The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
우리는 나눗셈과 같은 임의의 일변량 및 이변량 정수 함수를 동형적으로 평가하는 방법을 제안합니다. Okada et al.이 제안한 이전 작업. (WISTP'18)은 체계가 BFV 및 BGV 체계의 SIMD 연산과 여전히 호환되도록 다항식 평가를 사용하고 입력 도메인 ℤ로 구현됩니다.257. 그러나 Okada et al. 입력 도메인 크기에 2차 수의 일반 텍스트-암호문 곱셈 및 암호문-암호문 추가가 필요하며 이러한 작업은 암호문-암호문 곱셈보다 가볍지만 2차 복잡성으로 인해 더 큰 입력을 처리하는 것이 상당히 비효율적입니다. 이 연구에서는 먼저 이전 작업을 개선하고 SIMD 연산을 활성화하는 대신 더 큰 입력 도메인 크기를 처리하기 위해 패킹 방법을 활용하는 새로운 접근 방식을 제안하여 더 큰 입력 도메인 크기로 작업할 수 있도록 합니다. 예: ℤ215 합리적으로 효율적인 방법으로. 또한 입력 도메인 크기를 ℤ로 약간 확장하는 방법을 보여줍니다.216 비교적 적당한 오버헤드가 있습니다. 또한 두 개의 암호문을 사용하여 하나의 정수 일반 텍스트를 암호화하고 단변량/이변량 함수 평가를 위한 기술을 적용하여 더 큰 입력 도메인 크기를 처리하는 또 다른 접근 방식을 보여줍니다. 우리는 Okada et al.의 이전 작업, Okada et al.의 개선된 버전 및 PALISADE의 새로운 체계를 입력 도메인 ℤ로 구현합니다.215, 이전 작업과 이전 작업의 개선된 버전의 예상 실행 시간이 여전히 각각 약 117일과 59일인 반면 새 방식은 307초 안에 계산될 수 있음을 확인합니다.
Daisuke MAEDA
University of Tsukuba
Koki MORIMURA
University of Tsukuba
Shintaro NARISADA
KDDI Research, Inc.
Kazuhide FUKUSHIMA
KDDI Research, Inc.
Takashi NISHIDE
University of Tsukuba
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
부
Daisuke MAEDA, Koki MORIMURA, Shintaro NARISADA, Kazuhide FUKUSHIMA, Takashi NISHIDE, "Efficient Homomorphic Evaluation of Arbitrary Uni/Bivariate Integer Functions and Their Applications" in IEICE TRANSACTIONS on Fundamentals,
vol. E107-A, no. 3, pp. 234-247, March 2024, doi: 10.1587/transfun.2023CIP0010.
Abstract: We propose how to homomorphically evaluate arbitrary univariate and bivariate integer functions such as division. A prior work proposed by Okada et al. (WISTP'18) uses polynomial evaluations such that the scheme is still compatible with the SIMD operations in BFV and BGV schemes, and is implemented with the input domain ℤ257. However, the scheme of Okada et al. requires the quadratic numbers of plaintext-ciphertext multiplications and ciphertext-ciphertext additions in the input domain size, and although these operations are more lightweight than the ciphertext-ciphertext multiplication, the quadratic complexity makes handling larger inputs quite inefficient. In this work, first we improve the prior work and also propose a new approach that exploits the packing method to handle the larger input domain size instead of enabling the SIMD operation, thus making it possible to work with the larger input domain size, e.g., ℤ215 in a reasonably efficient way. In addition, we show how to slightly extend the input domain size to ℤ216 with a relatively moderate overhead. Further we show another approach to handling the larger input domain size by using two ciphertexts to encrypt one integer plaintext and applying our techniques for uni/bivariate function evaluation. We implement the prior work of Okada et al., our improved version of Okada et al., and our new scheme in PALISADE with the input domain ℤ215, and confirm that the estimated run-times of the prior work and our improved version of the prior work are still about 117 days and 59 days respectively while our new scheme can be computed in 307 seconds.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023CIP0010/_p
부
@ARTICLE{e107-a_3_234,
author={Daisuke MAEDA, Koki MORIMURA, Shintaro NARISADA, Kazuhide FUKUSHIMA, Takashi NISHIDE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Homomorphic Evaluation of Arbitrary Uni/Bivariate Integer Functions and Their Applications},
year={2024},
volume={E107-A},
number={3},
pages={234-247},
abstract={We propose how to homomorphically evaluate arbitrary univariate and bivariate integer functions such as division. A prior work proposed by Okada et al. (WISTP'18) uses polynomial evaluations such that the scheme is still compatible with the SIMD operations in BFV and BGV schemes, and is implemented with the input domain ℤ257. However, the scheme of Okada et al. requires the quadratic numbers of plaintext-ciphertext multiplications and ciphertext-ciphertext additions in the input domain size, and although these operations are more lightweight than the ciphertext-ciphertext multiplication, the quadratic complexity makes handling larger inputs quite inefficient. In this work, first we improve the prior work and also propose a new approach that exploits the packing method to handle the larger input domain size instead of enabling the SIMD operation, thus making it possible to work with the larger input domain size, e.g., ℤ215 in a reasonably efficient way. In addition, we show how to slightly extend the input domain size to ℤ216 with a relatively moderate overhead. Further we show another approach to handling the larger input domain size by using two ciphertexts to encrypt one integer plaintext and applying our techniques for uni/bivariate function evaluation. We implement the prior work of Okada et al., our improved version of Okada et al., and our new scheme in PALISADE with the input domain ℤ215, and confirm that the estimated run-times of the prior work and our improved version of the prior work are still about 117 days and 59 days respectively while our new scheme can be computed in 307 seconds.},
keywords={},
doi={10.1587/transfun.2023CIP0010},
ISSN={1745-1337},
month={March},}
부
TY - JOUR
TI - Efficient Homomorphic Evaluation of Arbitrary Uni/Bivariate Integer Functions and Their Applications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 234
EP - 247
AU - Daisuke MAEDA
AU - Koki MORIMURA
AU - Shintaro NARISADA
AU - Kazuhide FUKUSHIMA
AU - Takashi NISHIDE
PY - 2024
DO - 10.1587/transfun.2023CIP0010
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E107-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2024
AB - We propose how to homomorphically evaluate arbitrary univariate and bivariate integer functions such as division. A prior work proposed by Okada et al. (WISTP'18) uses polynomial evaluations such that the scheme is still compatible with the SIMD operations in BFV and BGV schemes, and is implemented with the input domain ℤ257. However, the scheme of Okada et al. requires the quadratic numbers of plaintext-ciphertext multiplications and ciphertext-ciphertext additions in the input domain size, and although these operations are more lightweight than the ciphertext-ciphertext multiplication, the quadratic complexity makes handling larger inputs quite inefficient. In this work, first we improve the prior work and also propose a new approach that exploits the packing method to handle the larger input domain size instead of enabling the SIMD operation, thus making it possible to work with the larger input domain size, e.g., ℤ215 in a reasonably efficient way. In addition, we show how to slightly extend the input domain size to ℤ216 with a relatively moderate overhead. Further we show another approach to handling the larger input domain size by using two ciphertexts to encrypt one integer plaintext and applying our techniques for uni/bivariate function evaluation. We implement the prior work of Okada et al., our improved version of Okada et al., and our new scheme in PALISADE with the input domain ℤ215, and confirm that the estimated run-times of the prior work and our improved version of the prior work are still about 117 days and 59 days respectively while our new scheme can be computed in 307 seconds.
ER -