<p>Computational protein design aims at identifying protein mutations and conformations with desired target properties (such as increased protein stability, switch of substrate specificity, or novel function) from a vast combinatorial space of candidate solutions. The development of algorithms to efficiently and accurately solve problems in protein design has thus posed significant computational and modeling challenges. Despite the inherent hardness of protein design, a number of computational techniques have been previously developed and applied to a wide range of protein design problems. In many cases, however, the available computational protein design techniques are deficient both in computational power and modeling accuracy. Typical simplifying modeling assumptions for computational protein design are the rigidity of the protein backbone and the discretization of the protein side-chain conformations. Here, we present the derivation, proofs of correctness and complexity, implementation, and application of novel algorithms for computational protein design that, unlike previous approaches, have provably-accurate guarantees even when backbone or continuous side-chain flexibility are incorporated into the model. We also describe novel divide-and-conquer and dynamic programming algorithms for improved computational efficiency that are shown to result in speed-ups of up to several orders of magnitude as compared to previously-available techniques. Our novel algorithms are further incorporated as part of K*, a provably-accurate ensemble-based algorithm for protein-ligand binding prediction and protein design. The application of our suite of protein design algorithms to a variety of problems, including enzyme redesign and small-molecule inhibitor design, is described. Experimental validation, performed by our collaborators, of a set of our computational predictions confirms the feasibility and usefulness of our novel algorithms for computational protein design.</p> / Dissertation

Machine learning (ML) has demonstrated great success in numerous complicated tasks. Fueled by these advances, many real-world systems like autonomous vehicles and aircraft are adopting ML techniques by adding learning-enabled components. Unfortunately, ML models widely used today, like neural networks, lack the necessary mathematical framework to provide formal guarantees on safety, causing growing concerns over these learning-enabled systems in safety-critical settings. In this dissertation, we tackle this problem by combining formal methods and machine learning to bring provable safety and robustness to learning-enabled systems. We first study the robustness verification problem of neural networks on classification tasks. We focus on providing provable safety guarantees on the absence of failures under arbitrarily strong adversaries. We propose an efficient neural network verifier LayR to compute a guaranteed and overapproximated range for the output of a neural network given an input set which contains all possible adversarially perturbed inputs. LayR relaxes nonlinear units in neural networks using linear bounds and refines such relaxations with mixed integer linear programming (MILP) to iteratively improve the approximation precision, which achieves tighter output range estimations compared to prior neural network verifiers. However, the neural network verifier focuses more on analyzing a trained neural network but less on learning provably safe neural networks. To tackle this problem, we study verifiable training that incorporates verification into training procedures to train provably safe neural networks and scale to larger models and datasets. We propose a novel framework, AdvIBP, for combining adversarial training and provable robustness verification. We show that the proposed framework can learn provable robust neural networks at a sublinear convergence rate. In the second part of the dissertation, we study the verification of system-level properties in neural-network controlled systems (NNCS). We focus on proving bounded-time safety properties by computing reachable sets. We first introduce two efficient NNCS verifiers ReachNN* and POLAR that construct polynomial-based overapproximations of neural-network controllers. We transfer NNCSs to tractable closed-loop systems with approximated polynomial controllers for computing reachable sets using existing reachability analysis tools of dynamical systems. The combination of polynomial overapproximations and reachability analysis tools opens promising directions for NNCS verification. We also include a survey and experimental study of existing NNCS verification methods, including combining state-of-the-art neural network verifiers with reachability analysis tools, to discuss what overapproximation is suitable for NNCS reachability analysis. While these verifiers enable proving safety properties of NNCS, the nonlinearity of neural-network controllers is the main bottleneck that limits their efficiency and scalability. We propose a novel framework of knowledge distillation to control “the degree of nonlinearity” of NN controllers to ease NNCS verification which improves provable safety of NNCSs especially when they are safe but cannot be verified due to their complexity. For the verification community, this opens up the possibility of reducing verification complexity by influencing how a system is trained. Though NNCS verification can prove safety when system models are known, modern deep learning, e.g., deep reinforcement learning (DRL), often targets tasks with unknown system models, also known as the model-free setting. To tackle this issue, we first focus on safe exploration of DRL and propose a novel Lyapunov-inspired method. Our method uses Gaussian Process models to provide probabilistic guarantees on the policies, and guide the exploration of the unknown environment in a safe fashion. Then, we study learning robust visual control policies in DRL to enhance the robustness against visual changes that were not seen during training. We propose a method DRIBO, which can learn robust state representations for RL via a novel contrastive version of the Multi-View Information Bottleneck (MIB). This approach enables us to train high-performance visual policies that are robust to visual distractions, and can generalize well to unseen environments.

An identity-based cryptosystem (IBC) is a public-key system where the public key can be represented by any arbitrary string such as an e-mail address. The notion was introduced by Shamir with the primary goal of simplifying certificate management. An identity-based signature(IBS) is the identity-based counter part of a digital signature. In the first (and primary) part of the work, we take a closer look at an IBS due to Galindo and Garcia–GG-IBS, for short. GG-IBS is derived through a simple and elegant concatenation of two Schnorr signatures and, importantly, does not rely on pairing. The security is established through two algorithms (both of) which use the Multiple-Forking(MF) Algorithm to reduce the problem of computing the discrete logarithm to breaking the IBS. Our focus is on the security argument : It turns out that the argument is flawed and, as a remedy, we sketch a new security argument. However, the resulting security bound is still quite loose, chiefly due to the usage of the MF Algorithm. We explore possible avenues for improving this bound and , to this end, introduce two notions pertaining to random oracles termed dependency and independency. Incorporating (in) dependency allows us to launch the nested replay attack far more effectively than in the MF Algorithm leading to a cleaner,(significantly) tighter security argument for GG-IBS, completing the final piece of the GG-IBS jigsaw. The second part of the work pertains to the notion of selective-identity (sID) for IBCs. The focus is on the problem of constructing a fully-secure IBS given an sID-secure IBS without using random oracles and with reasonable security degradation.

Le problème du « Shape From Shading » est aujourd'hui considéré comme un problème mal posé et difficile à résoudre. Afin de bien comprendre les difficultés de ce problème et d'apporter des solutions fiables et pertinentes, nous proposons une approche rigoureuse basée sur la notion de solution de viscosité.<br />Après avoir considéré et exploité au maximum les équations (aux dérivées partielles) obtenues à partir de la modélisation classique du problème du « Shape From Shading », nous proposons et étudions de nouvelles équations provenant de modélisations plus réalistes que celles qui avaient été traitées classiquement dans la littérature. Cette démarche nous permet alors de démontrer qu'avec de telles nouvelles modélisations, le problème du « Shape From Shading » est généralement un problème complètement bien posé. En d'autres termes, nous prouvons que la version classique du problème du « Shape from Shading » est devenu mal posée à cause d'une trop grande simplification de la modélisation.<br />Dans ce travail, nous proposons aussi une extension de la notion de solutions de viscosité singulières développée récemment par Camilli et Siconolfi. Cette extension nous permet de proposer une nouvelle caractérisation des solutions de viscosité discontinues. Ce nouveau cadre théorique nous permet aussi d'unifier les différents résultats théoriques proposés dans le domaine du « Shape From Shading ».

We study the problem of secure key establishment. We critically examine the security models of Bellare and Rogaway (1993) and Canetti and Krawczyk (2001) in the computational complexity approach, as these models are central in the understanding of the provable security paradigm. We show that the partnership definition used in the three-party key distribution (3PKD) protocol of Bellare and Rogaway (1995) is flawed, which invalidates the proof for the 3PKD protocol. We present an improved protocol with a new proof of security. We identify several variants of the key sharing requirement (i.e., two entities who have completed matching sessions, partners, are required to accept the same session key). We then present a brief discussion about the key sharing requirement. We identify several variants of the Bellare and Rogaway (1993) model. We present a comparative study of the relative strengths of security notions between the several variants of the Bellare-Rogaway model and the Canetti-Krawczyk model. In our comparative study, we reveal a drawback in the Bellare, Pointcheval, and Rogaway (2000) model with the protocol of Abdalla and Pointcheval (2005) as a case study. We prove a revised protocol of Boyd (1996) secure in the Bellare-Rogaway model. We then extend the model in order to allow more realistic adversary capabilities by incorporating the notion of resetting the long-term compromised key of some entity. This allows us to detect a known weakness of the protocol that cannot be captured in the original model. We also present an alternative protocol that is efficient in both messages and rounds. We prove the protocol secure in the extended model. We point out previously unknown flaws in several published protocols and a message authenticator of Bellare, Canetti, and Krawczyk (1998) by refuting claimed proofs of security. We also point out corresponding flaws in their existing proofs. We propose fixes to these protocols and their proofs. In some cases, we present new protocols with full proofs of security. We examine the role of session key construction in key establishment protocols, and demonstrate that a small change to the way that session keys are constructed can have significant benefits. Protocols that were proven secure in a restricted Bellare-Rogaway model can then be proven secure in the full model. We present a brief discussion on ways to construct session keys in key establishment protocols and also prove the protocol of Chen and Kudla (2003) secure in a less restrictive Bellare-Rogaway model. To complement the computational complexity approach, we provide a formal specification and machine analysis of the Bellare-Pointcheval-Rogaway model using an automated model checker, Simple Homomorphism Verification Tool (SHVT). We demonstrate that structural flaws in protocols can be revealed using our framework. We reveal previously unknown flaws in the unpublished preproceedings version of the protocol due to Jakobsson and Pointcheval (2001) and several published protocols with only heuristic security arguments. We conclude this thesis with a listing of some open problems that were encountered in the study.