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Verifiable Cryptographic Software

 

Zero-knowledge proofs are integral for deploying privacy-preserving cryptocurrencies and other blockchain applications, as they represent a fundamental building block for proving statements about confidential data.

The most popular framework for such proofs is based on cryptographic pairings defined over elliptic curves, where pairing-based zero-knowledge Succint Non-Interactive Arguments of Knowledge (zk-SNARKs) underlie private transactions.

There has been substantial progress in the past decade towards selecting parameters and implementing pairing-based cryptography efficiently in software. However, current record-setting implementations rely on hand-optimized architecture-specific Assembly code for the underlying field arithmetic and a great deal of manual tuning to unlock the best performance across a range of architectures. This introduces low-level code which is both hard to audit and to verify as correct, and a number of cryptographic libraries have suffered with simple bugs in their arithmetic backend layers as a direct consequence.

The project's main goal is then to investigate techniques to develop a formally verified efficient software library for pairing-based cryptography, as means to support current blockchain projects relying on zero-knowledge proofs. This requires extending current frameworks for generation of correct-by-design cryptographic software to efficiently handle arithmetic in extension fields and elliptic curves, among others.

tower_verifiable_cryptographic_software.pdf