Decision Oracles are Equivalent to Matching Oracles

One of the key directions in complexity theory which has also filtered through to cryptographic research, is the effort to classify related but seemingly distinct notions. Separation or reduction arguments are the basic means for this classification. Continuing this direction we identify a class of problems, called “matching problems,” which are related to the class of “decision problems.” In many cases, these classes are neither trivially equivalent nor distinct. Briefly, a “decision” problem consists of one instance and a supposedly related image of this instance; the problem is to decide whether the instance and the image indeed satisfy the given predicate. In a “matching” problem two such pairs of instances-images are given, and the problem is to “match” or “distinguish” which image corresponds to which instance. Clearly the decision problem is more difficult, since given a “decision” oracle one can simply test each of the two images to be matched ag...

• Type: Conference
• Year: 1999
• Where: PKC
• Authors: Helena Handschuh, Yiannis Tsiounis, Moti Yung
• Keywords: Cryptology, Decision Problem, Images, Matching Problem, PKC 1999