Lattice-based Fault Attacks on Deterministic Signature Schemes of ECDSA and EdDSA

The deterministic ECDSA and EdDSA signature schemes have found plenty of applications since their publication and standardization. Their theoretical security can be guaranteed under certain well-designed models, while their practical risks from the flaw of random number generators can be mitigated since no randomness is required by the algorithms anymore. But the situation is not completely optimistic, since it has been gradually found that delicately designed fault attacks can threaten the practical security of the schemes. We present a lattice-based fault analysis method to the deterministic ECDSA and EdDSA algorithms. The underlying fault injection model is a special case of the random fault model in~\cite{MMF2019}. By noticing the algebraic structures of the deterministic algorithms, we show that, when providing with some valid faulty signatures and an associated correct signature of the same input message, some instances of lattice problems can be constructed to recover the signing key. This makes the allowed faulty bits close to the size of the signing key, and obviously bigger than that of the existing differential fault attacks. Moreover, the lattice-based approach supports much more alternative targets of fault injection when comparing with the existing approaches, which further improves its applicability. Experiments are performed to validate the effectiveness of the key recovery method. It is demonstrated that, for 256-bit deterministic ECDSA/EdDSA, the signing key can be recovered efficiently with significant probability even if the targets are affected by 250 (or 247) faulty bits. This is, however, impractical for the existing faulty pattern enumerating approaches

Loop-Abort Faults on Lattice-Based Fiat–Shamir and Hash-and-Sign Signatures

As the advent of general-purpose quantum computers appears to be drawing closer, agencies and advisory bodies have started recommending that we prepare the transition away from factoring and discrete logarithm-based cryptography, and towards postquantum secure constructions, such as lattice- based schemes. Almost all primitives of classical cryptography (and more!) can be realized with lattices, and the efficiency of primitives like encryption and signatures has gradually improved to the point that key sizes are competitive with RSA at similar security levels, and fast performance can be achieved both in soft- ware and hardware. However, little research has been conducted on physical attacks targeting concrete implementations of postquantum cryptography in general and lattice-based schemes in particular, and such research is essential if lattices are going to replace RSA and elliptic curves in our devices and smart cards. In this paper, we look in particular at fault attacks against implementations of lattice-based signature schemes, looking both at Fiat–Shamir type constructions (particularly BLISS, but also GLP, PASSSing and Ring-TESLA) and at hash-and-sign schemes (particularly the GPV-based scheme of Ducas–Prest– Lyubashevsky). These schemes include essentially all practical lattice-based signatures, and achieve the best efficiency to date in both software and hardware. We present several fault attacks against those schemes yielding a full key recovery with only a few or even a single faulty signature, and discuss possible countermeasures to protect against these attacks

Safe-Errors on SPA Protected implementations with the Atomicity Technique

ECDSA is one of the most important public-key signature scheme, however it is vulnerable to lattice attack once a few bits of the nonces are leaked. To protect Elliptic Curve Cryptography (ECC) against Simple Power Analysis, many countermeasures have been proposed. Doubling and Additions of points on the given elliptic curve require several additions and multiplications in the base field and this number is not the same for the two operations. The idea of the atomicity protection is to use a fixed pattern, i.e. a small number of instructions and rewrite the two basic operations of ECC using this pattern. Dummy operations are introduced so that the different elliptic curve operations might be written with the same atomic pattern. In an adversary point of view, the attacker only sees a succession of patterns and is no longer able to distinguish which one corresponds to addition and doubling. Chevallier-Mames, Ciet and Joye were the first to introduce such countermeasure. In this paper, we are interested in studying this countermeasure and we show a new vulnerability since the ECDSA implementation succumbs now to C Safe-Error attacks. Then, we propose an effective solution to prevent against C Safe-Error attacks when using the Side-Channel Atomicity. The dummy operations are used in such a way that if a fault is introduced on one of them, it can be detected. Finally, our countermeasure method is generic, meaning that it can be adapted to all formulae. We apply our methods to different formulae presented for side-channel Atomicity

Secure Cryptographic Algorithm Implementation on Embedded Platforms

Sensitive systems that are based on smart cards use well-studied and well-developed cryptosystems. Generally these cryptosystems have been subject to rigorous mathematical analysis in an effort to uncover cryptographic weaknesses in the system. The cryptosystems used in smart cards are, therefore, not usually vulnerable to these types of attacks. Since smart cards are small objects that can be easily placed in an environment where physical vulnerabilities can be exploited, adversaries have turned to different avenues of attack. This thesis describes the current state-of-the-art in side channel and fault analysis against smart cards, and the countermeasures necessary to provide a secure implementation. Both attack techniques need to be taken into consideration when implementing cryptographic algorithms in smart cards. In the domain of side-channel analysis a new application of using cache accesses to attack an implementation of AES by observing the power consumption is described, including an unpublished extension. Several new fault attacks are proposed based on finding collisions between a correct and a fault-induced execution of a secure secret algorithm. Other new fault attacks include reducing the number of rounds of an algorithm to make a differential cryptanalysis trivial, and fixing portions of the random value used in DSA to allow key recovery. Countermeasures are proposed for all the attacks described. The use of random delays, a simple countermeasure, is improved to render it more secure and less costly to implement. Several new countermeasures are proposed to counteract the particular fault attacks proposed in this thesis. A new method of calculating a modular exponentiation that is secure against side channel analysis is described, based on ideas which have been proposed previously or are known within the smart card industry. A novel method for protecting RSA against fault attacks is also proposed based on securing the underlying Montgomery multiplication. The majority of the fault attacks detailed have been implemented against actual chips to demonstrate the feasibility of these attacks. Details of these experiments are given in appendices. The experiments conducted to optimise the performance of random delays are also described in an appendix

Signing Information in the Quantum Era

Signatures are primarily used as a mark of authenticity, to demonstrate that the sender of a message is who they claim to be. In the current digital age, signatures underpin trust in the vast majority of information that we exchange, particularly on public networks such as the internet. However, schemes for signing digital information which are based on assumptions of computational complexity are facing challenges from advances in mathematics, the capability of computers, and the advent of the quantum era. Here we present a review of digital signature schemes, looking at their origins and where they are under threat. Next, we introduce post-quantum digital schemes, which are being developed with the specific intent of mitigating against threats from quantum algorithms whilst still relying on digital processes and infrastructure. Finally, we review schemes for signing information carried on quantum channels, which promise provable security metrics. Signatures were invented as a practical means of authenticating communications and it is important that the practicality of novel signature schemes is considered carefully, which is kept as a common theme of interest throughout this review

Computer Science & Technology Series : XVI Argentine Congress of Computer Science - Selected papers

CACIC’10 was the sixteenth Congress in the CACIC series. It was organized by the School of Computer Science of the University of Moron. The Congress included 10 Workshops with 104 accepted papers, 1 main Conference, 4 invited tutorials, different meetings related with Computer Science Education (Professors, PhD students, Curricula) and an International School with 5 courses. (http://www.cacic2010.edu.ar/). CACIC 2010 was organized following the traditional Congress format, with 10 Workshops covering a diversity of dimensions of Computer Science Research. Each topic was supervised by a committee of three chairs of different Universities. The call for papers attracted a total of 195 submissions. An average of 2.6 review reports were collected for each paper, for a grand total of 507 review reports that involved about 300 different reviewers. A total of 104 full papers were accepted and 20 of them were selected for this book.Red de Universidades con Carreras en Informática (RedUNCI