposed approaches improve the best known results by a factor of 24.6% and 16.8% 160-bit operand over 8-bit AVR processor Atmel Corporation, San Jose, CA, USA, respectively. Finally, we realize the scalar multiplication over GF2163, which only requires 0.29s for a full scalar multiplication when the processor runs at 7.37MHz. This result outperforms the previous best implementation by a factor of 9.3%. The research results presented in this paper prove that it is also possible to achieve high performance over binary fields by combing the algorithm with sub-quadratic complexity. Furthermore, we suggest constant time KBC method. Block-Comb method does not provide constant time, and look-up table method is also vulnerable to memory address side channel attack. However, our method is establishing the scalar multiplication in 0.35s with high security against both attacks. Copyright © 2015 John Wiley & Sons, Ltd.