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Cocks IBE Scheme
Cocks IBE scheme is an identity based encryption system proposed by Clifford Cocks in 2001.Clifford CocksAn Identity Based Encryption Scheme Based on Quadratic Residues, ''Proceedings of the 8th IMA International Conference on Cryptography and Coding'', 2001 The security of the scheme is based on the hardness of the quadratic residuosity problem. Protocol Setup The PKG chooses: # a public RSA-modulus \textstyle n = pq, where \textstyle p,q,\,p \equiv q \equiv 3 \bmod 4 are prime and kept secret, # the message and the cipher space \textstyle \mathcal = \left\, \mathcal = \mathbb_n and # a secure public hash function \textstyle f: \left\^* \rightarrow \mathbb_n. Extract When user \textstyle ID wants to obtain his private key, he contacts the PKG through a secure channel. The PKG # derives \textstyle a with \textstyle \left(\frac\right) = 1 by a deterministic process from \textstyle ID (e.g. multiple application of \textstyle f), # computes \textstyle r = a^ \pmod n (which fulfils eit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Based Encryption
ID-based encryption, or identity-based encryption (IBE), is an important primitive of ID-based cryptography. As such it is a type of public-key encryption in which the public key of a user is some unique information about the identity of the user (e.g. a user's email address). This means that a sender who has access to the public parameters of the system can encrypt a message using e.g. the text-value of the receiver's name or email address as a key. The receiver obtains its decryption key from a central authority, which needs to be trusted as it generates secret keys for every user. ID-based encryption was proposed by Adi Shamir in 1984. He was however only able to give an instantiation of identity-based signatures. Identity-based encryption remained an open problem for many years. The pairing-based Boneh–Franklin scheme and Cocks's encryption scheme based on quadratic residues both solved the IBE problem in 2001. Usage Identity-based systems allow any party to generate a pu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Cocks
Clifford Christopher Cocks (born 28 December 1950) is a British mathematician and cryptographer. In 1973, while working at the United Kingdom Government Communications Headquarters (GCHQ), he invented a public-key cryptography algorithm equivalent to what would become (in 1977) the RSA algorithm. The idea was classified information and his insight remained hidden for 24 years, although it was independently invented by Ronald Rivest, Adi Shamir, and Leonard Adleman in 1977. Public-key cryptography using prime factorisation is now part of nearly every Internet transaction. Education Cocks was educated at Manchester Grammar School and went on to study the Mathematical Tripos as an undergraduate at King's College, Cambridge. He continued as a PhD student at the University of Oxford, where he specialised in number theory under Bryan Birch, but left academia without finishing his doctorate. Career Non-secret encryption Cocks left Oxford to join Communications-Electronics Securi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Residuosity Problem
The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers a and N, whether a is a quadratic residue modulo N or not. Here N = p_1 p_2 for two unknown primes p_1 and p_2, and a is among the numbers which are not obviously quadratic non-residues (see below). The problem was first described by Gauss in his ''Disquisitiones Arithmeticae'' in 1801. This problem is believed to be computationally difficult. Several cryptographic methods rely on its hardness, see . An efficient algorithm for the quadratic residuosity problem immediately implies efficient algorithms for other number theoretic problems, such as deciding whether a composite N of unknown factorization is the product of 2 or 3 primes. Precise formulation Given integers a and T, a is said to be a ''quadratic residue modulo T'' if there exists an integer b such that :a \equiv b^2 \pmod T. Otherwise we say it is a quadratic non-residue. When T = p is a prime, it is customary to us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Residue
In number theory, an integer ''q'' is called a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; i.e., if there exists an integer ''x'' such that: :x^2\equiv q \pmod. Otherwise, ''q'' is called a quadratic nonresidue modulo ''n''. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers. History, conventions, and elementary facts Fermat, Euler, Lagrange, Legendre, and other number theorists of the 17th and 18th centuries established theorems and formed conjectures about quadratic residues, but the first systematic treatment is § IV of Gauss's ''Disquisitiones Arithmeticae'' (1801). Article 95 introduces the terminology "quadratic residue" and "quadratic nonresidue", and states that if the context makes it clear, the adjective "quadratic" may be dropped. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Residue
In number theory, an integer ''q'' is called a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; i.e., if there exists an integer ''x'' such that: :x^2\equiv q \pmod. Otherwise, ''q'' is called a quadratic nonresidue modulo ''n''. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers. History, conventions, and elementary facts Fermat, Euler, Lagrange, Legendre, and other number theorists of the 17th and 18th centuries established theorems and formed conjectures about quadratic residues, but the first systematic treatment is § IV of Gauss's ''Disquisitiones Arithmeticae'' (1801). Article 95 introduces the terminology "quadratic residue" and "quadratic nonresidue", and states that if the context makes it clear, the adjective "quadratic" may be dropped. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA Modulus
RSA may refer to: Organizations Academia and education *Rabbinical Seminary of America, a yeshiva in New York City * Regional Science Association International (formerly the Regional Science Association), a US-based learned society *Renaissance Society of America, a scholarly organization based in New York City *Rhetoric Society of America, an academic organization for the study of rhetoric *Royal Scottish Academy, a Scottish institute of the Arts *Royal Society of Arts, formally the Royal Society for the encouragement of Arts, Manufactures and Commerce, a British institution Military *Redstone Arsenal, a United States Army post adjacent to Huntsville, Alabama * Royal New Zealand Returned and Services' Association, an organization for the welfare of veterans of New Zealand's military *Royal School of Artillery, a British Army training establishment for artillery warfare * Royal Signals Association, an organization for serving and retired members of the Royal Corps of Signals, of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Chosen Ciphertext Attack
An adaptive chosen-ciphertext attack (abbreviated as CCA2) is an interactive form of chosen-ciphertext attack in which an attacker first sends a number of ciphertexts to be decrypted chosen adaptively, and then uses the results to distinguish a target ciphertext without consulting the oracle on the challenge ciphertext. In an adaptive attack, the attacker is further allowed adaptive queries to be asked after the target is revealed (but the target query is disallowed). It is extending the chosen-ciphertext attack, indifferent (non-adaptive) chosen-ciphertext attack (CCA1) where the second stage of adaptive queries is not allowed. Charles Rackoff and Dan Simon defined CCA2 and suggested a system building on the non-adaptive CCA1 definition and system of Moni Naor and Moti Yung (which was the first treatment of chosen ciphertext attack immunity of public key systems). In certain practical settings, the goal of this attack is to gradually reveal information about an encrypted message ... [...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] |
