## CryptoDB

### Nicholas P. Ward

#### Publications

Year
Venue
Title
2019
EUROCRYPT
We design, implement, and evaluate a zero knowledge succinct non-interactive argument (SNARG) for Rank-1 Constraint Satisfaction (R1CS), a widely-deployed NP language undergoing standardization. Our SNARG has a transparent setup, is plausibly post-quantum secure, and uses lightweight cryptography. A proof attesting to the satisfiability of n constraints has size $O(\log ^2 n)$O(log2n); it can be produced with $O(n \log n)$O(nlogn) field operations and verified with O(n). At 128 bits of security, proofs are less than ${250}\,\mathrm{kB}$250kB even for several million constraints, more than $10{\times }$10× shorter than prior SNARGs with similar features.A key ingredient of our construction is a new Interactive Oracle Proof (IOP) for solving a univariate analogue of the classical sumcheck problem [LFKN92], originally studied for multivariate polynomials. Our protocol verifies the sum of entries of a Reed–Solomon codeword over any subgroup of a field.We also provide $\texttt {libiop}$libiop, a library for writing IOP-based arguments, in which a toolchain of transformations enables programmers to write new arguments by writing simple IOP sub-components. We have used this library to specify our construction and prior ones, and plan to open-source it.

#### Coauthors

Eli Ben-Sasson (1)
Alessandro Chiesa (1)
Michael Riabzev (1)
Nicholas Spooner (1)
Madars Virza (1)