ideal lattices
Ideal Multilinear Maps Based on Ideal Lattices
... Garg, Gentry, and Halevi (GGH) recently described the first candidate construction of multilinear maps from ideal lattices [GGH13]. The GGH construction, whose encodings are randomized with noise and ...
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Multilinear Maps Using Ideal Lattices without Encodings of Zero
... Following the GGH’s framework, Coron, Lepoint, and Tibouchi [CLT13] (CLT) described a relatively practical construction that works over integers instead of ideal lattices, and is implemented using heuristic ...
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Sieving for Shortest Vectors in Ideal Lattices: a Practical Perspective
... (non-ideal) lattices with additional stages of optimizations for negacyclic ideal ...generic lattices of dimensions 80, 88, and 96, using a variable number of nodes, clearly indi- cating the ...
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Implementing Candidate Graded Encoding Schemes from Ideal Lattices
... Abstract. Multilinear maps have become popular tools for designing cryptographic schemes since a first approximate realisation candidate was proposed by Garg, Gentry and Halevi (GGH). This construction was later improved ...
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ILTRU: An NTRU-Like Public Key Cryptosystem Over Ideal Lattices
... Abstract— In this paper we present a new NTRU-Like public key cryptosystem with security provably based on the worst case hardness of the approximate both Shortest Vector Problem (SVP) and Closest Vector Problem (CVP) in ...
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GGHLite: More Efficient Multilinear Maps from Ideal Lattices
... Abstract. The GGH Graded Encoding Scheme [10], based on ideal lattices, is the first plausible ap- proximation to a cryptographic multilinear map. Unfortunately, using the security analysis in [10], the ...
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Strongly Secure Authenticated Key Exchange from Ideal Lattices
... on lattices have appeared as a prospective replacement to more traditional ones based on the factoring and discrete logarithm ...from ideal lattices, which is secure in eCK ...
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Security Analysis of Cryptosystems Using Short Generators over Ideal Lattices
... In this paper, we analyzed the security of cryptosystems using short generators over ideal lattices against the RSG attack. We gave explicit estimates of the special values of Dirichlet L-functions at 1 for ...
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CONSTRUCTION OF NESTED REAL IDEAL LATTICES FOR INTERFERENCE CHANNEL CODING
... nested lattices. Such real ideal lattices are featured by their generator and Gram matrices which are developed by an algorithm [7] and, therefore, they can be described by their corresponding ...
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On the Relationship Between Two Embeddings of Ideals into Geometric Space and the Shortest Vector Problem in Principal Ideal Lattices.
... Many interesting research directions were outside the scope of this dissertation. In this work we ran experiments using the LLL lattice reduction algorithm to reduce a specific basis of a principal ideal lattice. ...
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On Ideal Lattices and Learning with Errors Over Rings
... the ideal’ I from an arbitrary ideal lattice instance (see Lemmas ...for ideal lattices following [Mic02] used samples from a principal subideal of I with known generator; however, this ...
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A Provably Secure Variant of ETRU Based on Extended Ideal Lattices Over Direct Product of Dedekind Domains
... SVP is the most important algorithmic problem on lattices. Given a basis of a lattice L, we aim to find a shortest vector in L \ 0. It can be generalized to γ- SVP by asking for a non-zero vector that is no longer ...
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Candidate Multilinear Maps from Ideal Lattices
... pal ideal lattices (Section ...principal ideal lattices (compared to general ideal lattices) to preserve ...Principal ideal lattices cer- tainly arise in our scheme ...
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Authenticated Key Exchange from Ideal Lattices
... from ideal lattices, which is conceptually simple and has similarities to the Diffie-Hellman based protocols such as HMQV (CRYPTO 2005) and OAKE (CCS ...
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New multilinear maps from ideal lattices
... Abstract. Recently, Hu and Jia presented an efficient attack on the GGH13 map. They show that the MPKE and WE based on GGH13 with public tools of encoding are not secure. Currently, an open problem is to fix GGH13 with ...
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CONSTRUCTION OF COMPLEX NESTED IDEAL LATTICES FOR COMPLEX-VALUED CHANNEL QUANTIZATION
... nested lattices. Such complex ideal lattices are described by their corresponding construction A which furnishes us, in this case, nested lattice codes (coset ...nested lattices, then we show ...
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Two-message Key Exchange with Strong Security from Ideal Lattices
... In the last game, i.e. Game 7 , the session key of the test oracle is changed to be a random value. No PPT adversary can distinguish this change because of the security of PRF. Since the[r] ...
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NTRU-LPR IND-CPA: A New Ideal Lattices-based Scheme
... In the context of linear codes, the hardness of BDD was studied by Vardy [61], and later in the context of lattices by Liu et al. [33]. In the case of uSVP(Unique SVP) and BDD, the connection established by [11, ...
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Identity-Based Key-Encapsulation Mechanism from Multilinear Maps
... In this paper we present an IB-KEM construction based on groups with a multilin- ear map [13]. We present our IB-KEM in a generic “leveled” multilinear map setting and prove its security in the selective-ID model. Then, ...
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Adaptive key recovery attacks on NTRU-based somewhat homomorphic encryption schemes
... [LPR13]. Lattices constructed using such rings are often called ideal ...that ideal lattices maintain the same security guarantees as conventional lattices, no significant improve- ment ...
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