Elliptic Curve Cryptosystems

2010 ◽  
pp. 239-257 ◽  
Author(s):  
Christof Paar ◽  
Jan Pelzl
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptosystems

Power Side-Channel Analysis of RNS GLV ECC Using Machine and Deep Learning Algorithms

2021 ◽  
Vol 21 (3) ◽  
pp. 1-20
Author(s):  
Mohamad Ali Mehrabi ◽  
Naila Mukhtar ◽  
Alireza Jolfaei
Keyword(s):  
Deep Learning ◽  
Elliptic Curve ◽  
Smart Cities ◽  
Information Leakage ◽  
Side Channel ◽  
Side Channel Attacks ◽  
Public Key Cryptosystems ◽  
Elliptic Curve Cryptosystems ◽  
Hardware Implementations ◽  
Substantial Progress

Many Internet of Things applications in smart cities use elliptic-curve cryptosystems due to their efficiency compared to other well-known public-key cryptosystems such as RSA. One of the important components of an elliptic-curve-based cryptosystem is the elliptic-curve point multiplication which has been shown to be vulnerable to various types of side-channel attacks. Recently, substantial progress has been made in applying deep learning to side-channel attacks. Conceptually, the idea is to monitor a core while it is running encryption for information leakage of a certain kind, for example, power consumption. The knowledge of the underlying encryption algorithm can be used to train a model to recognise the key used for encryption. The model is then applied to traces gathered from the crypto core in order to recover the encryption key. In this article, we propose an RNS GLV elliptic curve cryptography core which is immune to machine learning and deep learning based side-channel attacks. The experimental analysis confirms the proposed crypto core does not leak any information about the private key and therefore it is suitable for hardware implementations.

An Area-Efficient Composite Field Inverter for Elliptic Curve Cryptosystems

2014 ◽  
pp. 218-237
Author(s):  
M. M. Wong ◽  
M. L. D. Wong
Keyword(s):  
Elliptic Curve ◽  
Complexity Analysis ◽  
Extension Field ◽  
Arithmetic Operations ◽  
Hardware Cost ◽  
Elliptic Curve Cryptosystems ◽  
Look Up Table ◽  
Composite Field ◽  
Optimal Saving ◽  
Area Efficient

This chapter presents a new area-efficient composite field inverter of the form GF(q1) with q=2n.m suitable for the hardware realization of an elliptic curve (EC) cryptosystem. Considering both the security aspect and the hardware cost required, the authors propose the utilization of the composite field GF(((22)2)41) for EC cryptosystem. For efficient implementation, they have derived a compact inversion circuit over GF(2164)=GF(((22)2)41) to achieve an optimal saving in the hardware cost required. Furthermore, the authors have also developed a composite field digit serial Sunar-Koc multiplier for the multiplication in the extension field. All of the arithmetic operations in the subfield GF(24) are performed in its isomorphic composite field, GF((22)2), leading to a full combinatorial implementation without resorting to the conventional look-up table approach. To summarize the work, the final hardware implementation and the complexity analysis of the inversion is reported towards the end of this chapter.

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