On the Security of Lattice-Based Signature Schemes in a Post-Quantum World

• Main Author: Bindel, Nina
• Format: Others
• Language: en
• Published: 2018
• Online Access: https://tuprints.ulb.tu-darmstadt.de/8100/8/Dissertation_NBindel_v1.pdf; Bindel, Nina <http://tuprints.ulb.tu-darmstadt.de/view/person/Bindel=3ANina=3A=3A.html> (2018): On the Security of Lattice-Based Signature Schemes in a Post-Quantum World.Darmstadt, Technische Universität, [Ph.D. Thesis]

Digital signatures are indispensable for security on the Internet, because they guarantee authenticity, integrity, and non-repudiation, of namely e-mails, software updates, and in the Transport Layer Security (TLS) protocol which is used for secure data transfer, for example. Most signature schemes that are currently in use such as the RSA signature scheme, are considered secure as long as the integer factorization problem or the discrete logarithm (DL) problem are computationally hard. At present, no algorithms have yet been found to solve these problems on conventional computers in polynomial time. However, in 1997, Shor published a polynomial-time algorithm that uses quantum computation to solve the integer factorization and the DL problem. In particular, this means that RSA signatures are considered broken as soon as large-scale quantum computers exist. Due to significant advances in the area of quantum computing, it is reasonable to assume that within 20 years, quantum computers that are able to break the RSA scheme, could exist. In order to maintain authenticity, integrity, and non-repudiation of data, cryptographic schemes that cannot be broken by quantum attacks are required. In addition, these so-called post-quantum secure schemes should be sufficiently efficient to be suitable for all established applications. Furthermore, solutions enabling a timely and secure transition from classical to post-quantum schemes are needed. This thesis contributes to the above-mentioned transition. In this thesis, we present the two lattice-based digital signature schemes TESLA and qTESLA, whereby lattice-based cryptography is one of five approaches to construct post-quantum secure schemes. Furthermore, we prove that our signature schemes are secure as long as the so-called Learning With Errors (LWE) problem is computationally hard to solve. It is presumed that even quantum computers cannot solve the LWE problem in polynomial time. The security of our schemes is proven using security reductions. Since our reductions are tight and explicit, efficient instantiations are possible that provably guarantee a selected security level, as long as the corresponding LWE instance provides a certain hardness level. Since both our reductions (as proven in the quantum random oracle model) and instantiations, take into account quantum attackers, TESLA and qTESLA are considered post-quantum secure. Concurrently, the run-times for generating and verifying signatures of qTESLA are similar (or faster) than those of the RSA scheme. However, key and signature sizes of RSA are smaller than those of qTESLA. In order to protect both the theoretical signature schemes and their implementations against attacks, we analyze possible vulnerabilities against implementation attacks. In particular, cache-side-channel attacks resulting from observing the cache behavior and fault attacks, which recover secret information by actively disrupting the execution of an algorithm are focused. We present effective countermeasures for each implementation attack we found. Our analyses and countermeasures also influence the design and implementation of qTESLA. Although our schemes are considered (post-quantum) secure according to state-of-the-art LWE attacks, cryptanalysis of lattice-based schemes is still a relatively new field of research in comparison to RSA schemes. Hence, there is a lack of confidence in the concrete instantiations and their promised security levels. However, due to developments within the field of quantum computers, a transition to post-quantum secure solutions seems to be more urgently required than ever. To solve this dilemma, we present an approach to combine two schemes, e.g., qTESLA and the RSA signature scheme, so that the combination is secure as long as one of the two combined schemes is secure. We present several of such combiners to construct hybrid signature schemes and hybrid key encapsulation mechanisms to ensure both authenticity and confidentiality in our Public-Key Infrastructure (PKI). Lastly, we also demonstrate how to apply the resulting hybrid schemes in standards such as X.509 or TLS. To summarize, this work presents post-quantum secure candidates which can, using our hybrid schemes, add post-quantum security to the current classical security in our PKI.