A synthesis of side-channel attacks on elliptic curve cryptography in smart-cards

Elliptic curve cryptography in embedded systems is vulnerable to side-channel attacks. Those attacks exploit biases in various kinds of leakages, such as power consumption, electromagnetic emanation, execution time, ... The integration of countermeasures is required to thwart known attacks. No single countermeasure can cover the whole range of attacks; thus many of them shall be combined. However, as each of them has a non negligible cost, one cannot simply apply all of them. It is necessary to wisely select countermeasures, depending on the context and on the trade-off between security and performance. This paper summarizes the side-channel attacks and countermeasures on Elliptic Curve Cryptography. For each countermeasure, the cost in time and space is given. Some attacks are clarified such as the doubling attack; others are improved like the horizontal SVA, and new attacks are described like the horizontal attack against the unified formulae.