Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Non-interactive arguments enable a prover to convince a verifier that a statement is true. Recently there has been a lot of progress both in theory and practice on constructing highly efficient non-interactive arguments with small size and low verification complexity, so-called succinct non-interactive arguments SNARGs and succinct non-interactive arguments of knowledge SNARKs.#R##N##R##N#Many constructions of SNARGs rely on pairing-based cryptography. In these constructions a proof consists of a number of group elements and the verification consists of checking a number of pairing product equations. The question  address in this article is how efficient pairing-based SNARGs can be.#R##N##R##N#Our first contribution is a pairing-based preprocessing SNARK for arithmetic circuit satisfiability, which is an NP-complete language. In our SNARK  work with asymmetric pairings for higher efficiency, a proof is only 3 group elements, and verification consists of checking a single pairing product equations using 3 pairings ini¾?total. Our SNARK is zero-knowledge and does not reveal anything about the witness the prover uses to make the proof.#R##N##R##N#As our second contribution  ansr an open question of Bitansky, Chiesa, Ishai, Ostrovsky and Paneth TCC 2013 by showing that linear interactive proofs cannot have a linear decision procedure. It follows from this that SNARGs where the prover and verifier use generic asymmetric bilinear group operations cannot consist of a single group element. This gives the first lor bound for pairing-based SNARGs. It remains an intriguing open problem whether this lor bound can be extended to rule out 2 group element SNARGs, which would prove optimality of our 3 element construction.
['Jens Groth']
I am writing a research paper on a idea On the Size of Pairing-Based Non-interactive Arguments
[{"from": "human", "value": "I am writing a research paper on a idea On the Size of Pairing-Based Non-interactive Arguments"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Non-interactive arguments enable a prover to convince a verifier that a statement is true. Recently there has been a lot of progress both in theory and practice on constructing highly efficient non-interactive arguments with small size and low verification complexity, so-called succinct non-interactive arguments SNARGs and succinct non-interactive arguments of knowledge SNARKs.#R##N##R##N#Many constructions of SNARGs rely on pairing-based cryptography. In these constructions a proof consists of a number of group elements and the verification consists of checking a number of pairing product equations. The question  address in this article is how efficient pairing-based SNARGs can be.#R##N##R##N#Our first contribution is a pairing-based preprocessing SNARK for arithmetic circuit satisfiability, which is an NP-complete language. In our SNARK  work with asymmetric pairings for higher efficiency, a proof is only 3 group elements, and verification consists of checking a single pairing product equations using 3 pairings ini\u00be?total. Our SNARK is zero-knowledge and does not reveal anything about the witness the prover uses to make the proof.#R##N##R##N#As our second contribution  ansr an open question of Bitansky, Chiesa, Ishai, Ostrovsky and Paneth TCC 2013 by showing that linear interactive proofs cannot have a linear decision procedure. It follows from this that SNARGs where the prover and verifier use generic asymmetric bilinear group operations cannot consist of a single group element. This gives the first lor bound for pairing-based SNARGs. It remains an intriguing open problem whether this lor bound can be extended to rule out 2 group element SNARGs, which would prove optimality of our 3 element construction."}]