Digital Signature Schemes such as DSA, ECDSA, and RSA are widely deployed to protect the integrity of security protocols such as TLS, SSH, and IPSec. In TLS, for instance, RSA and (EC)DSA are used to sign the state of the agreed upon protocol parameters during the handshake phase. Naturally, RSA and (EC)DSA implementations have become the target of numerous attacks, including powerful side-channel attacks. Hence, cryptographic libraries were patched repeatedly over the years.Here we introduce Jolt, a novel attack targeting signature scheme implementations. Our attack exploits faulty signatures gained by injecting faults during signature generation. By using the signature verification primitive, we correct faulty signatures and, in the process deduce bits of the secret signing key. Compared to recent attacks that exploit single bit biases in the nonce that require 245signatures, our attack requires less than a thousand faulty signatures for a 256-bit (EC)DSA. The performance improvement is due to the fact that our attack targets the secret signing key, which does not change across signing sessions. We show that the proposed attack also works on Schnorr and RSA signatures with minor modifications.We demonstrate the viability of Jolt by running experiments targeting TLS handshakes in common cryptographic libraries such as WolfSSL, OpenSSL, Microsoft SymCrypt, LibreSSL, and Amazon s2n. On our target platform, the online phase takes less than 2 hours to recover 192 bits of a 256-bit ECDSA key, which is sufficient for full key recovery. We note that while RSA signatures are protected in popular cryptographic libraries, OpenSSL remains vulnerable to double fault injection. We have also reviewed their Federal Information Processing Standard (FIPS) hardened versions which are slightly less efficient but still vulnerable to our attack. We found that (EC)DSA signatures remain largely unprotected against software-only faults, posing a threat to real-life deployments such as TLS, and potentially other security protocols such as SSH and IPSec. This highlights the need for a thorough review and implementation of faults checking in security protocol implementations.

Motivated by the rise of quantum computers, existing public-key cryptosystems are expected to be replaced by post-quantum schemes in the next decade in billions of devices. To facilitate the transition, NIST is running a standardization process which is currently in its final Round. Only three digital signature schemes are left in the competition, among which Dilithium and Falcon are the ones based on lattices. Besides security and performance, significant attention has been given to resistance against implementation attacks that target side-channel leakage or fault injection response. Classical fault attacks on signature schemes make use of pairs of faulty and correct signatures to recover the secret key which only works on deterministic schemes. To counter such attacks, Dilithium offers a randomized version which makes each signature unique, even when signing identical messages. In this work, we introduce a novel Signature Correction Attack which not only applies to the deterministic version but also to the randomized version of Dilithium and is effective even on constant-time implementations using AVX2 instructions. The Signature Correction Attack exploits the mathematical structure of Dilithium to recover the secret key bits by using faulty signatures and the public-key. It can work for any fault mechanism which can induce single bit-flips. For demonstration, we are using Rowhammer induced faults. Thus, our attack does not require any physical access or special privileges, and hence could be also implemented on shared cloud servers. Using Rowhammer attack, we inject bit flips into the secret key s1 of Dilithium, which results in incorrect signatures being generated by the signing algorithm. Since we can find the correct signature using our Signature Correction algorithm, we can use the difference between the correct and incorrect signatures to infer the location and value of the flipped bit without needing a correct and faulty pair. To quantify the reduction in the security level, we perform a thorough classical and quantum security analysis of Dilithium and successfully recover 1,851 bits out of 3,072 bits of secret key$s_{1}$for security level 2. Fully recovered bits are used to reduce the dimension of the lattice whereas partially recovered coefficients are used to to reduce the norm of the secret key coefficients. Further analysis for both primal and dual attacks shows that the lattice strength against quantum attackers is reduced from 2128to 281while the strength against classical attackers is reduced from 2141 to 289. Hence, the Signature Correction Attack may be employed to achieve a practical attack on Dilithium (security level 2) as proposed in Round 3 of the NIST post-quantum standardization process.

Post-quantum schemes are expected to replace existing public-key schemes within a decade in billions of devices. To facilitate the transition, the US National Institute for Standards and Technology (NIST) is running a standardization process. Multivariate signatures is one of the main categories in NIST's post-quantum cryptography competition. Among the four candidates in this category, the LUOV and Rainbow schemes are based on the Oil and Vinegar scheme, first introduced in 1997 which has withstood over two decades of cryptanalysis. Beyond mathematical security and efficiency, security against side-channel attacks is a major concern in the competition. The current sentiment is that post-quantum schemes may be more resistant to fault-injection attacks due to their large key sizes and the lack of algebraic structure. We show that this is not true. We introduce a novel hybrid attack, QuantumHammer, and demonstrate it on the constant-time implementation of LUOV currently in Round 2 of the NIST post-quantum competition. The QuantumHammer attack is a combination of two attacks, a bit-tracing attack enabled via Rowhammer fault injection and a divide and conquer attack that uses bit-tracing as an oracle. Using bit-tracing, an attacker with access to faulty signatures collected using Rowhammer attack, can recover secret key bits albeit slowly. We employ a divide and conquer attack which exploits the structure in the key generation part of LUOV and solves the system of equations for the secret key more efficiently with few key bits recovered via bit-tracing. We have demonstrated the first successful in-the-wild attack on LUOV recovering all 11K key bits with less than 4 hours of an active Rowhammer attack. The post-processing part is highly parallel and thus can be trivially sped up using modest resources. QuantumHammer does not make any unrealistic assumptions, only requires software co-location (no physical access), and therefore can be used to target shared cloud servers or in other sandboxed environments.