LWE-based Homomorphic Encryption April 12-16, 2013 Scribe: Kina Winoto, Cl ement Canonne We are going to describe the LWE-based homomorphic encryption scheme based on the works from [Gen09, BV11, BGV12, Bra12]. Parameters : Let n0be the security parameter, and we have m= poly(n0), q>super-poly(n0) To start, we describe an LWE-based cryptosystem that has substantially smaller keys and ciphertexts than the more well-known systems in the literature (namely, the original system of Regev [Reg05] and its more efﬁcient amortized variants [PVW08, GPV08]) ** Jintai Ding LWE-based Authentication and Key Leakage Prevention**. Motivation Lattice-based Key Exchange Attack with key reuse Work in Progress. Attack Motivation - RLWE Key Exchange with key reuse. Initial attack by Scott Fluhrer for exploiting reused keys but the attack does not work for the KE described here mance of (R)LWE-based key exchange can be as ffi as tradi-tional schemes such as RSA or elliptic curve cryptography [1, 2], making (R)LWE-based algorithms an attractive candidate for the age of post-quantum security. The ring version of LWE, RLWE, is generally considered much more ffi than generic LWE (also known as standard LWE)

In this work, we construct novel LWE-based encryption schemes and for-mally analyze their correctness and security guarantees. With respect to our focus on privacy-preserving data aggregation, we showcase a particularly well-suited use case of LWE-based encryption due to the inherent proper-ties of the LWE problem R-LWE-based cryptography The R-LWE problem was introduced by Lyubashevsky, Peikert, and Regev in [5] as a hard lattice problem for constructing cryptographic schemes. Its additional ring structure leads to significant efficiency and bandwidth improvements over schemes built from the Learning With Errors (LWE) problem introduced by Regev in [6] A major advantage that RLWE based cryptography has over the original learning with errors (LWE) based cryptography is found in the size of the public and private keys. RLWE keys are roughly the square root of keys in LWE. For 128 bits of security an RLWE cryptographic algorithm would use public keys around 7000 bits in length Parameter Selection in Ring-LWE-based Fully Homomorphic Encryption. Rachel Player Information Security Group, Royal Holloway, University of London. based on joint works with Martin R. Albrecht, Hao Chen, Kim Laine, Sam Scott, and Yuhou Xia. London-ish Lattice Coding & Crypto Meeting | September 29, 2017

- device a technique to combine the LWE-based ABE scheme of Boneh et al. [14] (which we call BGG+-ABE) and the LWE-based IPFE scheme of Agrawal et al. [6] (which is abbreviated as ALS-IPFE). In an ABIPFE scheme, using a master secret-key msk, a central authority generates secret-keys of the form sk f;y for a tuple (f;y) where f is a depth-
- SIS +
**LWE****Based****Based**on NTRU Uses Discrete Gaussian Sampling**Based**on (Module-)**LWE**/ SIS Uses Uniform Sampling Additionally useful for IBE Additionally useful for ZK-Proofs Signature Size Digital Signature Overview (All are Zero-Knowledge in the QROM - Practical Implementation of Ring-SIS/LWE based Signature and IBE Pauline Bert, Pierre-Alain Fouque, Adeline Roux-Langlois, and Mohamed Sabt PQCrypto 2018, April 11 Univ Rennes, CNRS, IRISA
- tems. In order to assess the concrete security of LWE-based schemeswhen given the parameters, we need to investigate the current algorithms which can be used to solve LWE problem and their actual complexity. In this paper, we give a brie

Practical Implementation of Ring-SIS/LWE based Signature and IBE Pauline Bert, Pierre-Alain Fouque, Adeline Roux-Langlois, and Mohamed Sabt Univ Rennes, CNRS, IRISA first.last@irisa.fr Abstract. Lattice-based signature and Identity-Based Encryption are well-known cryptographic schemes, and having both e cient and provabl For instance, FrodoKEM, a standard LWE based NIST candidate, reported latencies around 500 micro-seconds while encrypting on a 3.4GHz Intel i7-6700 processor with AVX2 support. Additionally, LWE comes with a high ciphertext to plaintext cost, in terms of both storage and computation cryptographic primitives : unforgeable lattice-based signatures, LWE-based ho-momorphic encryption and trapdoors for lattices. The scheme is inspired by existing e-voting protocols, in particular Helios [2], which has already been used for medium-scale elections (and its variant Belenios). However, our scheme dif-fers in two principal ways proving just one plaintext, nor do they apply to Ring-LWE based encryption schemes. In particular, Ring-LWE based schemes are able to encrypt O(n) plaintext bits into one (or two) polynomial, which is often all that is needed. Yet, the techniques in [18] do not seem to be helpful here. The reason is that the challenge matrix required in [18] need

- 2. An LWE-based direct construction of CP-ABE: We show how to leverage any {0,1}-LSSS with the above extra property to get a CP-ABE scheme. Conceptually, to some extent the construction can be viewed as a translation of Waters' [Wat11, Section 6] construction of a CP-ABE scheme under the Decisional Bilinear Diffie-Hellman (DBDH) Assumption int
- In particular, if a quantum sample state could be created from classical samples, then it would be possible to break LWE-based schemes using our learning algorithm. Finally, we extend our results and show quantum learning algorithms for three related problems: learning parity with noise, learning with rounding, and short integer solution
- TFHE is an open-source library for fully homomorphic encryption, distributed under the terms of the Apache 2.0 license. The underlying scheme is described in best paper of the IACR conference Asiacrypt 2016: Faster fully homomorphic encryption: Bootstrapping in less than 0.1 seconds, presented by Ilaria Chillotti, Nicolas Gama, Mariya Georgieva and Malika Izabachène
- that ring-LWE-based cr yptog raphy can be applied on a g reater number of memor y-constrained devices. Our solution achieves a decr yption r unning time of about 7 s with a polynomial deg ree of 255. This is more than 10 times faster than our previous result) for an approximate security level of AES-128
- tion of LWE-based schemes.?Abridged parts of this paper was presented in INDOCRYPT 2013 [3]. L. T. Phong, L. Wang, and Y. Aono are with NICT, Japan. M. H. Nguyen was at Tokyo Institute of Technology. X. Boyen is with Queensland Institute of Technology. Emails: fphong, wlh, aonog@nict.go.jp

Lightweight R-LWE-based privacy preservation scheme for smart grid network Aarti Amod Agarkar* Symbiosis International (Deemed) University, Lavale, Mulshi Taluka, Pune, Maharashtra 412115, Indi Paillier-LWE-based-PHE CUDA版本：9.0与9.1皆可 PyTorch: 1.1.0 python-paillier-master python setup.py test python test.py LWE-based PHE mkdir key // 创建用于存储密钥的文件夹 python cpu_test.py | python cuda_test.py 数据集分割 python split_data.py LeNet训练 mkdir models // 创建用于存储模型的文件夹 LeNet.py、LeNet_subset.py与jointly_learning_demo.py可以独立运行（注意数据集路径） jointly_learning_with_encryption_demo.py需要注意. Multi-Authority Attribute Based Encryption Melissa Chase Computer Science Department Brown University Providence, RI 02912 mchase@cs.brown.edu Abstract LWE & Ring-LWE-based Key Exchange Protocols. LWE & Ring-LWE-based Key Exchange Protocols. Attacks (Key Reuse) 2015: NSA revealed key reuse issues for post-quantum encryption and key agreement 2016: Fluhrer proposed attack framework on Diﬃe-Hellman-like reconciliation-based key exchang We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of short vector problems on arbitrary lattices. Our construction improves on previous works in two aspects: 1) We show that somewhat homomorphic encryption can be based on.

* A fully homomorphic encryption (FHE) scheme allows anyone to transform an encryption of a message, $m$, into an encryption of any (efficient) function of that message, $f (m)$, without knowing the secret key*. We present a leveled FHE scheme that is based solely on the (standard) learning with errors ($\mathsf {LWE}$) assumption Ring-LWE based scheme . 3rd Candidate Submitted to NIST PQC NewHope: n=1024, = 8,.

This gives LWE-based cryp-tography strong security guarantees not shared by most other cryptographic constructions, such as conjectured security against quantum computers. In addition, LWE is attractive as it typically leads to efﬁcient implementations, involving low complexity operations (often mainly additions) * Dual LWE-Based Fully Homomorphic Encryption with Errorless Key Switching Abstract: Cloud computing raises new challenges for how to protect user privacy*. Fully homomorphic encryption is one way to solve the problem Practical Implementation of Ring-SIS/LWE based Signature and IBE Pauline Bert, Pierre-Alain Fouque, Adeline Roux-Langlois, and Mohamed Sabt PQCrypto 2018, April 1 The cryptosystem based on the Learning-with-Errors (LWE) problem is considered as a post-quantum cryptosystem, because it is not based on the factoring problem with large primes which is easily solved by a quantum computer. Moreover, the LWE-based cryptosystem allows fully homomorphic arithmetics so that two encrypted variables can be added and multiplied without decrypting them. This chapter. In this paper, we apply the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan (CRYPTO 2011) to secure matrix multiplication between two matrices. To reduce both the ciphertext size and the computation cost, we propose a new method to pack a matrix into a single ciphertexts so that it also enables efficient matrix.

Ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further. Title: An Homomorphic LWE based E-voting SchemeAuthors: Ilaria Chillotti, Nicolas Gama, Mariya Georgieva, and Malika Izabachene7th International Conference o.. Ideal lattice. In discrete mathematics, ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular, they have a significant place in cryptography. Micciancio defined a generalization of cyclic lattices as ideal. Classical hardness of the Learning with Errors problem AdelineLanglois Aric Team, LIP, ENS Lyon Joint work with Z. Brakerski, C. Peikert, O. Regev and D. Stehl

SIS + LWE Based Based on NTRU Uses Discrete Gaussian Sampling Based on (Module-) LWE / SIS Uses Uniform Sampling Additionally useful for IBE Additionally useful for ZK-Proofs Signature Size Digital Signature Overview (All are Zero-Knowledge in the QROM) Hash-and-Sign [HHPSW] [GVP] FALCON. FALCON 4 This paper proposes a practical hybrid solution for combining and switching between three popular Ring-LWE-based FHE schemes: TFHE, B/FV and HEAAN. This is achieved by first mapping the different plaintext spaces to a common algebraic structure and then by applying efficient switching algorithms. This approach has many practical applications What advantages and disadvantages can be distinguished in NTRU-based and LWE-based schemes relative to each other? In what cases which scheme gives advantage? UPD: I'm interesting in two things: 1)how well-studied their respective hardness problems are? 2)how fast existing NTRU-based and LWE-based PKE schemes relative to each other Some hard problems from lattices, like LWE (Learning with Errors), are particularly suitable for application in Cryptography due to the possibility of using worst-case to average-case reductions as evidence of strong security properties. In this work, we show two LWE-based constructions of zero-knowledge identification schemes and discuss their performance and security LWE -based schemes + [DM15] bootstrapping Final step: generalized version of [DM15] 1.Non binary messages 2.Lower noise amplitude 3 Post quantum: LWE (plus other PQ blocks) 12 / 25. Introduction The protocol Properties Conclusion LWE LWE Symmetric Encryption = 3 1 = 32

An homomorphic LWE based E-voting Scheme Ilaria Chillotti1, Nicolas Gama1;2, Mariya Georgieva3, and Malika Izabach ene4 1 Laboratoire de Math ematiques de Versailles, UVSQ, CNRS, Universit e Paris-Saclay, 78035 Versailles, France 2 Inpher, Switzerland 3 Gemalto, 6 rue de la Verrerie 92190, Meudon, France 4 CEA LIST, France Abstract. In this paper we present a new post-quantum electronic STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing On lattices, learning with errors, random linear codes, and cryptograph R-LWE-based cryptography. Since its introduction by Regev [32], the Learning With Er-rors (LWE) problem has been used as the foundation for many new lattice-based constructions with a variety of cryptographic functionalities. It is currently believed to be su ciently hard

Adding Distributed Decryption and Key Generation to a Ring-LWE Based CCA Encryption Scheme Michael Kraitsberg 3, Yehuda Lindell1 ;, Valery Osheter , Nigel P. Smart2 4, and Younes Talibi Alaoui2 1 Bar-Ilan University, Israel, 2 KU Leuven, Leuven, Belgium. 3 Unbound Technology, Israel, 4 University of Bristol, Bristol, UK. michael.kraitsberg@unboundtech.com, yehuda.lindell@biu.ac.il From July 2018 to Sep 2018, I did my summer research at the University of Tokyo focusing on security evaluation of LWE based cryptosystem, under the supervision of Prof. Tsuyoshi Takagi, and I did an intern in PlatON focusing on implementing a 2-party Ed25519 signature with Dr. Xiang Xie in April 2019 Better Key Sizes (and Attacks) for LWE-Based Encryption Richard Lindner, Chris Peikert. In CT-RSA 2011. An Efficient and Parallel Gaussian Sampler for Lattices Chris Peikert. In CRYPTO 2010. Bonsai Trees, or How to Delegate a Lattice Basis David Cash, Dennis Hofheinz, Eike Kiltz, Chris Peikert. (Merged version of this and this.

Some (Ring-)LWE-based schemes BGV-like B(G)V: [BV11], [BGV12] B/FV: [Bra12], [FV12] HEAAN: [CKKS17] GSW-like GSW: [GSW13] FHEW: [DM15] TFHE: [ C GGI16-17] In practice, they are less di erent than expcteed: Chimera [BGGJ19] Some implementations cuFHE FHEW HEAAN HElib Lattigo Microsoft SEAL NFLlib nuFHE Palisade TFHE.. The LWE-based FHEs [5, 9-13] enjoy higher efficiency and stronger security compared to the previous schemes [2-4, 7] (following a similar framework to Gentry's work), due to the simple algebraic structure of the well-studied LWE and classical (quantum) reduction from some apparently intractable lattice problems (e.g., GapSVP) to LWE [14, 15] EMBLEM: (Ring) **LWE-based** Key Encapsulation With a New Multi-bit Encoding Method Minhye Seo, Suhri Kim, Dong Hoon Lee, and Jong Hwan Park Abstract—Lattice-**based** cryptography is a promising candidate for post-quantum cryptosystems, and a large amount of research has been conducted on learning with errors (**LWE**) problems ** (2017) Implementing private k-means clustering using a LWE-based cryptosystem**. 2017 IEEE Symposium on Computers and Communications (ISCC), 88-93. (2017) Secure retrieval method of hyperspectral image in encrypted domain. Journal of Applied Remote Sensing 11:03, 1

We return to consider the ring-LWE-based BGV scheme, and we present a new bootstrapping technique with small depth growth, compared with previous methods, and which supports a larger choice of p and q. Instead of concentrating on the case of plaintext moduli p such that a power of p is close to q, we look at a much larger class of plaintext moduli ** Complexity estimates for running the primal-uSVP and dual attacks against all LWE-based, and the primal-uSVP attack against all NTRU-based, Round 1 schemes proposed as part of the PQC process run by NIST**. We make use of the [APS15] estimator. The code for generating this table is available on Github, as well as the paper

is a prime, are used in typical \Ring-LWE-based cryptosystems, and have none of our recommended defenses. { Fields of the form (Z=q)[x]=(xp x 1), where pis prime, are used in \NTRU Prime, introduced in this paper, and have all of our recommended defenses. Speci cally, we use only about 50000 cycles on one core of an Intel Haswell CP The most critical and computationally intensive operation of these Ring-LWE based cryptosystems is polynomial multiplication. In this paper, we exploit the number theoretic transform to build a high-speed polynomial multiplier for the Ring-LWE based public key cryptosystems constructed LWE-based cryptosystems with improved e ciency or additional functionality (e.g., [72, 105,104,61,34,31,62,24,64]). In particular, in work published in 2011, Lindner and Peikert [83] gave a more e cient LWE-based public-key encryption scheme that uses a square public matrix A 2Z n q instead of an oblong rectangular one In adapting prior LWE-based (semantically secure) cryptosystems [Reg05, PVW08, GPV08] to our hardness results, the modulus qis the main parameter governing efﬁciency, as well as the underlying worst-case problem and approximation factor. The public key size is O(n 2log q), and the amortized plaintext-to

Request PDF | High-Speed Polynomial Multiplier Architecture for Ring-LWE Based Public Key Cryptosystems | Many lattice-based cryptosystems are based on the security of the Ring learning with. For example, in the follow up work , a tighter LWE-based construction of one of the building blocks is provided resulting in a more efficient post-quantum SMP. The second goal in this work, centered on Message Loss Resilience, is motivated by the general desire to require minimal assumptions about the transport mechanism used by the messaging platform (and the adversaries behavior in. SIAM J. COMPUT. c 2014 the authors Vol. 43, No. 2, pp. 831-871 EFFICIENT FULLY HOMOMORPHIC ENCRYPTION FROM (STANDARD) LWE ∗ ZVIKA BRAKERSKI† AND VINOD VAIKUNTANATHAN‡ Abstract. A fully homomorphic encryption (FHE) scheme allows anyone to transform an en

The LWE-based somewhat-homomorphic scheme has depth-(log ) decryption circuit. is the security parameter. The ciphertext-size is Ω() bits. Key-switching matrix is of size Ω(3)bits Each multiplication takes at least Ω(3)times Ω(3)slowdown vs. computing in the clear (In)Efficiency of This Schem CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We analyze the concrete security and key sizes of theoretically sound lattice-based encryption schemes based on the learning with errors (LWE) problem. Our main contributions are: (1) a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success tradeoff, which. Ring-LWE based encryption (I pick up homomorphic encryption here) requires canonical embedding norm rather than $\ell_2$ norm to quantify the polynomial size (e.g. noise). Why is this better than $\ back to index. A List of FHE Paper Better Key Sizes (and Attacks) for LWE-Based Encryption (Lindner & Peikert, CT-RSA 2011). The encryption scheme presented in class is almost identical to the one in section 3 of the paper. There are also some preliminary lecture notes covering the part the lecture on relating different variants of LWE

lwe-based homomorphic encryption pvw method sv technique simd homomorphic operation standard lwe short note single regev-type ciphertext lwe-based scheme hardness assumption packed ciphertext different setting ideal lattice ring-lwe scheme practical advantage general-lwe scheme many plaintext element asymptotic efficienc Other. The impact of error dependencies on Ring/Mod-LWE/LWR based schemes . 13 0 0 0 Concrete security estimates and parameter selection for LWE-based schemes. PROMETHEUS H2020 Annual meeting, 25/11/2020, slides; Implementing Grover oracles for quantum key search on AES and LowMC. Eurocrypt 2020, video, Q&A, slides; Schloss Dagstuhl, Quantum Cryptanalysis seminar 2019, 17/10/2019, slide University of Wollongong Research Online Faculty of Engineering and Information Sciences - Papers: Part B Faculty of Engineering and Information Sciences 2016 Efficient Secure Ma

A Full RNS Variant of Approximate Homomorphic Encryption Jung HeeCheon, KyoohyungHan, Andrey Kim (Seoul National University) MiranKim (UTHealth), Yongsoo Song(UC San Diego) SAC 201 Consequently, the failure probability is an important factor in the security of these schemes and should be determined precisely. The common approach for computing this probability is calculating the failure rate for one bit of the message, from which the full failure rate is determined assuming the failures between the individual bits are independent Jean-Claude Bajard, Julien Eynard, Anwar Hasan, Paulo Martins, Leonel Sousa, et al.. Efficient reductions in cyclotomic rings - Application to Ring-LWE based FHE schemes. Selected Areas of Cryptography 2017, Aug 2017, Ottawa, Canada. 10.1007/978-3-319-72565-9_8 . hal-0158551 CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of short vector problems on arbitrary lattices ** A LWE-based Oblivious Transfer Protocol from Indistinguishability Obfuscation Shanshan Zhang1;2 (Corresponding author: Shanshan Zhang) State Key Laboratory of Integrated Services Networks, Xidian University1 No**. 2, Taibai South Road, Xi'an 710071, Shaanxi Province, Chin

• In both SIS and LWE-based cryptosystems, the public key consists of a random matrix of size m×n (≥log), requiring space (. 2. log. 2. ). - RSA and discrete-log based cryptosystems: public key size is linear in the security parameter. • To reduce the public key size, consider lattice More LWE-based crypto: Attribute-based encryption, functional encryption, reusable garbled circuits (the new works of Gorbunov et al. and Goldwasser et al.) Week 10. LWE-based homomorphic encryption: Based on (Gentry STOC 2009), (Brakerski-Vaikuntanathan FOCS 2011), (Brakerski-Gentry-Vaikuntanathan ITCS 2012), (Brakerski CRYPTO 2012). Weeks 11-12

We provide a tight security proof for an IND-CCA Ring-LWE based Key Encapsulation Mechanism that is derived from a generic construction of Dent (IMA Cryptography and Coding, 2003). Such a tight reduction is not known for the generic construction International Journal of Information and Computer Security; 2019 Vol.11 No.3; Title: Lightweight R-LWE-based privacy preservation scheme for smart grid network Authors: Aarti Amod Agarkar; Himanshu Agrawal. Addresses: Symbiosis International (Deemed) University, Lavale, Mulshi Taluka, Pune, Maharashtra 412115, India ' Department of Computer Science and Information Technology, Symbiosis. Sample topics include: Minkowski's First & Second Theorems, transference theorems in the geometry of numbers, algorithms for the Shortest (SVP) & Closest Vector Problems (CVP), Learning with Errors (LWE), Regev's LWE based public key cryptography scheme, Lattice based signatures, NTRU, Worst-case to average case reductions, and Discrete Gaussian sampling

encryption, and the LWE-based key exchange schemes. Jintai Ding Twenty Years Ago in the Notices August 1997: Review of Noncommutative Geometry by Alain Connes, reviewed by Vaughan Jones and Henri Moscovici. This article discusses Alain Connes's visionary 1994 book Noncommutative Geometry. Appearing in the same issue There are three general classes of attacks to LWE, based on primal lattice, dual lattice, and combinatorial techniques. Primal Lattice Attack. Primal lattice attacks to LWE results in an instance of the Bounded Distance Decoding or Unique Shortest Vector Problem. Revisiting the Expected Cost of Solving uSVP and Applications to LWE Tightly Secure Ring-LWE Based Key Encapsulation with Short Ciphertexts , ESORICS 2017. Full version available as eprint Report 2017/354. Marcel Keller, Emmanuela Orsini, Dragos Rotaru, Peter Scholl, Eduardo Soria- Vazquez and Srinivas Vivek. Faster Secure Multi-Party Computation of AES and DES Using Lookup Tables Duong, D. Hoang., Mishra, P. & Yasuda, M. (2016). Efficient Secure Matrix Multiplication over LWE-Based Homomorphic Encryption. Tatra Mountains Mathematical.