Further Limitations on Information-Theoretically Secure Quantum Homomorphic Encryption

Abstract

In this brief note, we review and extend existing limitations on information-theoretically (IT) secure quantum fully homomorphic encryption (QFHE). The essential ingredient remains Nayak's bound, which provides a tradeoff between the number of homomorphically implementable functions of an IT-secure QHE scheme and its efficiency. Importantly, the bound is robust to imperfect IT-security guarantees. We summarize these bounds in the context of existing QHE schemes, and discuss subtleties of the imposed restrictions.

Brief note adapted from author's thesis, 7 pages

References in corpus (2)

• Limitations on information theoretically secure quantum homomorphic encryption
• Practical quantum somewhat-homomorphic encryption with coherent states

Cited by in corpus (2)

• A quantum homomorphic encryption scheme for polynomial-sized circuits
• Interactive Leakage Chain Rule for Quantum Min-entropy