Enhanced Elliptic Curve Scalar Multiplication Secure Against Side Channel Attacks and Safe Errors

2017 ◽  
pp. 65-82 ◽  
Author(s):  
Jeremy Dubeuf ◽  
David Hely ◽  
Vincent Beroulle
Keyword(s):  
Elliptic Curve ◽  
Scalar Multiplication ◽  
Side Channel ◽  
Side Channel Attacks ◽  
Elliptic Curve Scalar Multiplication

scholarly journals Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xingran Li ◽  
Wei Yu ◽  
Bao Li
Keyword(s):  
Elliptic Curve ◽  
Efficient Algorithm ◽  
Multicore Processors ◽  
Scalar Multiplication ◽  
Side Channel ◽  
Elliptic Curve Cryptosystem ◽  
Side Channel Attacks ◽  
Binary Fields ◽  
Speed Up ◽  
Elliptic Curve Scalar Multiplication

Accelerating scalar multiplication has always been a significant topic when people talk about the elliptic curve cryptosystem. Many approaches have been come up with to achieve this aim. An interesting perspective is that computers nowadays usually have multicore processors which could be used to do cryptographic computations in parallel style. Inspired by this idea, we present a new parallel and efficient algorithm to speed up scalar multiplication. First, we introduce a new regular halve-and-add method which is very efficient by utilizing λ projective coordinate. Then, we compare many different algorithms calculating double-and-add and halve-and-add. Finally, we combine the best double-and-add and halve-and-add methods to get a new faster parallel algorithm which costs around 12.0% less than the previous best. Furthermore, our algorithm is regular without any dummy operations, so it naturally provides protection against simple side-channel attacks.

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.

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