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Si-Hui Tan1, Joshua A Kettlewell1, Yingkai Ouyang1

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This summary is machine-generated.

We developed a private-key quantum homomorphic encryption scheme using group theory. This enables quantum computations on encrypted data, with potential for strong information hiding.

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Area of Science:

  • Quantum Information Science
  • Cryptography
  • Algebraic Methods in Cryptography

Background:

  • Encryption schemes rely on algebraic properties.
  • Quantum computation offers new possibilities for secure data processing.

Purpose of the Study:

  • To present a private-key quantum homomorphic encryption scheme.
  • To enable broad quantum computation on encrypted data.

Main Methods:

  • Utilizing group theoretic tools, specifically the centralizer of a subgroup of operations.
  • Encoding quantum data on bosons in distinct spatial modes.
  • Performing species-independent manipulations of bosons for computation.

Main Results:

  • A private-key quantum homomorphic encryption scheme is presented.
  • The scheme allows for quantum computations on encrypted data.
  • A specific encoding hides a constant fraction of information, approaching unity with polynomial overhead.

Conclusions:

  • The proposed protocol demonstrates potential for non-trivial information hiding.
  • Suggests a class of encodings for enhanced security in quantum encryption.