Side-Channel Analysis of SM2

Tuveri, Nicola; Hassan, Sohaib ul; García, Cesar Pereida; Brumley, Billy Bob

doi:10.1145/3274694.3274725

Cited by 14 publications

(4 citation statements)

References 61 publications

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“…Prime curves. In curves defined over F p for large prime p, OpenSSL 1.0.2u employs the Montgomery ladder when precomputation is turned off, a scenario prevalent in practice since precomputation must be manually turned on for a certain point (typically a fixed generator) [67]. Parameters affected are NIST curves P-192, P-224, P-384 and P-521; and SECG curves secp192k1 and secp256k1 (i.e.…”

Section: Cache-timing Vulnerabilities In Openssl's Implementationmentioning

confidence: 99%

LadderLeak: Breaking ECDSA with Less than One Bit of Nonce Leakage

Aranha

Novaes

Takahashi

et al. 2020

Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security

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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 sidechannel 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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Section: Cache-timing Vulnerabilities In Openssl's Implementationmentioning

confidence: 99%

LadderLeak: Breaking ECDSA with Less than One Bit of Nonce Leakage

Aranha

Novaes

Takahashi

et al. 2020

Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security

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“…This feature could be interpreted as this model requires knowing one algorithm input to recover some bits of the other, especially because until now, it was only used under this scenario. For instance, in [ACSS17] and [Tuv+18] it was used to cryptanalyze modular inversion operations on secret data in DSA-like signature algorithms, where the modulus (one input) is known to the attacker. Also, in [Ald+19a] it was used to recover RSA private keys during generation: d = e −1 mod (p − 1)(q − 1), where the RSA public exponent, e, is also known to the attacker.…”

Section: Binary Gcd Algorithm and Side-channel Analysismentioning

confidence: 99%

When one vulnerable primitive turns viral: Novel single-trace attacks on ECDSA and RSA

Aldaya

Brumley

2020

TCHES

Self Cite

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Microarchitecture based side-channel attacks are common threats nowadays. Intel SGX technology provides a strong isolation from an adversarial OS, however, does not guarantee protection against side-channel attacks. In this paper, we analyze the security of the mbedTLS binary GCD algorithm, an implementation that offers interesting challenges when compared for example with OpenSSL, due to the usage of very tight loops in the former. Using practical experiments we demonstrate the mbedTLS binary GCD implementation is vulnerable to side-channel analysis using the SGX-Step framework against mbedTLS based SGX enclaves.We analyze the security of some use cases of this algorithm in this library, resulting in the discovery of a new vulnerability in the ECDSA code path that allows a single-trace attack against this implementation. This vulnerability is three-fold interesting: It resides in the implementation of a countermeasure which makes it more dangerous due to the false state of security the countermeasure currently offers. It reduces mbedTLS ECDSA security to an integer factorization problem. An unexpected GCD call inside the ECDSA code path compromises the countermeasure. We also cover an orthogonal use case, this time inside the mbedTLS RSA code path during the computation of a CRT parameter when loading a private key. The attack also exploits the binary GCD implementation threat, showing how a single vulnerable primitive leads to multiple vulnerabilities. We demonstrate both security threats with end-to-end attacks using 1000 trials each, showing in both cases single-trace attacks can be achieved with success rates very close to 100%.

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“…In theory the latticebased cryptanalysis described below can work even with a 2-bit leak [NS03], however, exploiting this small (fewer than three bits) leak for 256-bit elliptic curves has not been demonstrated in practice [TTA18]. On the other hand, exploiting a leak of at least three bits is a common practice [Ben+14,PGB17,Tuv+18,Ald+19b].…”

Section: Private Key Recovery Using Latticesmentioning

confidence: 99%

From A to Z: Projective coordinates leakage in the wild

Aldaya

García

Brumley

2020

TCHES

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At EUROCRYPT 2004, Naccache et al. showed that the projective coordinates representation of the resulting point of an elliptic curve scalar multiplication potentially allows to recover some bits of the scalar. However, this attack has received little attention by the scientific community, and the status of deployed mitigations to prevent it in widely adopted cryptography libraries is unknown. In this paper, we aim to fill this gap, by analyzing several cryptography libraries in this context. To demonstrate the applicability of the attack, we use a side-channel attack to exploit this vulnerability within libgcrypt in the context of ECDSA. To the best of our knowledge, this is the first practical attack instance. It targets the insecure binary extended Euclidean algorithm implementation using a microarchitectural side-channel attack that allows recovering the projective representation of the output point of scalar multiplication during ECDSA signature generation. We captured 100k traces to estimate the number of traces an attacker would need to compromise the libgcrypt ECDSA implementation, resulting in less than 2k for commonly used elliptic curve secp256r1, demonstrating the attack feasibility. During exploitation, we found two additional vulnerabilities. However, we remark the purpose of this paper is not merely exploiting a library but about providing an analysis on the projective coordinates vulnerability status in widely deployed open-source libraries, filling a gap between its original description in the academic literature and the adoption of countermeasures to thwart it in real-world applications.

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Side-Channel Analysis of SM2

Cited by 14 publications

References 61 publications

LadderLeak: Breaking ECDSA with Less than One Bit of Nonce Leakage

LadderLeak: Breaking ECDSA with Less than One Bit of Nonce Leakage

When one vulnerable primitive turns viral: Novel single-trace attacks on ECDSA and RSA

From A to Z: Projective coordinates leakage in the wild

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