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Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes
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Bilinear-type conversion is to translate a cryptographic scheme designed over symmetric bilinear groups into one that works over asymmetric bilinear groups with small overhead regarding the size of objects concerned in the target scheme. In this paper, we address scalability for converting complex cryptographic schemes. Our contribution is threefold. Investigating complexity of bilinear-type conversion. We show that there exists no polynomial-time algorithm for worst-case inputs under standard complexity assumption. It means that bilinear-type conversion in general is an inherently difficult problem. Presenting a new scalable conversion method. Nevertheless, we show that large-scale conversion is indeed possible in practice when the target schemes are built from smaller building blocks with some structure. We present a novel conversion method, called IPConv, that uses 0-1 Integer Programming instantiated with a widely available IP solver. It instantly converts schemes containing more than a thousand of variables and hundreds of pairings. Application to computer-aided design. Our conversion method is also useful in modular design of middle to large scale cryptographic applications; first construct over simpler symmetric bilinear groups and run over efficient asymmetric groups. Thus one can avoid complication of manually allocating variables over asymmetric bilinear groups. We demonstrate its usefulness by somewhat counter-intuitive examples where converted DLIN-based Groth-Sahai proofs are more compact than manually built SXDH-based proofs. Though the early purpose of bilinear-type conversion is to save existing schemes from attacks against symmetric bilinear groups, our new scalable conversion method will find more applications beyond the original goal. Indeed, the above computer-aided design can be seen as a step toward automated modular design of cryptographic schemes.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.1 pp.251-269
- Publication Date
- 2019/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.251
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Masayuki ABE
NTT Corporation,Kyoto University
Fumitaka HOSHINO
NTT Corporation,Tokyo Institute of Technology
Miyako OHKUBO
NICT
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Masayuki ABE, Fumitaka HOSHINO, Miyako OHKUBO, "Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 1, pp. 251-269, January 2019, doi: 10.1587/transfun.E102.A.251.
Abstract: Bilinear-type conversion is to translate a cryptographic scheme designed over symmetric bilinear groups into one that works over asymmetric bilinear groups with small overhead regarding the size of objects concerned in the target scheme. In this paper, we address scalability for converting complex cryptographic schemes. Our contribution is threefold. Investigating complexity of bilinear-type conversion. We show that there exists no polynomial-time algorithm for worst-case inputs under standard complexity assumption. It means that bilinear-type conversion in general is an inherently difficult problem. Presenting a new scalable conversion method. Nevertheless, we show that large-scale conversion is indeed possible in practice when the target schemes are built from smaller building blocks with some structure. We present a novel conversion method, called IPConv, that uses 0-1 Integer Programming instantiated with a widely available IP solver. It instantly converts schemes containing more than a thousand of variables and hundreds of pairings. Application to computer-aided design. Our conversion method is also useful in modular design of middle to large scale cryptographic applications; first construct over simpler symmetric bilinear groups and run over efficient asymmetric groups. Thus one can avoid complication of manually allocating variables over asymmetric bilinear groups. We demonstrate its usefulness by somewhat counter-intuitive examples where converted DLIN-based Groth-Sahai proofs are more compact than manually built SXDH-based proofs. Though the early purpose of bilinear-type conversion is to save existing schemes from attacks against symmetric bilinear groups, our new scalable conversion method will find more applications beyond the original goal. Indeed, the above computer-aided design can be seen as a step toward automated modular design of cryptographic schemes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.251/_p
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@ARTICLE{e102-a_1_251,
author={Masayuki ABE, Fumitaka HOSHINO, Miyako OHKUBO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes},
year={2019},
volume={E102-A},
number={1},
pages={251-269},
abstract={Bilinear-type conversion is to translate a cryptographic scheme designed over symmetric bilinear groups into one that works over asymmetric bilinear groups with small overhead regarding the size of objects concerned in the target scheme. In this paper, we address scalability for converting complex cryptographic schemes. Our contribution is threefold. Investigating complexity of bilinear-type conversion. We show that there exists no polynomial-time algorithm for worst-case inputs under standard complexity assumption. It means that bilinear-type conversion in general is an inherently difficult problem. Presenting a new scalable conversion method. Nevertheless, we show that large-scale conversion is indeed possible in practice when the target schemes are built from smaller building blocks with some structure. We present a novel conversion method, called IPConv, that uses 0-1 Integer Programming instantiated with a widely available IP solver. It instantly converts schemes containing more than a thousand of variables and hundreds of pairings. Application to computer-aided design. Our conversion method is also useful in modular design of middle to large scale cryptographic applications; first construct over simpler symmetric bilinear groups and run over efficient asymmetric groups. Thus one can avoid complication of manually allocating variables over asymmetric bilinear groups. We demonstrate its usefulness by somewhat counter-intuitive examples where converted DLIN-based Groth-Sahai proofs are more compact than manually built SXDH-based proofs. Though the early purpose of bilinear-type conversion is to save existing schemes from attacks against symmetric bilinear groups, our new scalable conversion method will find more applications beyond the original goal. Indeed, the above computer-aided design can be seen as a step toward automated modular design of cryptographic schemes.},
keywords={},
doi={10.1587/transfun.E102.A.251},
ISSN={1745-1337},
month={January},}
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TY - JOUR
TI - Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 251
EP - 269
AU - Masayuki ABE
AU - Fumitaka HOSHINO
AU - Miyako OHKUBO
PY - 2019
DO - 10.1587/transfun.E102.A.251
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2019
AB - Bilinear-type conversion is to translate a cryptographic scheme designed over symmetric bilinear groups into one that works over asymmetric bilinear groups with small overhead regarding the size of objects concerned in the target scheme. In this paper, we address scalability for converting complex cryptographic schemes. Our contribution is threefold. Investigating complexity of bilinear-type conversion. We show that there exists no polynomial-time algorithm for worst-case inputs under standard complexity assumption. It means that bilinear-type conversion in general is an inherently difficult problem. Presenting a new scalable conversion method. Nevertheless, we show that large-scale conversion is indeed possible in practice when the target schemes are built from smaller building blocks with some structure. We present a novel conversion method, called IPConv, that uses 0-1 Integer Programming instantiated with a widely available IP solver. It instantly converts schemes containing more than a thousand of variables and hundreds of pairings. Application to computer-aided design. Our conversion method is also useful in modular design of middle to large scale cryptographic applications; first construct over simpler symmetric bilinear groups and run over efficient asymmetric groups. Thus one can avoid complication of manually allocating variables over asymmetric bilinear groups. We demonstrate its usefulness by somewhat counter-intuitive examples where converted DLIN-based Groth-Sahai proofs are more compact than manually built SXDH-based proofs. Though the early purpose of bilinear-type conversion is to save existing schemes from attacks against symmetric bilinear groups, our new scalable conversion method will find more applications beyond the original goal. Indeed, the above computer-aided design can be seen as a step toward automated modular design of cryptographic schemes.
ER -
English
