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Computer-aided cryptography is an active area of research that develops and applies formal, machine-checkable approaches to the design, analysis, and implementation of cryptography. We present a cross-cutting systematization of the computer-aided cryptography literature, focusing on three main areas: (i) design-level security (both symbolic security and computational security), (ii) functional correctness and efficiency, and (iii) implementation-level security (with a focus on digital side-channel resistance). In each area, we first clarify the role of computer-aided cryptography---how it can help and what the caveats are---in addressing current challenges. We next present a taxonomy of state-of-the-art tools, comparing their accuracy, scope, trustworthiness, and usability. Then, we highlight their main achievements, trade-offs, and research challenges. After covering the three main areas, we present two case studies. First, we study efforts in combining tools focused on different areas to consolidate the guarantees they can provide. Second, we distill the lessons learned from the computer-aided cryptography community's involvement in the TLS 1.3 standardization effort. Finally, we conclude with recommendations to paper authors, tool developers, and standardization bodies moving forward. 

Protocols for password authenticated key exchange (PAKE) allow two parties who share only a weak password to agree on a cryptographic key. We revisit the notion of PAKE in the universal composability (UC) framework, and propose a relaxation of the PAKE functionality of Canetti et al. that we call lazy-extraction PAKE (lePAKE). Our relaxation allows the ideal-world adversary to postpone its password guess until after a session is complete. We argue that this relaxed notion still provides meaningful security in the password-only setting. As our main result, we show that several PAKE protocols that were previously only proven secure with respect to a “game-based” definition of security can be shown to UC-realize the lePAKE functionality in the random-oracle model. These include SPEKE, SPAKE2, and TBPEKE, the most efficient PAKE schemes currently known. 

We present a high-assurance and high-speed implementation of the SHA-3 hash function. Our implementation is written in the Jasmin programming language, and is formally verified for functional correctness, provable security and timing attack resistance in the EasyCrypt proof assistant. Our implementation is the first to achieve simultaneously the four desirable properties (efficiency, correctness, provable security, and side-channel protection) for a non-trivial cryptographic primitive. Concretely, our mechanized proofs show that: 1) the SHA-3 hash function is indifferentiable from a random oracle, and thus is resistant against collision, first and second preimage attacks; 2) the SHA-3 hash function is correctly implemented by a vectorized x86 implementation. Furthermore, the implementation is provably protected against timing attacks in an idealized model of timing leaks. The proofs include new EasyCrypt libraries of independent interest for programmable random oracles and modular indifferentiability proofs.