Abstract
Although it is one of the most popular signature schemes today, ECDSA presents a number of implementation pitfalls, in particular due to the very sensitive nature of the random value (known as the nonce) generated as part of the signing algorithm. It is known that any small amount of nonce exposure or nonce bias can in principle lead to a full key recovery: the key recovery is then a particular instance of Boneh and Venkatesan's hidden number problem (HNP). That observation has been practically exploited in many attacks in the literature, taking advantage of implementation defects or side-channel vulnerabilities in various concrete ECDSA implementations. However, most of the attacks so far have relied on at least 2 bits of nonce bias (except for the special case of curves at the 80-bit security level, for which attacks against 1-bit biases are known, albeit with a very high number of required signatures). In this paper, we uncover LadderLeak, a novel class of side-channel vulnerabilities in implementations of the Montgomery ladder used in ECDSA scalar multiplication. The vulnerability is in particular present in several recent versions of OpenSSL. However, it leaks less than 1 bit of information about the nonce, in the sense that it reveals the most significant bit of the nonce, but with probability
Original language | English |
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Title of host publication | Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security |
Publisher | ACM |
Pages | 225-242 |
Number of pages | 18 |
ISBN (Electronic) | 978-1-4503-7089-9 |
DOIs | |
Publication status | Published - 2 Nov 2020 |
Event | The 27th ACM Conference on Computer and Communications Security, 2020 - Online Duration: 9 Nov 2020 → 13 Nov 2020 Conference number: 27 https://sigsac.org/ccs/CCS2020/index.html |
Conference
Conference | The 27th ACM Conference on Computer and Communications Security, 2020 |
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Abbreviated title | CCS 2020 |
Period | 9/11/20 → 13/11/20 |
Internet address |
Keywords
- side-channel attack
- cache attack
- ECDSA
- OpenSSL
- Montgomery ladder
- hidden number problem
- Bleichenbacher’s attack
- generalized birthday problem