Further Lower Bounds for Structure-Preserving Signatures in Asymmetric Bilinear Groups

Ghadafi, Essam

doi:10.1007/978-3-030-23696-0_21

Cited by 4 publications

(2 citation statements)

References 49 publications

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“…We note that while lower bounds for digital signature schemes exist, they are either limited to very special types of signature schemes (like structure-preserving signatures [2,1,25,26] in the pairing setting), or to bounds on the efficiency of constructions from symmetric primitives [23,4]. To the best of our knowledge, e.g., the (space or time) complexity of group-based signature schemes (without pairings) is not well-understood.…”

Section: Introductionmentioning

confidence: 99%

On the Impossibility of Purely Algebraic Signatures

Döttling

Hartmann

Hofheinz

et al. 2021

Lecture Notes in Computer Science

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The existence of one-way functions implies secure digital signatures, but not public-key encryption (at least in a black-box setting). Somewhat surprisingly, though, efficient public-key encryption schemes appear to be much easier to construct from concrete algebraic assumptions (such as the factoring of Diffie-Hellman-like assumptions) than efficient digital signature schemes. In this work, we provide one reason for this apparent difficulty to construct efficient signature schemes. Specifically, we prove that a wide range of algebraic signature schemes (in which verification essentially checks a number of linear equations over a group) fall to conceptually surprisingly simple linear algebra attacks. In fact, we prove that in an algebraic signature scheme, sufficiently many signatures can be linearly combined to a signature of a fresh message. We present attacks both in known-order and hidden-order groups (although in hidden-order settings, we have to restrict our definition of algebraic signatures a little). More explicitly, we show:the insecurity of all algebraic signature schemes in Maurer's generic group model (in pairing-free groups), as long as these schemes do not rely on other cryptographic assumptions, such as hash functions.the insecurity of a natural class of signatures in hidden-order groups, where verification consists of linear equations over group elements. We believe that this highlights the crucial role of public verifiability in digital signature schemes. Namely, while public-key encryption schemes do not require any publicly verifiable structure on ciphertexts, it is exactly this structure on signatures that invites attacks like ours and makes it hard to construct efficient signatures.

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Section: Introductionmentioning

confidence: 99%

On the Impossibility of Purely Algebraic Signatures

Döttling

Hartmann

Hofheinz

et al. 2021

Lecture Notes in Computer Science

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show abstract

“…We briefly take a view to several facts related with asymmetric bilinear groups [ 15 ] . Let G be the group parameters generation algorithm which takes an security parameter 1 λ as input to output the tuple

(p, {double-struckG}_{1}, {double-struckG}_{2}, {double-struckG}_{T}, e, g, \tilde{g})

in which p represents the big prime,

{double-struckG}_{1}, {double-struckG}_{2}

and

G_{T}

denote multiplicative groups with order p , g and > are the generators of

G_{1}

and

G_{2}

respectively.…”

Section: Preliminariesmentioning

confidence: 99%

An Efficient SCF‐PEKS Without Random Oracle Under Simple Assumption

Wang¹,

Li²,

Fan³

et al. 2021

Chinese J of Electronics

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The Public key encryption scheme with keyword search (PEKS), firstly put forward by Boneh et al., can achieve the keyword searching without revealing any information of the initial data. However, the original PEKS scheme was required to construct a secure channel, which was usually expensive. Aimed at resolving this problem, Baek et al. put forward an improved scheme, which tried to construct a Secure channel free PEKS (SCF‐PEKS). Subsequently, several SCF‐PEKS schemes were proposed, however most of them turned out only secure in the random oracle model, which possibly lead to the construction of insecure schemes. Therefore, Fang et al. put forward an enhanced SCF‐PEKS construction, which was provably secure in the standard model, however this construction needed a strong and complicated assumption. Then Yang et al. put forward an SCF‐PEKS construction under simple assumption, but their construction had a big reduction in efficiency. In this article, we propose an SCF‐PEKS construction, which is provably secure under the same assumption as that of Yang et al.'s scheme, however, with better performance. Then we give its full security proof, along with the performance analysis. Finally, we improve the SCF‐PEKS construction to resist Keyword guessing attack (KGA) and give its security demonstration.

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Partially Structure-Preserving Signatures: Lower Bounds, Constructions and More

Ghadafi

2021

Applied Cryptography and Network Security

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Further Lower Bounds for Structure-Preserving Signatures in Asymmetric Bilinear Groups

Cited by 4 publications

References 49 publications

On the Impossibility of Purely Algebraic Signatures

On the Impossibility of Purely Algebraic Signatures

An Efficient SCF‐PEKS Without Random Oracle Under Simple Assumption

Partially Structure-Preserving Signatures: Lower Bounds, Constructions and More

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