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HEAAN
HEAAN (Homomorphic Encryption for Arithmetic of Approximate Numbers) is an open source homomorphic encryption (HE) library which implements an approximate HE scheme proposed by Cheon Jung-hee, Cheon, Kim, Kim and Song (CKKS). The first version of HEAAN was published on GitHub on 15 May 2016, and later a new version of HEAAN with a bootstrapping algorithmCheon Jung-hee, Jung Hee Cheon, Kyoohyung Han, Andrey Kim, Miran Kim and Yongsoo SongBootstrapping for Approximate Homomorphic Encryption In ''EUROCRYPT 2018(springer)''. was released. Currently, the latest version is Version 2.1. CKKS plaintext space Unlike other HE schemes, the CKKS scheme supports approximate arithmetics over complex numbers (hence, real numbers). More precisely, the plaintext space of the CKKS scheme is \mathbb^ for some power-of-two integer n . To deal with the complex plaintext vector efficiently, Cheon et al. proposed plaintext encoding/decoding methods which exploits a Ring homomorphism, ring isomorp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homomorphic Encryption
Homomorphic encryption is a form of encryption that permits users to perform computations on its encrypted data without first decrypting it. These resulting computations are left in an encrypted form which, when decrypted, result in an identical output to that produced had the operations been performed on the unencrypted data. Homomorphic encryption can be used for privacy-preserving outsourced storage and computation. This allows data to be encrypted and out-sourced to commercial cloud environments for processing, all while encrypted. For sensitive data, such as health care information, homomorphic encryption can be used to enable new services by removing privacy barriers inhibiting data sharing or increase security to existing services. For example, predictive analytics in health care can be hard to apply via a third party service provider due to medical data privacy concerns, but if the predictive analytics service provider can operate on encrypted data instead, these priva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homomorphic Encryption
Homomorphic encryption is a form of encryption that permits users to perform computations on its encrypted data without first decrypting it. These resulting computations are left in an encrypted form which, when decrypted, result in an identical output to that produced had the operations been performed on the unencrypted data. Homomorphic encryption can be used for privacy-preserving outsourced storage and computation. This allows data to be encrypted and out-sourced to commercial cloud environments for processing, all while encrypted. For sensitive data, such as health care information, homomorphic encryption can be used to enable new services by removing privacy barriers inhibiting data sharing or increase security to existing services. For example, predictive analytics in health care can be hard to apply via a third party service provider due to medical data privacy concerns, but if the predictive analytics service provider can operate on encrypted data instead, these priva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cheon Jung-hee
Jung Hee Cheon is a South Korean cryptographer and mathematician whose research interest includes computational number theory, cryptography, and information security. He is one of the inventors of braid cryptography, one of group-based cryptography, and approximate homomorphic encryption HEAAN. As one of co-inventors of approximate homomorphic encryption HEaaN, he is actively working on homomorphic encryptions and their applications including machine learning, homomorphic control systems, and DNA computation on encrypted data. He is particularly known for his work on an efficient algorithm on strong DH problem. He received the best paper award in Asiacrypt 2008 for improving Pollard rho algorithm, and the best paper award in Eurocrypt 2015 for attacking Multilinear Maps. He was also selected as Scientist of the month by Korean government in 2018 and won the POSCO TJ Park Prize in 2019. He is a professor of Mathematical Sciences at the Seoul National University (SNU) and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CC BY-NC
A Creative Commons NonCommercial license (CC NC, CC BY-NC or NC license) is a Creative Commons license which a copyright holder can apply to their media to give public permission for anyone to reuse that media only for noncommercial activities. Creative Commons is an organization which develops a variety of public copyright licenses, and the "noncommercial" licenses are a subset of these. Unlike the CC0, CC BY, and CC BY-SA licenses, the CC BY-NC license is considered non-free. A challenge with using these licenses is determining what noncommercial use is. Defining "Noncommercial" In September 2009 Creative Commons published a report titled, "Defining 'Noncommercial'". The report featured survey data, analysis, and expert opinions on what "noncommercial" means, how it applied to contemporary media, and how people who share media interpret the term. The report found that in some aspects there was public agreement on the meaning of "noncommercial", but for other aspects, there is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitHub
GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, it has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. As of June 2022, GitHub reported having over 83 million developers and more than 200 million repositories, including at least 28 million public repositories. It is the largest source code host . History GitHub.com Development of the GitHub.com platform began on October 19, 2007. The site was launched in April 2008 by Tom Preston-Werner, Chris Wanstrath, P. J. Hyett and Scott Chacon after it had been made available for a few months prior as a beta release. GitHub has an annual keynote called GitHub Universe. Organizational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bootstrapping
In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input. Etymology Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers or a boot hook tool to help pulling the boots on. The saying "to " was already in use during the 19th century as an example of an impossible task. The idiom dates at least to 1834, when it appeared in the ''Workingman's Advocate'': "It is conjectured that Mr. Murphee will now be enabled to hand himself over the Cumberland river or a barn yard fence by the straps of his boots."Jan FreemanBootstraps and Baron Munchausen ''Boston.com'', January 27, 2009 In 1860 it appeared in a comment on philosophy of mind: "The attempt of the mind to analyze itself san effort analogous to one who would lift himself by his own bootstraps." Bootstrap as a metaphor, meaning to better oneself by one's own unaided efforts, was in use in 1922. This metaphor spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring Homomorphism
In ring theory, a branch of abstract algebra, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if ''R'' and ''S'' are rings, then a ring homomorphism is a function such that ''f'' is: :addition preserving: ::f(a+b)=f(a)+f(b) for all ''a'' and ''b'' in ''R'', :multiplication preserving: ::f(ab)=f(a)f(b) for all ''a'' and ''b'' in ''R'', :and unit (multiplicative identity) preserving: ::f(1_R)=1_S. Additive inverses and the additive identity are part of the structure too, but it is not necessary to require explicitly that they too are respected, because these conditions are consequences of the three conditions above. If in addition ''f'' is a bijection, then its inverse ''f''−1 is also a ring homomorphism. In this case, ''f'' is called a ring isomorphism, and the rings ''R'' and ''S'' are called ''isomorphic''. From the standpoint of ring theory, isomorphic rings cannot be distinguished. If ''R'' and ''S'' are rngs, then the cor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadamard Product (matrices)
In mathematics, the Hadamard product (also known as the element-wise product, entrywise product or Schur product) is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimension as the operands, where each element is the product of elements of the original two matrices. It is to be distinguished from the more common matrix product. It is attributed to, and named after, either French mathematician Jacques Hadamard or German Russian mathematician Issai Schur. The Hadamard product is associative and distributive. Unlike the matrix product, it is also commutative. Definition For two matrices and of the same dimension , the Hadamard product A \circ B (or A \odot B) is a matrix of the same dimension as the operands, with elements given by :(A \circ B)_ = (A \odot B)_ = (A)_ (B)_. For matrices of different dimensions ( and , where or ), the Hadamard product is undefined. Example For example, the Hadamard product for a 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IND-CPA
Ciphertext indistinguishability is a property of many encryption schemes. Intuitively, if a cryptosystem possesses the property of indistinguishability, then an adversary will be unable to distinguish pairs of ciphertexts based on the message they encrypt. The property of indistinguishability under chosen plaintext attack is considered a basic requirement for most provably secure public key cryptosystems, though some schemes also provide indistinguishability under chosen ciphertext attack and adaptive chosen ciphertext attack. Indistinguishability under chosen plaintext attack is equivalent to the property of semantic security, and many cryptographic proofs use these definitions interchangeably. A cryptosystem is considered ''secure in terms of indistinguishability'' if no adversary, given an encryption of a message randomly chosen from a two-element message space determined by the adversary, can identify the message choice with probability significantly better than that of rand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring Learning With Errors
In post-quantum cryptography, 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 information is available, but are easy to solve if some information used in the problem construction is known. Some problems of this sort that are currently used in cryptography are at risk of attack if sufficiently large quantum computers can ever be built, so resistant problems are sought. Homomorphic encryption is a form of encryption that allows computation on ciphertext, such as arithmetic on numeric values stored in an encrypted database. RLWE is more properly called ''learning with errors over rings'' and is simply the larger learning with errors (LWE) problem spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Learning With Errors
Learning with errors (LWE) is the computational problem of inferring a linear n-ary function f over a finite ring from given samples y_i = f(\mathbf_i) some of which may be erroneous. The LWE problem is conjectured to be hard to solve, and thus to be useful in cryptography. More precisely, the LWE problem is defined as follows. Let \mathbb_q denote the ring of integers modulo q and let \mathbb_q^n denote the set of n- vectors over \mathbb_q . There exists a certain unknown linear function f:\mathbb_q^n \rightarrow \mathbb_q, and the input to the LWE problem is a sample of pairs (\mathbf,y), where \mathbf\in \mathbb_q^n and y \in \mathbb_q, so that with high probability y=f(\mathbf). Furthermore, the deviation from the equality is according to some known noise model. The problem calls for finding the function f, or some close approximation thereof, with high probability. The LWE problem was introduced by Oded Regev in 2005 (who won the 2018 Gödel Prize for this work), it is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O\left(N^2\right), which arises if one simply applies the definition of DFT, to O(N \log N), where N is the data size. The difference in speed can be enormous, especially for long data sets where ''N'' may be in the thousands or millions. In the presence of round-off error, many FFT algorithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
