Faster Homomorphic Trace-Type Function Evaluation

Yu Ishimaki*, Hayato Yamana

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Homomorphic encryption enables computations over encrypted data without decryption, and can be used for outsourcing computations to some untrusted source. In homomorphic encryption based on the hardness of ring-learning with errors, offering promising security and functionality, a plaintext is represented by a polynomial. A plaintext is treated as a vector whose homomorphic evaluation enables component-wise addition and multiplication, as well as rotation across the components. We focus on a commonly used and time-consuming subroutine that enables homomorphically summing-up the components of the vector or homomorphically extracting the coefficients of the polynomial, and call it homomorphic trace-type function. We improve the efficiency of the homomorphic trace-type function evaluation. The homomorphic trace-type function evaluation is performed by repeating homomorphic rotation followed by addition (rotations-and-sums). To correctly add up a rotated ciphertext and an unrotated one, a special operation called key-switching should be performed on the rotated one. As key-switching is computationally expensive, the rotations-and-sums is inherently inefficient. We propose a more efficient trace-type function evaluation by using loop-unrolling, which is compatible with other optimization techniques such as hoisting, and can exploit multi-threading. We show that the rotations-and-sums is not the optimal solution in terms of runtime complexity and that a trade-off exists between time and space. Experimental results demonstrate that our proposed method works 1.32-2.12 times faster than the previous method.

Original languageEnglish
Article number9395438
Pages (from-to)53061-53077
Number of pages17
JournalIEEE Access
Publication statusPublished - 2021


  • Homomorphic encryption
  • ring-learning with errors
  • secure outsourcing

ASJC Scopus subject areas

  • Computer Science(all)
  • Materials Science(all)
  • Engineering(all)


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