Converting Cryptographic Schemes from Symmetric to Asymmetric Bilinear Groups

Abe, Masayuki; Groth, Jens; Ohkubo, Miyako; Tango, Takeya

doi:10.1007/978-3-662-44371-2_14

Cited by 28 publications

(64 citation statements)

References 20 publications

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“…We for the first time investigate the complexity of bilinear-conversion and formally prove the difficulty of the problem. In the framework of [21] a scheme over Type-I group is represented by a graph called a dependency graph. It describes a flow of group operations in G over variables in the scheme.…”

Section: Our Contributionmentioning

confidence: 99%

“…As vast number of schemes have been built over Type-I groups, e.g, [9][10][11][12][13][14][15], bilinear-type conversion methods that translate schemes designed for Type-I groups into ones that work over Type-III groups have been developed [16][17][18][19][20][21][22]. Recall that cryptographic schemes designed over Type-I groups do not necessarily work over Type-III groups due to the presence of symmetric pairings, e(X, X ).…”

Section: Introductionmentioning

confidence: 99%

“…Automated conversion methods in the literature [20][21][22] are only for small-scale schemes consisting of up to tens of group operations. To follow the secure conversion framework introduced in [21], one needs to convert not only the algorithms in the target scheme but those that appear in security proofs. It makes the target of conversion much larger than the scheme itself.…”

Section: Introductionmentioning

confidence: 99%

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Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes

Abe

Hoshino

Ohkubo³

2019

IEICE Trans. Fundamentals

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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 computeraided 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.

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Section: Our Contributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes

Abe

Hoshino

Ohkubo³

2019

IEICE Trans. Fundamentals

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“…Our tool 6 for the synthesis of SPS schemes consists of two components. The first component takes the description of a search space and generates all included SPS schemes.…”

Section: Synthesis Of Schemesmentioning

confidence: 99%

“…Their tool AutoGroup converts schemes in the Type I setting into schemes in the Type III setting, whereas their tool AutoStrong transforms an existentially unforgeable signature into a strongly unforgeable one, using SMT solvers to check whether the original signature satisfies a criterion allowing an efficient transformation. The idea of automatically transforming constructions from the symmetric to the asymmetric setting was further considered by Abe, Groth, Ohkubo and Tango [6], who develop an automated transformation of Type I protocols into Type III protocols.…”

Section: Other Related Workmentioning

confidence: 99%

Strongly-Optimal Structure Preserving Signatures from Type II Pairings: Synthesis and Lower Bounds

Barthe

Fagerholm

Fiore

et al. 2015

Lecture Notes in Computer Science

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Abstract. Recent work on structure-preserving signatures studies optimality of these schemes in terms of the number of group elements needed in the verification key and the signature, and the number of pairing-product equations in the verification algorithm. While the size of keys and signatures is crucial for many applications, another important aspect to consider for performance is the time it takes to verify a given signature. By far, the most expensive operation during verification is the computation of pairings. However, the concrete number of pairings that one needs to compute is not captured by the number of pairing-product equations considered in earlier work. To fill this gap, we consider the question of what is the minimal number of pairings that one needs to compute in the verification of structure-preserving signatures. First, we prove lower bounds for schemes in the Type II setting that are secure under chosen message attacks in the generic group model, and we show that three pairings are necessary and that at most one of these pairings can be precomputed. We also extend our lower bound proof to schemes secure under random message attacks and show that in this case two pairings are still necessary. Second, we build an automated tool to search for schemes matching our lower bounds. The tool can generate automatically and exhaustively all valid structure-preserving signatures within a user-specified search space, and analyze their (bounded) security in the generic group model. Interestingly, using this tool, we find a new randomizable structure-preserving signature scheme in the Type II setting that is optimal with respect to the lower bound on the number of pairings, and also minimal with respect to the number of group operations that have to be computed during verification.

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A Practical Compiler for Attribute-Based Encryption: New Decentralized Constructions and More

Venema

2023

Lecture Notes in Computer Science

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Converting Cryptographic Schemes from Symmetric to Asymmetric Bilinear Groups

Cited by 28 publications

References 20 publications

Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes

Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes

Strongly-Optimal Structure Preserving Signatures from Type II Pairings: Synthesis and Lower Bounds

A Practical Compiler for Attribute-Based Encryption: New Decentralized Constructions and More

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