Statistical Zaps and New Oblivious Transfer Protocols

Explore a comprehensive presentation on statistical zaps and novel oblivious transfer protocols delivered at Eurocrypt 2020. Delve into the intricacies of statistical security in two-party protocols, interactive proof systems, and witness indistinguishability. Examine the concept of zaps as two-round public-coin witness-indistinguishable protocols and their application to oblivious transfer. Investigate the development of weakly secure statistical zaps and methods to amplify their security. Learn about statistical receiver-private oblivious transfer and the crucial role of statistical hash commitments. Gain insights into the three-round statistical receiver-private oblivious transfer protocol derived from statistical hash commitments, and understand how these commitments can be constructed from two-round oblivious transfer. Conclude with a summary of the key findings and their implications for cryptographic research.

Intro
Statistical Security in 2-party Protocols
Interactive Proof System
Witness Indistinguishability (WI)
Zaps: 2-round Public-Coin WI (ONDO)
Oblivious Transfer (OT)
Natural Question
Starting Idea
Idea for Security
Hiding & Extractability in Plain Model • Use a 2-round statistical sender private oblivious transfer
Weakly Secure' Statistical Zaps
Amplify the Security
Statistical Receiver-Private OT
Main Tool: Statistical Hash Commitments (SHC)
Statistical Hiding Property
Computational Binding
3-round Statistical Receiver - Private OT from SHC
Statistical Hash Commitment from 2-round OT
Summary of Results