How to utilize the transformability of digital signatures for solving the oracle problem

Abstract

Transformability is a property of a digital signature such that one valid signature can be transformed into another valid signature of the same signature scheme. Usually digital signatures should not be forged so that the transformability is regarded as an unfavorable property. Contrarily we show that the transformability can be positively utilized for solving the oracle problem. The oracle problem is the following problem existing in some cryptographic protocols. An entity following a protocol receives a message from an adversary, and returns a certain value computed by a procedure specified in the protocol. In this process the adversary may obtain useful information by interacting with the oracle entity. The blind signature scheme and the blind decoding scheme are examples of such a protocol. Since these blinding techniques are very important in cryptographic applications, e.g. electronic money and digital pay magazine, a method to prevent illegal information leakage should be found. In this paper an oracle problem in the blind decoding scheme based on the ElGamal cryptosystem is solved with the use of a transformable digital signature. As in the original blind decoding scheme, the proposed blind decoding protocol offers users perfect untraceability. We also discuss the relevance of the transformable signature to the blind signature, the divertible zeroknowledge interactive proof and other schemes.