The Geometry of Lattice Cryptography

Micciancio, Daniele

doi:10.1007/978-3-642-23082-0_7

Cited by 8 publications

(6 citation statements)

References 84 publications

(129 reference statements)

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“…First, we review some previous work as following. Combining the above two lemmas, we have the following result which is also shown in reference [19]. Combining Klein's algorithm [17] and the relationship between primal and dual lattices, we first improve Lemma 3.3 using a randomized reduction algorithm.…”

Section: Lemma 29 ([17]) There Is a Randomized Algorithm Klein(b Tmentioning

confidence: 66%

Solving Closest Vector Instances Using an Approximate Shortest Independent Vectors Oracle

Tian

Wei

Lin

2015

J. Comput. Sci. Technol.

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Given a lattice L ⊂ R n and some target vector, this paper studies the algorithms for approximate closest vector problem (CVP γ ) by using an approximate shortest independent vectors problem oracle (SIVP γ ). More precisely, if the distance between the target vector and the lattice is no larger than c γn λ 1 (L) for any constant c > 0, we give randomized and deterministic polynomial time algorithms to find a closest vector, which improves the known result by a factor of 2c. Moreover, if the distance between the target vector and the lattice is larger than some quantity with respect to λ n (L), using SIVP γ oracle and Babai's nearest plane algorithm, we can solve CVP γ √ n in deterministic polynomial time. Specially, if the approximate factor γ ∈ (1, 2) in the SIVP γ oracle, we obtain a better reduction factor for CVP.

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Section: Lemma 29 ([17]) There Is a Randomized Algorithm Klein(b Tmentioning

confidence: 66%

Solving Closest Vector Instances Using an Approximate Shortest Independent Vectors Oracle

Tian

Wei

Lin

2015

J. Comput. Sci. Technol.

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“…The generalization denoted as the i-th successive minima is defined such that the ballB(0, r) = {x ∈ R m | x ≤ r}, of radius r and center 0, contains at least i linearly independent vectors [Mic11].…”

Section: Lattices and Ideal Latticesmentioning

confidence: 99%

“…The SIVP asks for n short linearly independent vectors and is also provided as it plays an important role in the construction of cryptographic primitives [Mic11].…”

Section: Computational Problems On Latticesmentioning

confidence: 99%

Efficient implementation of ideal lattice-based cryptography

Pöppelmann¹

2017

It - Information Technology

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Digital signatures and public-key encryption are used to protect almost any secure communication channel on the Internet or between embedded devices. Currently, protocol designers and engineers usually rely on schemes that are either based on the factoring assumption (RSA) or on the hardness of the discrete logarithm problem (DSA/ECDSA). But in case of advances in classical cryptanalysis or progress on the development of quantum computers the hardness of these closely related problems might be seriously weakened. In order to prepare for such an event, research on alternatives is required to provide long-term security.In this thesis, we focus on the efficient implementation of such alternative public-key cryptosystems whose security is based on the intractability of certain computational problems on ideal lattices. While an extensive theoretical background exists for lattice-based and ideal latticebased cryptography, not much is known about the efficiency of practical instantiations, especially on constrained and cost-sensitive platforms. We thus investigate novel algorithms and implementation techniques for fast and flexible polynomial multiplication and Gaussian sampling and then use these building blocks to implement public-key encryption and signature schemes. The results provided in this thesis show that lattice-based schemes can be optimized for high performance or resource efficiency on embedded microcontrollers and reconfigurable hardware. Our implementations of a public-key encryption scheme based on the ring learning with errors problems (RLWE) or of the bimodal lattice signature scheme (BLISS) can even outperform classical ECC-and RSA-based implementations.Lattice-based cryptography can also be used to realize homomorphic cryptography that allows computation on encrypted data. However, due to the large parameter sets and complex operations required, even for simple homomorphic evaluation operations, the performance of these schemes is a major issue preventing practical usage. In this thesis we investigate options for acceleration of homomorphic cryptography in a cloud environment using reconfigurable hardware. We implement all evaluation operations of the YASHE homomorphic encryption scheme and propose methods to deal with large ciphertext and key sizes as well as limited memory bandwidth. KeywordsPost-quantum cryptography, public-key cryptosystem, embedded system, microcontroller, FPGA KurzfassungDigitale Signaturen und Public-Key-Verschlüsselung werden für den Schutz nahezu jeder sicheren Kommunikation über das Internet oder zwischen eingebetteten Systemen genutzt. Die Sicherheit basiert dabei entweder auf der Faktorisierungsannahme (RSA) oder der Annahme, dass es schwer ist, das diskrete Logarithmus-Problem (DSA/ECDSA) zu lösen. Durch Fortschritte in der klassischen Kryptoanalyse oder bei der Entwicklung von Quantencomputern könnten diese Probleme allerdings in Zukunft ernsthaft geschwächt oder gelöst werden. Daher ist Forschung zu alternativen Public-Key-Kryptosystemen erforderlich, die in ...

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“…Over a data set Q , let + , × , E n c , D e c , K r , and K u denotes the addition operation, the multiplication operation, the encryption process, the decryption process, the private key, and the public key, respectively. HOM allows homomorphic addition as follows:

a + b = D e c_{K_{r}} ((), E n c_{K_{u}} (a) + E n c_{K_{u}} (b)), a, b \in Q .

HOM allows homomorphic multiplication as follows:

a \times b = D e c_{K_{r}} ((), E n c_{K_{u}} (a) \times E n c_{K_{u}} (b)), a, b \in Q .

There are various encryption methods for the HOM layer, including those in . Random (RND) : The RND layer does not allow any efficient computation on ciphertext because it maps the same plaintext into different ciphertexts with overwhelming probability. This layer is the strongest among all the layers.…”

Section: Background Techniquesmentioning

confidence: 99%

“…The authors propose a scheme for smart grid in the paper , which processes data of all the dimensions. Other research on homomorphic encryption include .…”

Section: Related Workmentioning

confidence: 99%

IP²DM: integrated privacy-preserving data management architecture for smart grid V2G networks

Han

Xiao

2016

Wirel. Commun. Mob. Comput.

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With the development of battery vehicles, vehicle-to-grid (V2G) networks are becoming more and more important in smart grid. Although battery vehicles are environmentally friendly and flexible to use two-way communication and two-way electricity flow, they also raise privacy-preservation challenges, such as location and movement privacy. On the one hand, utility companies have to monitor the grid and analyze user data to control the power production, distribution, scheduling, and billing process, while typical users need to access their data later online. On the other hand, users are not willing to provide their personal data because they do not trust the system security of the utility companies where their data stored, and it may potentially expose their privacy. Therefore, in this paper, we study data management of V2G networks in smart grid with privacy-preservation to benefit both the customers and the utility companies. Both data aggregation and data publication of V2G networks are protected in the proposed architecture. To check its security, we analyze this architecture in several typical V2G networks attacks. We conduct several experiments to show that the proposed architecture is effective and efficient, and it can enhance user privacy protection while providing enough information for utility companies to analyze and monitor the grid.

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The Geometry of Lattice Cryptography

Cited by 8 publications

References 84 publications

Solving Closest Vector Instances Using an Approximate Shortest Independent Vectors Oracle

Solving Closest Vector Instances Using an Approximate Shortest Independent Vectors Oracle

Efficient implementation of ideal lattice-based cryptography

IP²DM: integrated privacy-preserving data management architecture for smart grid V2G networks

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The Geometry of Lattice Cryptography

Cited by 8 publications

References 84 publications

Solving Closest Vector Instances Using an Approximate Shortest Independent Vectors Oracle

Solving Closest Vector Instances Using an Approximate Shortest Independent Vectors Oracle

Efficient implementation of ideal lattice-based cryptography

IP2DM: integrated privacy-preserving data management architecture for smart grid V2G networks

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Product

Resources

About

IP²DM: integrated privacy-preserving data management architecture for smart grid V2G networks