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Lecture notes in computer science

How to Share a Lattice Trapdoor: Threshold Protocols for Signatures and (H)IBE

Rikke Bendlin, Sara Krehbiel, Chris Peikert

Published Jan 1, 2013• 72 citations
Publisher
DOI
10.1007/978-3-642-38980-1_14

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How to Share a Lattice Trapdoor: Threshold Protocols for Signatures and (H)IBE.

Rikke Bendlin, Sara Krehbiel, Chris Peikert

We develop secure threshold protocols for two important operations in lattice cryptography, namely, generating a hard lattice Λ together with a “strong ” trapdoor, and sampling from a discrete Gaussian distribution over a desired coset of Λ using the trapdoor. These are the central operations of many cryptographic schemes: for example, they are exactly the key-generation and signing operations (respectively) for the GPV signature scheme, and they are the public parameter generation and private key extraction operations (respectively) for the GPV IBE. We also provide a protocol for trapdoor delegation, which is used in lattice-based hierarchical IBE schemes. Our work therefore directly transfers all these systems to the threshold setting. Our protocols provide information-theoretic (i.e., statistical) security against adaptive corruptions in the UC framework, and they are private and robust against an optimal number of semi-honest or malicious parties. Our Gaussian sampling protocol is both noninteractive and efficient, assuming either a trusted setup phase (e.g., performed as part of key generation) or a sufficient amount of interactive but offline precomputation, which can be performed before the inputs to the sampling phase are known.

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Novel efficient lattice-based IBE schemes with CPK for fog computing

Yanfeng Shi, Shuo Qiu, Jiqiang Liu +1 more

The data security of fog computing is a key problem for the Internet of things. Identity-based encryption (IBE) from lattices is extremely suitable for fog computing. It is able to not only simplify certificate management, but also resist quantum attacks. In this paper, firstly, we construct a novel efficient lattice-based IBE scheme with Combined Public Key (CPK) technique by keeping from consumptive trapdoor generation algorithm and preimage sampling algorithm, which is required by the existing lattice-based IBE schemes based on learning with errors (LWE). In addition, its key storage cost is lower and it is IND-ID-CPA secure in the random oracle model. Furthermore, based on this, an enhanced lattice-based IBE scheme with IND-ID-CCA security is developed by employing strong one-time signature. Our schemes only need O(n3/log n) additions of vectors, while the existing schemes need at least O(n3) of additions and multiplications in Setup and Extract phase.

Mathematical Biosciences & Engineering•Jan 1, 2020•2 citations
We develop secure threshold protocols for two important operations in lattice cryptography, namely, generating a hard lattice Λ together with a “strong ” trapdoor, and sampling from a discrete Gaussian distribution over a desired coset of Λ using the trapdoor. These are the central operations of many cryptographic schemes: for example, they are exactly the key-generation and signing operations (respectively) for the GPV signature scheme, and they are the public parameter generation and private key extraction operations (respectively) for the GPV IBE. We also provide a protocol for trapdoor delegation, which is used in lattice-based hierarchical IBE schemes. Our work therefore directly transfers all these systems to the threshold setting. Our protocols provide information-theoretic (i.e., statistical) security against adaptive corruptions in the UC framework, and they are private and robust against an optimal number of semi-honest or malicious parties. Our Gaussian sampling protocol is both noninteractive and efficient, assuming either a trusted setup phase (e.g., performed as part of key generation) or a sufficient amount of interactive but offline precomputation, which can be performed before the inputs to the sampling phase are known.
The data security of fog computing is a key problem for the Internet of things. Identity-based encryption (IBE) from lattices is extremely suitable for fog computing. It is able to not only simplify certificate management, but also resist quantum attacks. In this paper, firstly, we construct a novel efficient lattice-based IBE scheme with Combined Public Key (CPK) technique by keeping from consumptive trapdoor generation algorithm and preimage sampling algorithm, which is required by the existing lattice-based IBE schemes based on learning with errors (LWE). In addition, its key storage cost is lower and it is IND-ID-CPA secure in the random oracle model. Furthermore, based on this, an enhanced lattice-based IBE scheme with IND-ID-CCA security is developed by employing strong one-time signature. Our schemes only need O(n3/log n) additions of vectors, while the existing schemes need at least O(n3) of additions and multiplications in Setup and Extract phase.