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Noise Distributions in Homomorphic Ring-LWE [article]

Sean Murphy, Rachel Player
2017 IACR Cryptology ePrint Archive  
In the Ring-LWE literature, there are several works that use a statistical framework based on δ-subgaussian random variables.  ...  In this paper, we completely characterise δ-subgaussian random variables. In particular, we show that this relaxation from a subgaussian random variable corresponds only to the shifting of the mean.  ...  Statistical arguments based on δ-subgaussian random variables have been used in Ring-LWE cryptography in many application settings including signature schemes [7] , key exchange [10] and homomorphic  ... 
dblp:journals/iacr/MurphyP17 fatcat:fg6hlhvyenbfjdqls4cg2nxjg4

A General Design Method of Constructing Fully Homomorphic Encryption with Ciphertext Matrix

2019 KSII Transactions on Internet and Information Systems  
We use decryption structure as tool to analyze homomorphic property and noise growth during homomorphic evaluation.  ...  It is important to construct fully homomorphic encryption with ciphertext matrix that makes fully homomorphic encryption become very nature and simple.  ...  Since it is unknown how to exploit the ring structure of ring LWE to improve lattice reduction, the distinguishing attack can also be applied in ring LWE by embedding ring LWE instance into a LWE lattice  ... 
doi:10.3837/tiis.2019.05.022 fatcat:gnpwo6x5dzdpzjk64aitsptkbi

Automatize parameter tuning in Ring-Learning-With-Errors-based leveled homomorphic cryptosystem implementations [article]

Vincent Herbert
2019 IACR Cryptology ePrint Archive  
It makes use of the LWE-Estimator to obtain up-to-date security estimations.  ...  We focus on one of them, a leveled homomorphic cryptosystem (LHE): Brakersi/Fan-Vercauteren's (BFV) one.  ...  size q = q/scale return q The BFV case Maximal noise in a fresh ciphertext and maximal noise of a (homomorphic) ciphertext have been computed in [26] for some ring-LWE-based LHE schemes.  ... 
dblp:journals/iacr/Herbert19 fatcat:c7gnyo4mfvbujdqoyv6b7obuuu

Efficient Homomorphic Conversion Between (Ring) LWE Ciphertexts [article]

Hao Chen, Wei Dai, Miran Kim, Yongsoo Song
2020 IACR Cryptology ePrint Archive  
In the past few years, significant progress on homomorphic encryption (HE) has been made toward both theory and practice.  ...  The most promising HE schemes are based on the hardness of the Learning With Errors (LWE) problem or its ring variant (RLWE).  ...  (Ring) Learning with Errors Given the dimension N , modulus q and error distribution ψ over Z, the LWE distribution with secret s ∈ Z N is a distribution over Z N +1 q which samples a ← U (Z N q ) and  ... 
dblp:journals/iacr/0030DKS20 fatcat:wbpzy6ucorhepar4amyydcfj44

Homomorphism learning problems and its applications to public-key cryptography [article]

Christopher Leonardi, Luis Ruiz-Lopez
2019 IACR Cryptology ePrint Archive  
We proved, however, that in order to obtain a quantum resistant encryption scheme, commutative groups cannot be used to instantiate this protocol.  ...  Elements sampled form the noise distribution χ are all contained in the kernel of the secret homomorphism ψ.  ...  Strictly speaking, the resulting sample is under a new LWE distribution, since the noise of some of the elements in the public key was added.  ... 
dblp:journals/iacr/LeonardiR19 fatcat:raztkwdyzfdrnimwllcya5ymza

Ring Packing and Amortized FHEW Bootstrapping

Daniele Miccianco, Jessica Sorrell, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
allows to homomorphically evaluate arbitrary NAND boolean circuits.  ...  The FHEW fully homomorphic encryption scheme (Ducas and Micciancio, Eurocrypt 2015) offers very fast homomorphic NAND-gate computations (on encrypted data) and a relatively fast refreshing procedure that  ...  We start with ϕ(d) (high noise) ciphertexts in LWE 2/q n [∆], as produced by the FHEW HomNAND operation, working on LWE encryption in dimension n.  ... 
doi:10.4230/lipics.icalp.2018.100 dblp:conf/icalp/MicciancoS18 fatcat:yiow62hm6fffha5s2kf6a3ccze

A Central Limit Framework for Ring-LWE Decryption [article]

Sean Murphy, Rachel Player
2019 IACR Cryptology ePrint Archive  
Ring-LWE.  ...  We apply our framework and results to a homomorphic Ring-LWE cryptosystem of Lyubashevsky, Peikert and Regev (Eurocrypt 2013, full version) in order to illustrate the benefit of this approach.  ...  In Proposition 3, we apply Proposition 2 to approximate the distribution of the noise in a Ring-LWE ciphertext expressed in an appropriate decryption basis.  ... 
dblp:journals/iacr/MurphyP19 fatcat:vrc2u6tmtncdxexelpleuk5svm

Batched Multi-hop Multi-key FHE from Ring-LWE with Compact Ciphertext Extension [chapter]

Long Chen, Zhenfeng Zhang, Xueqing Wang
2017 Lecture Notes in Computer Science  
In this work, we focus on MKFHE constructions from standard assumptions and propose a new construction of ring-LWE-based multi-hop MKFHE scheme.  ...  Therefore, our construction can encrypt a ring element rather than a single bit and naturally inherits the advantages in aspects of the ciphertext/plaintext ratio and the complexity of homomorphic operations  ...  It has been shown for ring-LWE that one can equivalently assume that s is alternatively sampled from the noise distribution χ [LPR13a].  ... 
doi:10.1007/978-3-319-70503-3_20 fatcat:eht45ov3jjd6dnlmlcouvw4w64

Fully dynamic Multi-Key FHE without Gaussian Noise

Yu Huang, Kaigui Wu, Ming Chen
2021 IEEE Access  
Fully dynamic multi-key fully homomorphic encryption (FHE) that allows an unlimited number of homomorphic operations for unconstrained parties.  ...  The paper proposed a fully dynamic multi-key FHE that based on the learning with rounding (LWR) problem which leaves out the time-consuming Gaussian sampling required in the LWE problem while sustaining  ...  LWE to LWR reduction by a reduction from Ring-LWE to Module Ring-LWR, their central techniques is a new ring leftover hash lemma.  ... 
doi:10.1109/access.2021.3069214 fatcat:rroc4mp3unddpgqx6nky63xav4

Fully Homomorphic Encryption Based on the Ring Learning with Rounding Problem

Fucai Luo, Fuqun Wang, Kunpeng Wang, Kefei Chen
2019 IET Information Security  
Almost all existing well-known fully homomorphic encryption (FHE) schemes, which are based on either the learning with errors (LWE) or the ring LWE problem, require expensive Gaussian noise sampling.  ...  In this study, the authors propose an FHE scheme based on the ring learning with rounding (RLWR) problem.  ...  Acknowledgments This work was supported in part by the National Key Research and Development Program of China (no. 2017YFB0802000), the National Nature Science Foundation of China (nos. 61672030 and U1705264  ... 
doi:10.1049/iet-ifs.2018.5427 fatcat:bu2rcd4esjdani7rr4elihevm4

Bootstrapping in FHEW-like Cryptosystems [article]

Daniele Micciancio, Yuriy Polyakov
2020 IACR Cryptology ePrint Archive  
The FHEW cryptosystem was originally designed based on standard (Ring, circular secure) LWE assumptions, and its initial implementation was able to run bootstrapping in less than 1 second.  ...  The TFHE cryptosystem used somewhat stronger assumptions, such as (Ring, circular secure) LWE over the torus with binary secret distribution, and applied several other optimizations to reduce the bootstrapping  ...  We recall the construction of homomorphic encryption schemes from the Ring LWE problem following the modular approach of [20] .  ... 
dblp:journals/iacr/MicciancioP20 fatcat:sokm7hq5k5du7dpvx2oyvmo3uq

FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second [chapter]

Léo Ducas, Daniele Micciancio
2015 Lecture Notes in Computer Science  
We present a new method to homomorphically compute simple bit operations, and refresh (bootstrap) the resulting output, which runs on a personal computer in just about half a second.  ...  Bootstrapping in the latest implementation of FHE, the HElib library of Halevi and Shoup (Crypto 2014), requires about half an hour.  ...  Acknowledgments The authors wish to thank Igors Stepanovs for interesting conversations about circular security that lead us to the new homomorphic NAND procedure.  ... 
doi:10.1007/978-3-662-46800-5_24 fatcat:pzev7g7ix5e5tgp6kz4ydw6aue

Polly Cracker, Revisited [chapter]

Martin R. Albrecht, Pooya Farshim, Jean-Charles Faugère, Ludovic Perret
2011 Lecture Notes in Computer Science  
We then show that noisy encoding of messages results in a fully IND-CPA-secure somewhat homomorphic encryption scheme.  ...  These problems can be seen as natural generalisations of the LWE problem and the approximate GCD problem over polynomial rings.  ...  Let P be a polynomial ring distribution and χ α,q be the discrete Gaussian distribution.  ... 
doi:10.1007/978-3-642-25385-0_10 fatcat:osym22c3arcmjiqrdmebsmpuym

Ring-LWE: Applications to Cryptography and Their Efficient Realization [chapter]

Sujoy Sinha Roy, Angshuman Karmakar, Ingrid Verbauwhede
2016 Lecture Notes in Computer Science  
Later for efficiency LWE was adapted for ring polynomials known as Ring-LWE. In this paper we discuss some of these ring-LWE based schemes that have been designed.  ...  The learning with errors problem introduced by Oded Regev offers a way to design secure cryptography schemes in the post-quantum world.  ...  The secret in a ring-LWE based scheme is a polynomial and arithmetic operations involve masking data and the secret using discrete Gaussian noise.  ... 
doi:10.1007/978-3-319-49445-6_18 fatcat:7y34eqtumvhexap5rusvgjzppy

Integer-Wise Functional Bootstrapping on TFHE: Applications in Secure Integer Arithmetics

Hiroki Okada, Shinsaku Kiyomoto, Carlos Cid
2021 Information  
TFHE is a fast fully homomorphic encryption scheme proposed by Chillotti et al. in Asiacrypt' 2018.  ...  In this paper, we construct a technique for operating any 1-variable function in only one bootstrapping of the integer-wise TFHE.  ...  As mentioned before, TLWE includes the LWE problem and the Ring-LWE problem. When N > 1 is large and k = 1, TLWE is the (binary-secret) Ring-LWE.  ... 
doi:10.3390/info12080297 fatcat:xtlstbgrwbertcmgzjqevousam
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