IEICE TRANSACTIONS on Fundamentals
Key Generation for Fast Inversion of the Paillier Encryption Function
Summary :
We study fast inversion of the Paillier encryption function. Especially, we focus only on key generation, and do not modify the Paillier encryption function. We propose three key generation algorithms based on the speeding-up techniques for the RSA encryption function. By using our algorithms, the size of the private CRT exponent is half of that of Paillier-CRT. The first algorithm employs the extended Euclidean algorithm. The second algorithm employs factoring algorithms, and can construct the private CRT exponent with low Hamming weight. The third algorithm is a variant of the second one, and has some advantage such as compression of the private CRT exponent and no requirement for factoring algorithms. We also propose the settings of the parameters for these algorithms and analyze the security of the Paillier encryption function by these algorithms against known attacks. Finally, we give experimental results of our algorithms.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.6 pp.1111-1121
- Publication Date
- 2010/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E93.A.1111
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Cryptography and Information Security
Authors
Keyword
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Takato HIRANO, Keisuke TANAKA, "Key Generation for Fast Inversion of the Paillier Encryption Function" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 6, pp. 1111-1121, June 2010, doi: 10.1587/transfun.E93.A.1111.
Abstract: We study fast inversion of the Paillier encryption function. Especially, we focus only on key generation, and do not modify the Paillier encryption function. We propose three key generation algorithms based on the speeding-up techniques for the RSA encryption function. By using our algorithms, the size of the private CRT exponent is half of that of Paillier-CRT. The first algorithm employs the extended Euclidean algorithm. The second algorithm employs factoring algorithms, and can construct the private CRT exponent with low Hamming weight. The third algorithm is a variant of the second one, and has some advantage such as compression of the private CRT exponent and no requirement for factoring algorithms. We also propose the settings of the parameters for these algorithms and analyze the security of the Paillier encryption function by these algorithms against known attacks. Finally, we give experimental results of our algorithms.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1111/_p
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@ARTICLE{e93-a_6_1111,
author={Takato HIRANO, Keisuke TANAKA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Key Generation for Fast Inversion of the Paillier Encryption Function},
year={2010},
volume={E93-A},
number={6},
pages={1111-1121},
abstract={We study fast inversion of the Paillier encryption function. Especially, we focus only on key generation, and do not modify the Paillier encryption function. We propose three key generation algorithms based on the speeding-up techniques for the RSA encryption function. By using our algorithms, the size of the private CRT exponent is half of that of Paillier-CRT. The first algorithm employs the extended Euclidean algorithm. The second algorithm employs factoring algorithms, and can construct the private CRT exponent with low Hamming weight. The third algorithm is a variant of the second one, and has some advantage such as compression of the private CRT exponent and no requirement for factoring algorithms. We also propose the settings of the parameters for these algorithms and analyze the security of the Paillier encryption function by these algorithms against known attacks. Finally, we give experimental results of our algorithms.},
keywords={},
doi={10.1587/transfun.E93.A.1111},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - Key Generation for Fast Inversion of the Paillier Encryption Function
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1111
EP - 1121
AU - Takato HIRANO
AU - Keisuke TANAKA
PY - 2010
DO - 10.1587/transfun.E93.A.1111
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2010
AB - We study fast inversion of the Paillier encryption function. Especially, we focus only on key generation, and do not modify the Paillier encryption function. We propose three key generation algorithms based on the speeding-up techniques for the RSA encryption function. By using our algorithms, the size of the private CRT exponent is half of that of Paillier-CRT. The first algorithm employs the extended Euclidean algorithm. The second algorithm employs factoring algorithms, and can construct the private CRT exponent with low Hamming weight. The third algorithm is a variant of the second one, and has some advantage such as compression of the private CRT exponent and no requirement for factoring algorithms. We also propose the settings of the parameters for these algorithms and analyze the security of the Paillier encryption function by these algorithms against known attacks. Finally, we give experimental results of our algorithms.
ER -
English
