Application of NTRU using group rings to partial decryption technique

Takanori Yasuda, Hiroaki Anada, Kouichi Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Partial decryption enables a ciphertext to be decrypted partially according to provided secret keys. In this paper, we propose a public key encryption scheme with the functionality of partial decryption. Our strategy is to use the NTRU cryptosystem. Under a design principle of the mathematical structure “group ring”, we extend the original NTRU into group ring NTRU (GR-NTRU). First, we propose a generic framework of our GR-NTRU. Our GR-NTRU allows partial decryption with a single encryption process using a single public key. Besides, when we execute partial decryption under a secret key of GR-NTRU, we need no information to identify each part in a whole ciphertext. Consequently, management of a public key and a corresponding set of secret keys is rather easier than the naive method. Next, we propose a concrete instantiation of our generic GR-NTRU. A multivariate polynomial ring NTRU scheme is obtained by employing a product of different cyclic groups as the basis of the group ring structure.We will show examples of those new variants of NTRU schemes with concrete parameter values, and explain how we can employ them to use the functionality of partial decryption.

Original languageEnglish
Title of host publicationTrusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers
EditorsMoti Yung, Jianbiao Zhang, Zhen Yang
PublisherSpringer Verlag
Pages203-213
Number of pages11
ISBN (Print)9783319315492
DOIs
Publication statusPublished - Jan 1 2016
Event7th International Conference on the Theory, Technologies and Applications of Trusted Systems, INTRUST 2015 - Beijing, China
Duration: Dec 7 2015Dec 8 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9565
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Conference on the Theory, Technologies and Applications of Trusted Systems, INTRUST 2015
CountryChina
CityBeijing
Period12/7/1512/8/15

Fingerprint

Group Ring
Cryptography
Partial
Public key
Polynomials
Concretes
Public Key Encryption
Multivariate Polynomials
Cryptosystem
Polynomial ring
Cyclic group
Encryption

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yasuda, T., Anada, H., & Sakurai, K. (2016). Application of NTRU using group rings to partial decryption technique. In M. Yung, J. Zhang, & Z. Yang (Eds.), Trusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers (pp. 203-213). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9565). Springer Verlag. https://doi.org/10.1007/978-3-319-31550-8_13

Application of NTRU using group rings to partial decryption technique. / Yasuda, Takanori; Anada, Hiroaki; Sakurai, Kouichi.

Trusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers. ed. / Moti Yung; Jianbiao Zhang; Zhen Yang. Springer Verlag, 2016. p. 203-213 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9565).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yasuda, T, Anada, H & Sakurai, K 2016, Application of NTRU using group rings to partial decryption technique. in M Yung, J Zhang & Z Yang (eds), Trusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9565, Springer Verlag, pp. 203-213, 7th International Conference on the Theory, Technologies and Applications of Trusted Systems, INTRUST 2015, Beijing, China, 12/7/15. https://doi.org/10.1007/978-3-319-31550-8_13
Yasuda T, Anada H, Sakurai K. Application of NTRU using group rings to partial decryption technique. In Yung M, Zhang J, Yang Z, editors, Trusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers. Springer Verlag. 2016. p. 203-213. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-31550-8_13
Yasuda, Takanori ; Anada, Hiroaki ; Sakurai, Kouichi. / Application of NTRU using group rings to partial decryption technique. Trusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers. editor / Moti Yung ; Jianbiao Zhang ; Zhen Yang. Springer Verlag, 2016. pp. 203-213 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{5fb4318e90004debbb7f3acc992c8897,
title = "Application of NTRU using group rings to partial decryption technique",
abstract = "Partial decryption enables a ciphertext to be decrypted partially according to provided secret keys. In this paper, we propose a public key encryption scheme with the functionality of partial decryption. Our strategy is to use the NTRU cryptosystem. Under a design principle of the mathematical structure “group ring”, we extend the original NTRU into group ring NTRU (GR-NTRU). First, we propose a generic framework of our GR-NTRU. Our GR-NTRU allows partial decryption with a single encryption process using a single public key. Besides, when we execute partial decryption under a secret key of GR-NTRU, we need no information to identify each part in a whole ciphertext. Consequently, management of a public key and a corresponding set of secret keys is rather easier than the naive method. Next, we propose a concrete instantiation of our generic GR-NTRU. A multivariate polynomial ring NTRU scheme is obtained by employing a product of different cyclic groups as the basis of the group ring structure.We will show examples of those new variants of NTRU schemes with concrete parameter values, and explain how we can employ them to use the functionality of partial decryption.",
author = "Takanori Yasuda and Hiroaki Anada and Kouichi Sakurai",
year = "2016",
month = "1",
day = "1",
doi = "10.1007/978-3-319-31550-8_13",
language = "English",
isbn = "9783319315492",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "203--213",
editor = "Moti Yung and Jianbiao Zhang and Zhen Yang",
booktitle = "Trusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers",
address = "Germany",

}

TY - GEN

T1 - Application of NTRU using group rings to partial decryption technique

AU - Yasuda, Takanori

AU - Anada, Hiroaki

AU - Sakurai, Kouichi

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Partial decryption enables a ciphertext to be decrypted partially according to provided secret keys. In this paper, we propose a public key encryption scheme with the functionality of partial decryption. Our strategy is to use the NTRU cryptosystem. Under a design principle of the mathematical structure “group ring”, we extend the original NTRU into group ring NTRU (GR-NTRU). First, we propose a generic framework of our GR-NTRU. Our GR-NTRU allows partial decryption with a single encryption process using a single public key. Besides, when we execute partial decryption under a secret key of GR-NTRU, we need no information to identify each part in a whole ciphertext. Consequently, management of a public key and a corresponding set of secret keys is rather easier than the naive method. Next, we propose a concrete instantiation of our generic GR-NTRU. A multivariate polynomial ring NTRU scheme is obtained by employing a product of different cyclic groups as the basis of the group ring structure.We will show examples of those new variants of NTRU schemes with concrete parameter values, and explain how we can employ them to use the functionality of partial decryption.

AB - Partial decryption enables a ciphertext to be decrypted partially according to provided secret keys. In this paper, we propose a public key encryption scheme with the functionality of partial decryption. Our strategy is to use the NTRU cryptosystem. Under a design principle of the mathematical structure “group ring”, we extend the original NTRU into group ring NTRU (GR-NTRU). First, we propose a generic framework of our GR-NTRU. Our GR-NTRU allows partial decryption with a single encryption process using a single public key. Besides, when we execute partial decryption under a secret key of GR-NTRU, we need no information to identify each part in a whole ciphertext. Consequently, management of a public key and a corresponding set of secret keys is rather easier than the naive method. Next, we propose a concrete instantiation of our generic GR-NTRU. A multivariate polynomial ring NTRU scheme is obtained by employing a product of different cyclic groups as the basis of the group ring structure.We will show examples of those new variants of NTRU schemes with concrete parameter values, and explain how we can employ them to use the functionality of partial decryption.

UR - http://www.scopus.com/inward/record.url?scp=84962299524&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962299524&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-31550-8_13

DO - 10.1007/978-3-319-31550-8_13

M3 - Conference contribution

AN - SCOPUS:84962299524

SN - 9783319315492

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 203

EP - 213

BT - Trusted Systems - 7th International Conference, INTRUST 2015, Revised Selected Papers

A2 - Yung, Moti

A2 - Zhang, Jianbiao

A2 - Yang, Zhen

PB - Springer Verlag

ER -