IACR News item: 25 May 2020
Diego F. Aranha, Felipe Rodrigues Novaes, Akira Takahashi, Mehdi Tibouchi, Yuval Yarom
ePrint Report
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 $<1$. Exploiting such a mild leakage would be intractable using techniques present in the literature so far. However, we present a number of theoretical improvements of the Fourier analysis approach to solving the HNP (an approach originally due to Bleichenbacher), and this lets us practically break LadderLeak-vulnerable ECDSA implementations instantiated over the sect163r1 and NIST P-192 elliptic curves. In so doing, we achieve several significant computational records in practical attacks against the HNP.
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 $<1$. Exploiting such a mild leakage would be intractable using techniques present in the literature so far. However, we present a number of theoretical improvements of the Fourier analysis approach to solving the HNP (an approach originally due to Bleichenbacher), and this lets us practically break LadderLeak-vulnerable ECDSA implementations instantiated over the sect163r1 and NIST P-192 elliptic curves. In so doing, we achieve several significant computational records in practical attacks against the HNP.
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