Pseudorandom intermixing: A tool for shared cryptography

Abstract

Designing distributed cryptographic protocols that combine correctness, security, efficiency and practical constraints can be very difficult. Here, we suggest a new modular tool that we call “pseudorandom intermixing”which allows parties (or architectural components, such as hardware devices) sharing pseudorandomness to mix extra correlated pseudorandom information inside their computational results. We show how the pseudorandom intermixing may ease the design, increase efficiency and allow more refined control of cryptographic protocols for several important tasks, while maintaining “provable security.” It can even turn a “heuristic protocol” into a “provably secure” one. We concentrate on the area of “distributed public key systems,” which has been a very active area of research in the last decade, and for which there is a great interest in practical implementations of protocols. Among other things, we demonstrate the first “fault-free non-interactive” proactive maintenance protocol for RSA, which involves a single broadcast round to perform an update, if parties do not behave maliciously. We also demonstrate how to interlace access control within the messaging of proactive RSA; this assures elimination of corrupted entities.