IEICE TRANSACTIONS on Fundamentals
A Note on Subgroup Security in Discrete Logarithm-Based Cryptography
Summary :
The membership check of a group is an important operation to implement discrete logarithm-based cryptography in practice securely. Since this check requires costly scalar multiplication or exponentiation operation, several efficient methods have been investigated. In the case of pairing-based cryptography, this is an extended research area of discrete logarithm-based cryptography, Barreto et al. (LATINCRYPT 2015) proposed a parameter choice called subgroup-secure elliptic curves. They also claimed that, in some schemes, if an elliptic curve is subgroup-secure, costly scalar multiplication or exponentiation operation can be omitted from the membership check of bilinear groups, which results in faster schemes than the original ones. They also noticed that some schemes would not maintain security with this omission. However, they did not show the explicit condition of what schemes become insecure with the omission. In this paper, we show a concrete example of insecurity in the sense of subgroup security to help developers understand what subgroup security is and what properties are preserved. In our conclusion, we recommend that the developers use the original membership check because it is a general and straightforward method to implement schemes securely. If the developers want to use the subgroup-secure elliptic curves and to omit the costly operation in a scheme for performance reasons, it is critical to carefully analyze again that correctness and security are preserved with the omission.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.1 pp.104-120
- Publication Date
- 2021/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2020CIP0019
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
Authors
Tadanori TERUYA
National Institute of Advanced Industrial Science and Technology
Keyword
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Tadanori TERUYA, "A Note on Subgroup Security in Discrete Logarithm-Based Cryptography" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 1, pp. 104-120, January 2021, doi: 10.1587/transfun.2020CIP0019.
Abstract: The membership check of a group is an important operation to implement discrete logarithm-based cryptography in practice securely. Since this check requires costly scalar multiplication or exponentiation operation, several efficient methods have been investigated. In the case of pairing-based cryptography, this is an extended research area of discrete logarithm-based cryptography, Barreto et al. (LATINCRYPT 2015) proposed a parameter choice called subgroup-secure elliptic curves. They also claimed that, in some schemes, if an elliptic curve is subgroup-secure, costly scalar multiplication or exponentiation operation can be omitted from the membership check of bilinear groups, which results in faster schemes than the original ones. They also noticed that some schemes would not maintain security with this omission. However, they did not show the explicit condition of what schemes become insecure with the omission. In this paper, we show a concrete example of insecurity in the sense of subgroup security to help developers understand what subgroup security is and what properties are preserved. In our conclusion, we recommend that the developers use the original membership check because it is a general and straightforward method to implement schemes securely. If the developers want to use the subgroup-secure elliptic curves and to omit the costly operation in a scheme for performance reasons, it is critical to carefully analyze again that correctness and security are preserved with the omission.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020CIP0019/_p
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@ARTICLE{e104-a_1_104,
author={Tadanori TERUYA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Note on Subgroup Security in Discrete Logarithm-Based Cryptography},
year={2021},
volume={E104-A},
number={1},
pages={104-120},
abstract={The membership check of a group is an important operation to implement discrete logarithm-based cryptography in practice securely. Since this check requires costly scalar multiplication or exponentiation operation, several efficient methods have been investigated. In the case of pairing-based cryptography, this is an extended research area of discrete logarithm-based cryptography, Barreto et al. (LATINCRYPT 2015) proposed a parameter choice called subgroup-secure elliptic curves. They also claimed that, in some schemes, if an elliptic curve is subgroup-secure, costly scalar multiplication or exponentiation operation can be omitted from the membership check of bilinear groups, which results in faster schemes than the original ones. They also noticed that some schemes would not maintain security with this omission. However, they did not show the explicit condition of what schemes become insecure with the omission. In this paper, we show a concrete example of insecurity in the sense of subgroup security to help developers understand what subgroup security is and what properties are preserved. In our conclusion, we recommend that the developers use the original membership check because it is a general and straightforward method to implement schemes securely. If the developers want to use the subgroup-secure elliptic curves and to omit the costly operation in a scheme for performance reasons, it is critical to carefully analyze again that correctness and security are preserved with the omission.},
keywords={},
doi={10.1587/transfun.2020CIP0019},
ISSN={1745-1337},
month={January},}
Copy
TY - JOUR
TI - A Note on Subgroup Security in Discrete Logarithm-Based Cryptography
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 104
EP - 120
AU - Tadanori TERUYA
PY - 2021
DO - 10.1587/transfun.2020CIP0019
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2021
AB - The membership check of a group is an important operation to implement discrete logarithm-based cryptography in practice securely. Since this check requires costly scalar multiplication or exponentiation operation, several efficient methods have been investigated. In the case of pairing-based cryptography, this is an extended research area of discrete logarithm-based cryptography, Barreto et al. (LATINCRYPT 2015) proposed a parameter choice called subgroup-secure elliptic curves. They also claimed that, in some schemes, if an elliptic curve is subgroup-secure, costly scalar multiplication or exponentiation operation can be omitted from the membership check of bilinear groups, which results in faster schemes than the original ones. They also noticed that some schemes would not maintain security with this omission. However, they did not show the explicit condition of what schemes become insecure with the omission. In this paper, we show a concrete example of insecurity in the sense of subgroup security to help developers understand what subgroup security is and what properties are preserved. In our conclusion, we recommend that the developers use the original membership check because it is a general and straightforward method to implement schemes securely. If the developers want to use the subgroup-secure elliptic curves and to omit the costly operation in a scheme for performance reasons, it is critical to carefully analyze again that correctness and security are preserved with the omission.
ER -
English
