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Pascal Paillier
The Paillier cryptosystem, invented by and named after Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography. The problem of computing ''n''-th residue classes is believed to be computationally difficult. The decisional composite residuosity assumption is the intractability hypothesis upon which this cryptosystem is based. The scheme is an additive homomorphic cryptosystem; this means that, given only the public key and the encryption of m_1 and m_2, one can compute the encryption of m_1+m_2. Algorithm The scheme works as follows: Key generation #Choose two large prime numbers p and q randomly and independently of each other such that \gcd(pq, (p-1)(q-1))=1. This property is assured if both primes are of equal length.Jonathan Katz, Yehuda Lindell, "Introduction to Modern Cryptography: Principles and Protocols," Chapman & Hall/CRC, 2007 #Compute n=pq and \lambda=\operatorname(p-1,q-1). lcm means Least Common Multiple. #Select random integ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymmetric Algorithm
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. There are many kinds of public-key cryptosystems, with different security goals, including digital signature, Diffie–Hellman key exchange, Key encapsulation mechanism, public-key key encapsulation, and public-key encryption. Public key algorithms are fundamental security primitives in modern cryptosystems, including applications and protocols that offer assurance of the confidentiality and authenticity of electronic communications and data storage. They underpin numerous Internet standards, such as Transport Layer Security, T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Threshold Cryptosystem
A threshold cryptosystem, the basis for the field of threshold cryptography, is a cryptosystem that protects information by encrypting it and distributing it among a cluster of fault-tolerant computers. The message is encrypted using a public key, and the corresponding private key is shared among the participating parties. With a threshold cryptosystem, in order to decrypt an encrypted message or to sign a message, several parties (more than some threshold number) must cooperate in the decryption or signature protocol. History Perhaps the first system with complete threshold properties for a trapdoor function (such as RSA) and a proof of security was published in 1994 by Alfredo De Santis, Yvo Desmedt, Yair Frankel, and Moti Yung. Historically, only organizations with very valuable secrets, such as certificate authorities, the military, and governments made use of this technology. One of the earliest implementations was done in the 1990s by Certco for the planned deployment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Okamoto–Uchiyama Cryptosystem
The Okamoto–Uchiyama cryptosystem is a public key cryptosystem proposed in 1998 by Tatsuaki Okamoto and Shigenori Uchiyama. The system works in the multiplicative group of integers modulo n, (\mathbb/n\mathbb)^*, where ''n'' is of the form ''p''2''q'' and ''p'' and ''q'' are large primes. Background Let p be an odd prime. Define \Gamma = \. \Gamma is a subgroup of (\mathbb/p^2 \mathbb)^* with , \Gamma, = p (the elements of \Gamma are 1, 1+p, 1+2p \dots 1 + (p-1)p). Define L: \Gamma \to \mathbb/p\mathbb by L(x) = \frac L is a homomorphism between \Gamma and the additive group \mathbb/p\mathbb: that is, L(ab) = L(a) + L(b) \bmod p. Since L is bijective, it is an isomorphism. One can now show the following as a corollary: Let x \in \Gamma such that L(x) \neq 0 \bmod p and y = x^m \bmod p^2 for 0 \leq m < p. Then : The corollary is a direct consequence of . Operation Like ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naccache–Stern Cryptosystem
The Naccache–Stern cryptosystem is a homomorphic public-key cryptosystem whose security rests on the higher residuosity problem. The Naccache–Stern cryptosystem was discovered by David Naccache and Jacques Stern in 1998. Scheme Definition Like many public key cryptosystems, this scheme works in the group (\mathbb/n\mathbb)^* where ''n'' is a product of two large primes. This scheme is homomorphic and hence malleable. Key Generation *Pick a family of ''k'' small distinct primes ''p''1,...,''p''k. *Divide the set in half and set u = \prod_^ p_i and v = \prod_^k p_i. *Set \sigma = uv = \prod_^k p_i *Choose large primes ''a'' and ''b'' such that both ''p'' = 2''au''+1 and ''q''=2''bv''+1 are prime. *Set ''n''=''pq''. *Choose a random ''g'' mod ''n'' such that ''g'' has order φ(''n'')/4. The public key is the numbers σ,''n'',''g'' and the private key is the pair ''p'',''q''. When ''k''=1 this is essentially the Benaloh cryptosystem. Message Encryption This system allows e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Threshold Cryptosystem
A threshold cryptosystem, the basis for the field of threshold cryptography, is a cryptosystem that protects information by encrypting it and distributing it among a cluster of fault-tolerant computers. The message is encrypted using a public key, and the corresponding private key is shared among the participating parties. With a threshold cryptosystem, in order to decrypt an encrypted message or to sign a message, several parties (more than some threshold number) must cooperate in the decryption or signature protocol. History Perhaps the first system with complete threshold properties for a trapdoor function (such as RSA) and a proof of security was published in 1994 by Alfredo De Santis, Yvo Desmedt, Yair Frankel, and Moti Yung. Historically, only organizations with very valuable secrets, such as certificate authorities, the military, and governments made use of this technology. One of the earliest implementations was done in the 1990s by Certco for the planned deployment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Auction
An online auction (also electronic auction, e-auction, virtual auction, or eAuction) is an auction held over the internet and accessed by internet connected devices. Similar to in-person auctions, online auctions come in a variety of types, with different bidding and selling rules. eCommerce sales for businesses have been steadily increasing for years, and with the migration of virtually all transactions to digital due to the COVID-19 pandemic, worldwide sales through ecommerce channels such as websites and online marketplaces increased overall in 2020 and beyond. There are two primary markets for online auctions: business to business (B2B) and business to consumer (B2C). B2C is forecast to have over a 1% annual growth rate, achieving a nearly 22% share of total global retail sales by 2024. B2B ecommerce gross merchandise value showed a similarly steady rate through 2019, as to mirror its retail B2C counterpart. The largest consumer-to-consumer online auction site is eBay, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Chaum
David Lee Chaum (born 1955) is an American computer scientist, List of cryptographers, cryptographer, and inventor. He is known as a pioneer in cryptography and privacy-preserving technologies, and widely recognized as the inventor of Digital currency, digital cash. His 1982 dissertation "Computer Systems Established, Maintained, and Trusted by Mutually Suspicious Groups" is the first known proposal for a blockchain protocol. Complete with the code to implement the protocol, Chaum's dissertation proposed all but one element of the blockchain later detailed in the Bitcoin White paper, whitepaper. He has been referred to as "the father of online anonymity", and "the godfather of cryptocurrency". He is also known for developing ecash, an electronic cash application that aims to preserve a user's anonymity, and inventing many cryptography, cryptographic protocols like the blind signature, mix networks and the Dining cryptographers protocol. In 1995 his company DigiCash created the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blinding (cryptography)
In cryptography, blinding first became known in the context of blind signatures, where the message author ''blinds'' the message with a random ''blinding factor'', the signer then signs it and the message author "''unblinds"'' it'';'' signer and message author are different parties. Since the late 1990s, blinding mostly refer to countermeasures against side-channel attacks on encryption devices, where the random ''blinding'' and the "''unblinding"'' happen on the encryption devices. Blinding must be applied with care, for example Rabin–Williams signatures. If blinding is applied to the formatted message but the random value does not honor Jacobi requirements on ''p'' and ''q'', then it could lead to private key recovery. A demonstration of the recovery can be seen in "Common Vulnerabilities and Exposures" discovered by Evgeny Sidorov. The one-time pad (OTP) is an application of blinding to the secure communication problem, by its very nature. Alice would like to send a message ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Voting
Electronic voting is voting that uses electronic means to either aid or handle casting and counting ballots including voting time. Depending on the particular implementation, e-voting may use standalone '' electronic voting machines'' (also called EVM) or computers connected to the Internet (online voting). It may encompass a range of Internet services, from basic transmission of tabulated results to full-function online voting through common connectable household devices. The degree of automation may be limited to marking a paper ballot, or may be a comprehensive system of vote input, vote recording, data encryption and transmission to servers, and consolidation and tabulation of election results. A worthy e-voting system must perform most of these tasks while complying with a set of standards established by regulatory bodies, and must also be capable to deal successfully with strong requirements associated with security, accuracy, speed, privacy, auditability, accessib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Oracle Model
In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every ''unique query'' with a (truly) random response chosen uniformly from its output domain. If a query is repeated, it responds the same way every time that query is submitted. Stated differently, a random oracle is a mathematical function chosen uniformly at random, that is, a function mapping each possible query to a (fixed) random response from its output domain. Random oracles first appeared in the context of complexity theory, in which they were used to argue that complexity class separations may face relativization barriers, with the most prominent case being the P vs NP problem, two classes shown in 1981 to be distinct relative to a random oracle almost surely. They made their way into cryptography by the publication of Mihir Bellare and Phillip Rogaway in 1993, which introduced them as a formal cryptographic model to be used in reduction proofs. They are typically used whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cramer–Shoup Cryptosystem
The Cramer–Shoup system is an asymmetric key encryption algorithm, and was the first efficient scheme proven to be secure against adaptive chosen ciphertext attack using standard cryptographic assumptions. Its security is based on the computational intractability (widely assumed, but not proved) of the Decisional Diffie–Hellman assumption. Developed by Ronald Cramer and Victor Shoup in 1998, it is an extension of the ElGamal cryptosystem. In contrast to ElGamal, which is extremely malleable, Cramer–Shoup adds other elements to ensure non-malleability even against a resourceful attacker. This non-malleability is achieved through the use of a universal one-way hash function and additional computations, resulting in a ciphertext which is twice as large as in ElGamal. Adaptive chosen ciphertext attacks The definition of security achieved by Cramer–Shoup is formally termed " indistinguishability under adaptive chosen ciphertext attack" (IND-CCA2). This security definiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
