Despite the notable advances in the development of high-assurance, verified implementations of cryptographic protocols, such implementations typically face significant performance overheads, particularly due to the penalties induced by formal verification and automated extraction of executable code. In this paper, we address some core performance challenges facing computer-aided cryptography by presenting a formal treatment for accelerating such verified implementations based on multiple generic optimizations covering parallelism and memory access. We illustrate our techniques for addressing such performance bottlenecks using the Line-Point Zero-Knowledge (LPZK) protocol as a case study. Our starting point is a new verified implementation of LPZK that we formalize and synthesize using EasyCrypt; our first implementation is developed to reduce the proof effort and without considering the performance of the extracted executable code. We then show how such (automatically) extracted code can be optimized in three different ways to obtain a 3000x speedup and thus matching the performance of the manual implementation of LPZK of lpzkv2.[13] We obtain such performance gains by first modifying the algorithmic specifications, then by adopting a provably secure parallel execution model, and finally by optimizing the memory access structures. All optimizations are first formally verified inside EasyCrypt, and then executable code is automatically synthesized from each step of the formalization. For each optimization, we analyze performance gains resulting from it and also address challenges facing the computer-aided security proofs thereof, and challenges facing automated synthesis of executable code with such an optimization.

MPC-in-the-Head (MitH) is a general framework that enables constructing efficient zero-knowledge (ZK) protocols for NP relations from secure multiparty computation (MPC) protocols. In this paper we present the first machine-checked implementations of MitH.

Secure Multiparty Computation (MPC) enables a group of n</> distrusting parties to jointly compute a function using private inputs. MPC guarantees correctness of computation and confidentiality of inputs if no more than a threshold t</> of the parties are corrupted. Proactive MPC (PMPC) addresses the stronger threat model of a \emphmobile adversary that controls a changing set of parties (but only up to t</> at any instant), and may eventually corrupt all n</> parties over a long time. This paper takes a first stab at developing high-assurance implementations of (P)MPC. We formalize in \EasyCrypt, a tool-assisted framework for building high-confidence cryptographic proofs, several abstract and reusable variations of secret sharing and of (P)MPC protocols building on them. Using those, we prove a series of abstract theorems for the proactive setting. We implement and perform computer-checked security proofs of concrete instantiations of the required (abstract) protocols in \EasyCrypt. We also develop a new tool-chain to extract high-assurance executable implementations of protocols formalized and verified in \EasyCrypt. Our tool-chain uses \Why as an intermediate tool, and enables us to extract executable code from our (P)MPC formalizations. We conduct an evaluation of the extracted executables by comparing their performance to performance of manually implemented versions using \textsfPython -based \textsfCharm framework for prototyping cryptographic schemes. We argue that the small overhead of our high-assurance executables is a reasonable price to pay for the increased confidence about their correctness and security.

We give a language-based security treatment of domain-specific languages and compilers for secure multi-party computation, a cryptographic paradigm that enables collaborative computation over encrypted data. Computations are specified in a core imperative language, as if they were intended to be executed by a trusted-third party, and formally verified against an information-flow policy modelling (an upper bound to) their leakage. This allows non-experts to assess the impact of performance-driven authorized disclosure of intermediate values. Specifications are then compiled to multi-party protocols. We formalize protocol security using (distributed) probabilistic information-flow and prove security-preserving compilation: protocols only leak what is allowed by the source policy. The proof exploits a natural but previously missing correspondence between simulation-based cryptographic proofs and (composable) probabilistic non-interference. Finally, we extend our framework to justify leakage cancelling, a domain-specific optimization that allows to first write an efficient specification that fails to meet the allowed leakage upper-bound, and then apply a probabilistic pre-processing that brings leakage to the acceptable range.

We present a high-assurance software stack for secure function evaluation (SFE). Our stack consists of three components: i. a verified compiler (CircGen) that translates C programs into Boolean circuits; ii. a verified implementation of Yao's SFE protocol based on garbled circuits and oblivious transfer; and iii. transparent application integration and communications via FRESCO, an open-source framework for secure multiparty computation (MPC). CircGen is a general purpose tool that builds on CompCert, a verified optimizing compiler for C. It can be used in arbitrary Boolean circuit-based cryptography deployments. The security of our SFE protocol implementation is formally verified using EasyCrypt, a tool-assisted framework for building high-confidence cryptographic proofs, and it leverages a new formalization of garbled circuits based on the framework of Bellare, Hoang, and Rogaway (CCS 2012). We conduct a practical evaluation of our approach, and conclude that it is competitive with state-of-the-art (unverified) approaches. Our work provides concrete evidence of the feasibility of building efficient, verified, implementations of higher-level cryptographic systems. All our development is publicly available.