ECCC-Report TR24-096https://eccc.weizmann.ac.il/report/2024/096Comments and Revisions published for TR24-096en-usWed, 21 Aug 2024 22:18:14 +0300
Revision 2
| Constant-Round Arguments for Batch-Verification and Bounded-Space Computations from One-Way Functions |
Noga Amit,
Guy Rothblum
https://eccc.weizmann.ac.il/report/2024/096#revision2What are the minimal cryptographic assumptions that suffice for constructing efficient argument systems, and for which tasks? Recently, Amit and Rothblum [STOC 2023] showed that one-way functions suffice for constructing constant-round arguments for bounded-depth computations. In this work we ask: what other tasks have efficient argument systems based only on one-way functions? We show two positive results:
First, we construct a new argument system for batch-verification of $k$ $UP$ statements ($NP$ statements with a unique witness) for witness relations that are verifiable in bounded depth. The communication is quasi-linear in the length of a single witness, and the number of rounds is constant. The honest prover runs in polynomial time given witnesses for all $k$ inputs' membership in the language.
Our second result is a constant-round doubly-efficient argument system for languages in $P$ that are computable by bounded-space Turing machines. For this class of computations, we obtain an exponential improvement in the trade-off between the number of rounds and the (exponent of the) communication complexity, compared to known unconditionally sound protocols [Reingold, Rothblum and Rothblum, STOC 2016].Wed, 21 Aug 2024 22:18:14 +0300https://eccc.weizmann.ac.il/report/2024/096#revision2
Revision 1
| Constant-Round Arguments for Batch-Verification and Bounded-Space Computations from One-Way Functions |
Noga Amit,
Guy Rothblum
https://eccc.weizmann.ac.il/report/2024/096#revision1What are the minimal cryptographic assumptions that suffice for constructing efficient argument systems, and for which tasks? Recently, Amit and Rothblum [STOC 2023] showed that one-way functions suffice for constructing constant-round arguments for bounded-depth computations. In this work we ask: what other tasks have efficient argument systems based only on one-way functions? We show two positive results:
First, we construct a new argument system for batch-verification of $k$ $UP$ statements ($NP$ statements with a unique witness) for witness relations that are verifiable in depth $D$.
Taking $M$ to be the length of a single witness, the communication complexity is $O(\log k) \cdot (M + k \cdot D \cdot n^{\sigma})$, where $\sigma > 0$ is an arbitrarily small constant. In particular, the communication is quasi-linear in the length of a single witness, so long as $k < M / (D \cdot n^{\sigma})$.
The number of rounds is constant and the honest prover runs in polynomial time given witnesses for all $k$ inputs' membership in the language.
Our second result is a constant-round doubly-efficient argument system for languages in $P$ that are computable by bounded-space Turing machines. For this class of computations, we obtain an exponential improvement in the trade-off between the number of rounds and the (exponent of the) communication complexity, compared to known unconditionally sound protocols [Reingold, Rothblum and Rothblum, STOC 2016].Thu, 30 May 2024 12:51:59 +0300https://eccc.weizmann.ac.il/report/2024/096#revision1
Paper TR24-096
| Constant-Round Arguments for Batch-Verification and Bounded-Space Computations from One-Way Functions |
Noga Amit,
Guy Rothblum
https://eccc.weizmann.ac.il/report/2024/096What are the minimal cryptographic assumptions that suffice for constructing efficient argument systems, and for which tasks? Recently, Amit and Rothblum [STOC 2023] showed that one-way functions suffice for constructing constant-round arguments for bounded-depth computations. In this work we ask: what other tasks have efficient argument systems based only on one-way functions? We show two positive results:
First, we construct a new argument system for batch-verification of $k$ $UP$ statements ($NP$ statements with a unique witness) for witness relations that are verifiable in bounded depth. The communication is quasi-linear in the length of a single witness, and the number of rounds is constant. The honest prover runs in polynomial time given witnesses for all $k$ inputs' membership in the language.
Our second result is a constant-round doubly-efficient argument system for languages in $P$ that are computable by bounded-space Turing machines. For this class of computations, we obtain an exponential improvement in the trade-off between the number of rounds and the (exponent of the) communication complexity, compared to known unconditionally sound protocols [Reingold, Rothblum and Rothblum, STOC 2016].Mon, 27 May 2024 22:43:01 +0300https://eccc.weizmann.ac.il/report/2024/096