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Rabin Signature Algorithm
In cryptography, the Rabin signature algorithm is a method of digital signature originally proposed by Michael O. Rabin in 1978. The Rabin signature algorithm was one of the first digital signature schemes proposed. By introducing the use of hashing as an essential step in signing, it was the first design to meet what is now the modern standard of security against forgery, existential unforgeability under chosen-message attack, assuming suitably scaled parameters. Rabin signatures resemble RSA signatures with exponent e=2, but this leads to qualitative differences that enable more efficient implementation (additional information at https://cr.yp.to/sigs.html) and a security guarantee relative to the difficulty of integer factorization, which has not been proven for RSA. However, Rabin signatures have seen relatively little use or standardization outside IEEE P1363 in comparison to RSA signature schemes such as RSASSA-PKCS1-v1_5 and RSASSA-PSS. Definition The Rabin signat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), adversarial behavior. More generally, cryptography is about constructing and analyzing Communication protocol, 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 (confidentiality, data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, Smart card#EMV, chip-based payment cards, digital currencies, password, computer passwords, and military communications. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael O
Michael may refer to: People * Michael (given name), a given name * Michael (surname), including a list of people with the surname Michael Given name * Michael (bishop elect), English 13th-century Bishop of Hereford elect * Michael (Khoroshy) (1885–1977), cleric of the Ukrainian Orthodox Church of Canada * Michael Donnellan (fashion designer), Michael Donnellan (1915–1985), Irish-born London fashion designer, often referred to simply as "Michael" * Michael (footballer, born 1982), Brazilian footballer * Michael (footballer, born 1983), Brazilian footballer * Michael (footballer, born 1993), Brazilian footballer * Michael (footballer, born February 1996), Brazilian footballer * Michael (footballer, born March 1996), Brazilian footballer * Michael (footballer, born 1999), Brazilian footballer Rulers Byzantine emperors *Michael I Rangabe (d. 844), married the daughter of Emperor Nikephoros I *Michael II (770–829), called "the Stammerer" and "the Amorian" *Michael III ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptographic Hash Function
A cryptographic hash function (CHF) is a hash algorithm (a map (mathematics), map of an arbitrary binary string to a binary string with a fixed size of n bits) that has special properties desirable for a cryptography, cryptographic application: * the probability of a particular n-bit output result (hash value) for a random input string ("message") is 2^ (as for any good hash), so the hash value can be used as a representative of the message; * finding an input string that matches a given hash value (a ''pre-image'') is infeasible, ''assuming all input strings are equally likely.'' The ''resistance'' to such search is quantified as security strength: a cryptographic hash with n bits of hash value is expected to have a ''preimage resistance'' strength of n bits, unless the space of possible input values is significantly smaller than 2^ (a practical example can be found in ); * a ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signature Forgery
In a cryptographic digital signature or MAC system, digital signature forgery is the ability to create a pair consisting of a message, m, and a signature (or MAC), \sigma, that is valid for m, but has not been created in the past by the legitimate signer. There are different types of forgery. To each of these types, security definitions can be associated. A signature scheme is secure by a specific definition if no forgery of the associated type is possible. Types The following definitions are ordered from lowest to highest achieved security, in other words, from most powerful to the weakest attack. The definitions form a hierarchy, meaning that an attacker able to mount a specific attack can execute all the attacks further down the list. Likewise, a scheme that reaches a certain security goal also reaches all prior ones. Total break More general than the following attacks, there is also a ''total break'': when an adversary can recover the private information and keys used by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA (cryptosystem)
The RSA (Rivest–Shamir–Adleman) cryptosystem is a public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ), the British signals intelligence agency, by the English mathematician Clifford Cocks. That system was declassified in 1997. In a public-key cryptosystem, the encryption key is public and distinct from the decryption key, which is kept secret (private). An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone via the public key, but can only be decrypted by someone who knows the private key. The security of RSA relies on the practical difficulty of factoring the product o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Factorization
In mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a composite number, or it is not, in which case it is a prime number. For example, is a composite number because , but is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example . Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer using mental or pen-and-paper arithmetic, the simplest method is trial division: checking if the number is divisible by prime numbers , , , and so on, up to the square root of . For larger numbers, especially when using a computer, various more sophis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA Problem
In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key. The RSA algorithm raises a ''message'' to an '' exponent'', modulo a composite number ''N'' whose factors are not known. Thus, the task can be neatly described as finding the ''e''th roots of an arbitrary number, modulo N. For large RSA key sizes (in excess of 1024 bits), no efficient method for solving this problem is known; if an efficient method is ever developed, it would threaten the current or eventual security of RSA-based cryptosystems—both for public-key encryption and digital signatures. More specifically, the RSA problem is to efficiently compute ''P'' given an RSA public key (''N'', ''e'') and a ciphertext ''C'' ≡ ''P'' ''e'' (mod ''N''). The structure of the RSA public key requires that ''N'' be a large semiprime (i.e., a product of two large prime numbers), that 2 < ''e'' < ''N'', that ''e'' be |
IEEE P1363
IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for: * Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004) * Lattice-based public-key cryptography (IEEE Std 1363.1-2008) * Password-based public-key cryptography (IEEE Std 1363.2-2008) * Identity-based public-key cryptography using pairings (IEEE Std 1363.3-2013) The chair of the working group as of October 2008 is William Whyte of NTRU Cryptosystems, Inc., who has served since August 2001. Former chairs were Ari Singer, also of NTRU (1999–2001), and Burt Kaliski of RSA Security (1994–1999). The IEEE Standard Association withdrew all of the 1363 standards except 1363.3-2013 on 7 November 2019. Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004) This specification includes key agreement, signature, and encryption schemes using several mathematical approaches: integer factorizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PKCS 1
In cryptography, PKCS #1 is the first of a family of standards called Public-Key Cryptography Standards (PKCS), published by RSA Laboratories. It provides the basic definitions of and recommendations for implementing the RSA algorithm for public-key cryptography. It defines the mathematical properties of public and private keys, primitive operations for encryption and signatures, secure cryptographic schemes, and related ASN.1 syntax representations. The current version is 2.2 (2012-10-27). Compared to 2.1 (2002-06-14), which was republished as RFC 3447, version 2.2 updates the list of allowed hashing algorithms to align them with FIPS 180-4, therefore adding SHA-224, SHA-512/224 and SHA-512/256. Keys The PKCS #1 standard defines the mathematical definitions and properties that RSA public and private keys must have. The traditional key pair is based on a modulus, , that is the product of two distinct large prime numbers, and , such that n = pq. Starting with version 2. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Signature Scheme
Probabilistic Signature Scheme (PSS) is a cryptographic signature scheme designed by Mihir Bellare and Phillip Rogaway. RSA-PSS is an adaptation of their work and is standardized as part of PKCS#1 v2.1. In general, RSA-PSS should be used as a replacement for RSA-PKCS#1 v1.5. Design PSS was specifically developed to allow modern methods of security analysis to prove that its security directly relates to that of the RSA problem. There is no such proof for the traditional PKCS#1 v1.5 scheme. Implementations *OpenSSL OpenSSL is a software library for applications that provide secure communications over computer networks against eavesdropping, and identify the party at the other end. It is widely used by Internet servers, including the majority of HTTPS web ... * wolfSSL GnuTLS References {{cite web , url=http://grouper.ieee.org/groups/1363/P1363a/contributions/pss-submission.pdf , title=PSS: Provably Secure Encoding Method for Digital Signatures , first1=Mihir , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Nonresidue
In number theory, an integer ''q'' is a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; that is, if there exists an integer ''x'' such that :x^2\equiv q \pmod. Otherwise, ''q'' is a quadratic nonresidue modulo ''n''. Quadratic residues are 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 says that if the context makes it clear, the adjective "quadratic" may be dropped. For a given ''n'', a list of the quadratic residues modulo ''n'' may be obtained by simply squaring all the numbers 0, 1, ..., . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
