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Efficient Probabilistic Public-Key Encryption Scheme
EPOC (Efficient Probabilistic Public Key Encryption) is a probabilistic public-key encryption scheme. EPOC was developed in 1999 by T. Okamoto, S. Uchiyama and E. Fujisaki of NTT Labs in Japan. It is based on the random oracle model, in which a primitive public-key encryption function is converted to a secure encryption scheme by use of a truly random hash function; the resulting scheme is designed to be semantically secure against a chosen ciphertext attack. EPOC's primitive encryption function is the OU (Okamoto–Uchiyama) function, in which to invert the OU function is proven to be as hard as factoring a composite integer public key. There are three versions of EPOC: * EPOC-1 uses a one-way trapdoor function and a random function (hash function); * EPOC-2 uses a one-way trapdoor function, two random functions (hash functions) and a symmetric-key encryption (e.g., one-time padding and block-ciphers); * EPOC-3 uses the Okamoto–Uchiyama one-way trapdoor function and two rand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Encryption
Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts. The term "probabilistic encryption" is typically used in reference to public key encryption algorithms; however various symmetric key encryption algorithms achieve a similar property (e.g., block ciphers when used in a chaining mode such as CBC), and stream ciphers such as Freestyle which are inherently random. To be semantically secure, that is, to hide even partial information about the plaintext, an encryption algorithm must be probabilistic. History The first provably-secure probabilistic public-key encryption scheme was proposed by Shafi Goldwasser and Silvio Micali, based on the hardness of the quadratic residuosity problem and had a message expansion factor equal to the public key size. More efficient probabilistic encryption algorithms include Elgamal, Paillier, and various constructio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public-key Cryptography
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. In a public-key encryption system, anyone with a public key can encrypt a message, yielding a ciphertext, but only those who know the corresponding private key can decrypt the ciphertext to obtain the original message. For example, a journalist can publish the public key of an encryption key pair on a web site so that sources can send secret messages to the news organization in ciphertext. Only the journalist who knows the corresponding private key can decrypt the ciphertexts to obtain the sources' messages—an eavesdropp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decipher a ciphertext back to plaintext and access the original information. Encryption does not itself prevent interference but denies the intelligible content to a would-be interceptor. For technical reasons, an encryption scheme usually uses a pseudo-random encryption key generated by an algorithm. It is possible to decrypt the message without possessing the key but, for a well-designed encryption scheme, considerable computational resources and skills are required. An authorized recipient can easily decrypt the message with the key provided by the originator to recipients but not to unauthorized users. Historically, various forms of encryption have been used to aid in cryptography. Early encryption techniques were often used in military ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nippon Telegraph And Telephone
, commonly known as NTT, is a Japanese telecommunications company headquartered in Tokyo, Japan. Ranked 55th in Fortune Global 500, ''Fortune'' Global 500, NTT is the fourth largest telecommunications company in the world in terms of revenue, as well as the third largest publicly traded company in Japan after Toyota and Sony, as of June 2022. The company is incorporated pursuant to the NTT Law (). The purpose of the company defined by the law is to own all the shares issued by Nippon Telegraph and Telephone East Corporation (NTT East) and Nippon Telegraph and Telephone West Corporation (NTT West) and to ensure proper and stable provision of telecommunications services all over Japan including remote rural areas by these companies as well as to conduct research relating to the telecommunications technologies that will form the foundation for telecommunications. On 1 July 2019, NTT Corporation launched NTT Ltd., an $11 billion de facto holding company business consisting of 28 brand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Oracle
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 as a mathematical abstraction were first used in rigorous cryptographic proofs in the 1993 publication by Mihir Bellare and Phillip Rogaway (1993). They are typically used when the proof cannot be carried out using weaker assumptions on the cryptographic hash function. A system that is proven secure when every hash function is replaced by a random oracle is described as being secure in the random oracle model, as opposed to secure in the standard model of cryptography. Applications Random oracles are typicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantic Security
In cryptography, a semantically secure cryptosystem is one where only negligible information about the plaintext can be feasibly extracted from the ciphertext. Specifically, any probabilistic, polynomial-time algorithm (PPTA) that is given the ciphertext of a certain message m (taken from any distribution of messages), and the message's length, cannot determine any partial information on the message with probability non-negligibly higher than all other PPTA's that only have access to the message length (and not the ciphertext). S. Goldwasser and S. MicaliProbabilistic encryption & how to play mental poker keeping secret all partial information Annual ACM Symposium on Theory of Computing, 1982. This concept is the computational complexity analogue to Shannon's concept of perfect secrecy. Perfect secrecy means that the ciphertext reveals no information at all about the plaintext, whereas semantic security implies that any information revealed cannot be feasibly extracted. Goldreich, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chosen Ciphertext Attack
A chosen-ciphertext attack (CCA) is an attack model for cryptanalysis where the cryptanalyst can gather information by obtaining the decryptions of chosen ciphertexts. From these pieces of information the adversary can attempt to recover the hidden secret key used for decryption. For formal definitions of security against chosen-ciphertext attacks, see for example: Michael Luby and Mihir Bellare et al. Introduction A number of otherwise secure schemes can be defeated under chosen-ciphertext attack. For example, the El Gamal cryptosystem is semantically secure under chosen-plaintext attack, but this semantic security can be trivially defeated under a chosen-ciphertext attack. Early versions of RSA padding used in the SSL protocol were vulnerable to a sophisticated adaptive chosen-ciphertext attack which revealed SSL session keys. Chosen-ciphertext attacks have implications for some self-synchronizing stream ciphers as well. Designers of tamper-resistant cryptographic sma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorization
In mathematics, factorization (or factorisation, see American and British English spelling differences#-ise, -ize (-isation, -ization), English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind. For example, is a factorization of the integer , and is a factorization of the polynomial . Factorization is not usually considered meaningful within number systems possessing division ring, division, such as the real number, real or complex numbers, since any x can be trivially written as (xy)\times(1/y) whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by Greek mathematics, ancient Greek mathematicians in the case of integers. They proved the fundamental theorem o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trapdoor Function
In theoretical computer science and cryptography, a trapdoor function is a function that is easy to compute in one direction, yet difficult to compute in the opposite direction (finding its inverse) without special information, called the "trapdoor". Trapdoor functions are a special case of one-way functions and are widely used in public-key cryptography. In mathematical terms, if ''f'' is a trapdoor function, then there exists some secret information ''t'', such that given ''f''(''x'') and ''t'', it is easy to compute ''x''. Consider a padlock and its key. It is trivial to change the padlock from open to closed without using the key, by pushing the shackle into the lock mechanism. Opening the padlock easily, however, requires the key to be used. Here the key ''t'' is the trapdoor and the padlock is the trapdoor function. An example of a simple mathematical trapdoor is "6895601 is the product of two prime numbers. What are those numbers?" A typical " brute-force" solution wou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...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. Operation Like many public key cryptosystems, this scheme works in the group (\mathbb/n\mathbb)^*. This scheme is homomorphic and hence malleable. Key generation A public/private key pair is generated as follows: # Generate two large primes p and q. # Compute n = p^2 q. # Choose a random integer g \in \ such that g^ \not\equiv 1 \mod p^2. # Compute h = g^n \bmod n. The public key is then (n,g,h) and the private key is (p,q). Encryption A message m < p can be encrypted with the public key as follows. # Choose a random integer . # Compute . The value is the encryption of .
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