Succinct Cryptographic Proof Systems: Theory and Practice

A proof system allows a power prover to convince a weak party (the verifier) of the validity of large computations. Proof systems are a powerful and versatile tool that is central to complexity theory and cryptography.

Since their introduction, they have led to breakthroughs such as the celebrated PCP theorem, zero-knowledge proofs, hardness of approximation, and more.

The rise of cloud computing, lockchain technologies, and distributed computing have created a vast demand for practical implementations.

Cryptographic proofs leverage the use of cryptographic primitives to gain efficiency benefits including succinct proofs with fast proving and verifying time, suitable for practical implementations.

These days, cryptographic proof systems maintain the integrity of blockchain networks, securing trillions of dollars in transactions.The goal of the CRYPTOPROOF project is to advance the efficiency of crytographic proof systems:1. High-soundness: For oracle proofs, the query complexity of the verifier is the main bottleneck towards succinctness.

Obtaining proof systems with polynomially small error and constant query complexity would resolve the four-decades-old sliding-scale conjecture and would have significant practical implications. 2.

Improving the compilation efficiency: cryptographic proof systems are usually obtained by compiling a proof system with several cryptographic primitives which yields crucial properties such as noninteractivity and succinctness that are required for most applications.3. Limitations: limitations of proof systems and cryptographic proof systems are a scarce resource.

They build the boundaries of possibilities and guide us to new constructions.

Beyond the above, the end goal of the CRYPTOPROOF project is to design and implement a new cryptographic proof system with efficiency measures that surpasses the current state-of-the-art.