Chapter

Theory of Cryptography

Volume 7785 of the series Lecture Notes in Computer Science pp 281-296

Feasibility and Completeness of Cryptographic Tasks in the Quantum World

  • Serge FehrAffiliated withCentrum Wiskunde & Informatica (CWI)
  • , Jonathan KatzAffiliated withUniversity of Maryland
  • , Fang SongAffiliated withPennsylvania State University
  • , Hong-Sheng ZhouAffiliated withUniversity of Maryland
  • , Vassilis ZikasAffiliated withUCLA

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Abstract

It is known that cryptographic feasibility results can change by moving from the classical to the quantum world. With this in mind, we study the feasibility of realizing functionalities in the framework of universal composability, with respect to both computational and information-theoretic security. With respect to computational security, we show that existing feasibility results carry over unchanged from the classical to the quantum world; a functionality is “trivial” (i.e., can be realized without setup) in the quantum world if and only if it is trivial in the classical world. The same holds with regard to functionalities that are complete (i.e., can be used to realize arbitrary other functionalities).

In the information-theoretic setting, the quantum and classical worlds differ. In the quantum world, functionalities in the class we consider are either complete, trivial, or belong to a family of simultaneous-exchange functionalities (e.g., XOR). However, other results in the information-theoretic setting remain roughly unchanged.