ECCC-Report TR13-183https://eccc.weizmann.ac.il/report/2013/183Comments and Revisions published for TR13-183en-usSun, 05 Apr 2015 20:32:42 +0300
Revision 1
| How to Delegate Computations: The Power of No-Signaling Proofs |
Yael Tauman Kalai,
Ran Raz,
Ron Rothblum
https://eccc.weizmann.ac.il/report/2013/183#revision1We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t=t(n), where the running time of the prover is poly(t) and the running time of the verifier is n*polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. Our construction relies on the existence of a computational sub-exponentially secure private information retrieval (PIR) scheme.
The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies, a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light.
For any language computable in time t=t(n), we construct a multi-prover interactive proof (MIP) that is sound against no-signaling strategies, where the running time of the provers is poly(t), the number of provers is polylog(t), and the running time of the verifier is n*polylog(t).
In particular, this shows that the class of languages that have polynomial-time MIPs that are sound against no-signaling strategies, is exactly EXP. Previously, this class was only known to contain PSPACE.
To convert our MIP into a 1-round delegation scheme, we use the method suggested by Aiello et-al (ICALP, 2000), which makes use of a PIR scheme. This method lacked a proof of security. We prove that this method is secure assuming the underlying MIP is secure against no-signaling provers.
Sun, 05 Apr 2015 20:32:42 +0300https://eccc.weizmann.ac.il/report/2013/183#revision1
Paper TR13-183
| How to Delegate Computations: The Power of No-Signaling Proofs |
Yael Tauman Kalai,
Ran Raz,
Ron Rothblum
https://eccc.weizmann.ac.il/report/2013/183We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t=t(n), where the running time of the prover is poly(t) and the running time of the verifier is n*polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. Our construction relies on the existence of a computational sub-exponentially secure private information retrieval (PIR) scheme.
The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies, a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light.
For any language computable in time t=t(n), we construct a multi-prover interactive proof (MIP) that is sound against no-signaling strategies, where the running time of the provers is poly(t), the number of provers is polylog(t), and the running time of the verifier is n*polylog(t).
In particular, this shows that the class of languages that have polynomial-time MIPs that are sound against no-signaling strategies, is exactly EXP. Previously, this class was only known to contain PSPACE.
To convert our MIP into a 1-round delegation scheme, we use the method suggested by Aiello et-al (ICALP, 2000), which makes use of a PIR scheme. This method lacked a proof of security. We prove that this method is secure assuming the underlying MIP is secure against no-signaling provers.
Sun, 22 Dec 2013 23:03:58 +0200https://eccc.weizmann.ac.il/report/2013/183