Quantum Ciphertext Authentication and Key Recycling with the Trap Code

Authors Yfke Dulek, Florian Speelman

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Author Details

Yfke Dulek
  • Qusoft, Centrum voor Wiskunde en Informatica, Amsterdam, the Netherlands
Florian Speelman
  • QMATH, Department of Mathematical Sciences, University of Copenhagen, Denmark

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Yfke Dulek and Florian Speelman. Quantum Ciphertext Authentication and Key Recycling with the Trap Code. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 111, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We investigate quantum authentication schemes constructed from quantum error-correcting codes. We show that if the code has a property called purity testing, then the resulting authentication scheme guarantees the integrity of ciphertexts, not just plaintexts. On top of that, if the code is strong purity testing, the authentication scheme also allows the encryption key to be recycled, partially even if the authentication rejects. Such a strong notion of authentication is useful in a setting where multiple ciphertexts can be present simultaneously, such as in interactive or delegated quantum computation. With these settings in mind, we give an explicit code (based on the trap code) that is strong purity testing but, contrary to other known strong-purity-testing codes, allows for natural computation on ciphertexts.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
  • Theory of computation → Error-correcting codes
  • Security and privacy → Information-theoretic techniques
  • Security and privacy → Symmetric cryptography and hash functions
  • Theory of computation → Quantum information theory
  • quantum authentication
  • ciphertext authentication
  • trap code
  • purity-testing codes
  • quantum computing on encrypted data


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