ECCC-Report TR16-118https://eccc.weizmann.ac.il/report/2016/118Comments and Revisions published for TR16-118en-usSun, 31 Jul 2016 23:54:15 +0300
Paper TR16-118
| On the impossibility of entropy reversal, and its application to zero-knowledge proofs |
Jiapeng Zhang,
Shachar Lovett
https://eccc.weizmann.ac.il/report/2016/118Zero knowledge proof systems have been widely studied in cryptography. In the statistical setting, two classes of proof systems studied are Statistical Zero Knowledge (SZK) and Non-Interactive Statistical Zero Knowledge (NISZK), where the difference is that in NISZK only very limited communication is allowed between the verifier and the prover. It is an open problem whether these two classes are in fact equal. In this paper, we rule out efficient black box reductions between SZK and NISZK.
We achieve this by studying algorithms which can reverse the entropy of a function. The problem of estimating the entropy of a circuit is complete for NISZK. Hence, reversing the entropy of a function is equivalent to a black box reduction of NISZK to its complement, which is known to be equivalent to a black box reduction of SZK to NISZK [Goldreich et al, CRYPTO 1999].
We show that any such algorithm incurs an exponential loss of parameters, and hence cannot be implemented efficiently.Sun, 31 Jul 2016 23:54:15 +0300https://eccc.weizmann.ac.il/report/2016/118