122 relations: Abstract Syntax Notation One, Acoustic cryptanalysis, Acronym, Adaptive chosen-ciphertext attack, Adi Shamir, Alice and Bob, Arjen Lenstra, Atmospheric noise, Bit, Bit-length, Blinding (cryptography), Brady Haran, Branch predictor, Carmichael function, Chinese remainder theorem, Chosen-ciphertext attack, Chosen-plaintext attack, Ciphertext, Classified information, Clifford Cocks, Communications of the ACM, Computational complexity theory, Coppersmith's attack, Coprime integers, Cryptographic hash function, Cryptographically secure pseudorandom number generator, Cryptosystem, Dan Boneh, Daniel Bleichenbacher, Daniel J. Bernstein, David Brumley, Derwent World Patents Index, Deterministic algorithm, Diffie–Hellman key exchange, Digital signature, Don Coppersmith, Encryption, Euclidean algorithm, Euler's theorem, Euler's totient function, Eurocrypt, Exponentiation by squaring, Factorization, Fermat's factorization method, Fermat's little theorem, General number field sieve, Generalized Riemann hypothesis, Glossary of patent law terms, Government Communications Headquarters, Greatest common divisor, ..., Hamming weight, IEEE P1363, Infineon Technologies, Integer factorization, International Cryptology Conference, Introduction to Algorithms, Java (programming language), Johan Håstad, Journal of Cryptology, Key (cryptography), Key exchange, Key management, Key size, Knapsack problem, Lagrange's theorem (group theory), Least common multiple, Leonard Adleman, Manischewitz, Martin Hellman, Masaryk University, Massachusetts Institute of Technology, Mathematician, Modular arithmetic, Modular exponentiation, Modular multiplicative inverse, Multiplicative group of integers modulo n, Neal Koblitz, Notices of the American Mathematical Society, OpenSSL, Optimal asymmetric encryption padding, Padding (cryptography), Passover, Patent, Patent application, Paul Kocher, Personal computer, Peter Shor, PKCS, PKCS 1, Plaintext, Pollard's p − 1 algorithm, Primality test, Prime number, Primitive data type, Probabilistic signature scheme, Public-key cryptography, Quantum computing, Random number generation, ROCA vulnerability, Ron Rivest, RSA numbers, RSA problem, RSA Security, Semantic security, Shafi Goldwasser, Shor's algorithm, Silvio Micali, Simultaneous multithreading, Standardization, Symmetric-key algorithm, Term of patent, The New York Times, Time complexity, Transport Layer Security, Trapdoor function, TWIRL, United Kingdom, United States, University of Bristol, Whitfield Diffie, .NET Framework, 65,537. Expand index (72 more) »

## Abstract Syntax Notation One

Abstract Syntax Notation One (ASN.1) is an interface description language for defining data structures that can be serialized and deserialized in a standard, cross-platform way.

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## Acoustic cryptanalysis

Acoustic cryptanalysis is a type of side channel attack that exploits sounds emitted by computers or other devices.

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## Acronym

An acronym is a word or name formed as an abbreviation from the initial components in a phrase or a word, usually individual letters (as in NATO or laser) and sometimes syllables (as in Benelux).

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## Adaptive chosen-ciphertext attack

An adaptive chosen-ciphertext attack (abbreviated as CCA2) is an interactive form of chosen-ciphertext attack in which an attacker sends a number of ciphertexts to be decrypted, then uses the results of these decryptions to select subsequent ciphertexts.

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## Adi Shamir

Adi Shamir (עדי שמיר; born July 6, 1952) is an Israeli cryptographer.

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## Alice and Bob

Alice and Bob are fictional characters commonly used as placeholder names in cryptology, as well as science and engineering literature.

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## Arjen Lenstra

Arjen Klaas Lenstra (born 2 March 1956, Groningen) is a Dutch mathematician.

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## Atmospheric noise

Atmospheric noise is radio noise caused by natural atmospheric processes, primarily lightning discharges in thunderstorms.

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## Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

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## Bit-length

Bit-length is the number of binary digits, called bits, necessary to represent an integer in the binary number system.

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## Blinding (cryptography)

In cryptography, blinding is a technique by which an agent can provide a service to (i.e., compute a function for) a client in an encoded form without knowing either the real input or the real output.

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## Brady Haran

Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.

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## Branch predictor

In computer architecture, a branch predictor is a digital circuit that tries to guess which way a branch (e.g. an if–then–else structure) will go before this is known definitively.

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## Carmichael function

In number theory, the Carmichael function associates to every positive integer n a positive integer \lambda(n), defined as the smallest positive integer m such that (Dropping the phrase "between 1 and n" leads to an equivalent definition.) In algebraic terms, \lambda(n) equals the exponent of the multiplicative group of integers modulo ''n''.

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## Chinese remainder theorem

The Chinese remainder theorem is a theorem of number theory, which states that if one knows the remainders of the Euclidean division of an integer by several integers, then one can determine uniquely the remainder of the division of by the product of these integers, under the condition that the divisors are pairwise coprime.

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## 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.

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## Chosen-plaintext attack

A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts.

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## Ciphertext

In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher.

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## Classified information

Classified information is material that a government body deems to be sensitive information that must be protected.

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## Clifford Cocks

Clifford Christopher Cocks CB FRS (born 28 December 1950) is a British mathematician and cryptographer.

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## Communications of the ACM

Communications of the ACM is the monthly journal of the Association for Computing Machinery (ACM).

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## Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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## Coppersmith's attack

Coppersmith's attack describes a class of cryptographic attacks on the public-key cryptosystem RSA based on the Coppersmith method.

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## Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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## Cryptographic hash function

A cryptographic hash function is a special class of hash function that has certain properties which make it suitable for use in cryptography.

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## Cryptographically secure pseudorandom number generator

A cryptographically secure pseudo-random number generator (CSPRNG) or cryptographic pseudo-random number generator (CPRNG) is a pseudo-random number generator (PRNG) with properties that make it suitable for use in cryptography.

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## Cryptosystem

In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, most commonly for achieving confidentiality (encryption).

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## Dan Boneh

Dan Boneh (דן בונה) is a teacher and researcher in applied cryptography and computer security.

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## Daniel Bleichenbacher

Daniel Bleichenbacher (born 1964) is a Swiss cryptographer, previously a researcher at Bell Labs, and currently employed at Google.

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## Daniel J. Bernstein

Daniel Julius Bernstein (sometimes known simply as djb; born October 29, 1971) is a German-American mathematician, cryptologist, and programmer.

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## David Brumley

David Brumley is a Professor and Director of CyLab Security and Privacy Institute at Carnegie Mellon University.

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## Derwent World Patents Index

The Derwent World Patents Index (DWPI) is a database containing patent applications and grants from 44 of the world's patent issuing authorities.

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## Deterministic algorithm

In computer science, a deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states.

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## Diffie–Hellman key exchange

Diffie–Hellman key exchange (DH)Synonyms of Diffie–Hellman key exchange include.

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## Digital signature

A digital signature is a mathematical scheme for presenting the authenticity of digital messages or documents.

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## Don Coppersmith

Don Coppersmith (born 1950) is a cryptographer and mathematician.

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## Encryption

In cryptography, encryption is the process of encoding a message or information in such a way that only authorized parties can access it and those who are not authorized cannot.

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## Euclidean algorithm

. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.

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## Euler's theorem

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that if n and a are coprime positive integers, then where \varphi(n) is Euler's totient function.

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## Euler's totient function

In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.

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## Eurocrypt

Eurocrypt (or EUROCRYPT) is a conference for cryptography research.

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## Exponentiation by squaring

In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix.

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## Factorization

In mathematics, factorization (also factorisation in some forms of British English) 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.

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## Fermat's factorization method

Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: That difference is algebraically factorable as (a+b)(a-b); if neither factor equals one, it is a proper factorization of N. Each odd number has such a representation.

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## Fermat's little theorem

Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.

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## General number field sieve

In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than.

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## Generalized Riemann hypothesis

The Riemann hypothesis is one of the most important conjectures in mathematics.

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## Glossary of patent law terms

This is a list of legal terms relating to patents.

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## Government Communications Headquarters

The Government Communications Headquarters (GCHQ) is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance to the government and armed forces of the United Kingdom.

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## Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

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## Hamming weight

The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used.

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## IEEE P1363

IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography.

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## Infineon Technologies

Infineon Technologies AG is a German semiconductor manufacturer founded on 1 April 1999, when the semiconductor operations of the parent company Siemens AG were spun off to form a separate legal entity.

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## Integer factorization

In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.

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## International Cryptology Conference

CRYPTO, the International Cryptology Conference, is one of the largest academic conferences in cryptography and cryptanalysis.

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## Introduction to Algorithms

Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.

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## Java (programming language)

Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

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## Johan Håstad

Johan Torkel Håstad (born 19 November 1960) is a Swedish theoretical computer scientist most known for his work on computational complexity theory.

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## Journal of Cryptology

The Journal of Cryptology is a scientific journal in the field of cryptology and cryptography.

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## Key (cryptography)

In cryptography, a key is a piece of information (a parameter) that determines the functional output of a cryptographic algorithm.

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## Key exchange

Key exchange (also key establishment) is any method in cryptography by which cryptographic keys are exchanged between two parties, allowing use of a cryptographic algorithm.

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## Key management

Key management refers to management of cryptographic keys in a cryptosystem.

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## Key size

In cryptography, key size or key length is the number of bits in a key used by a cryptographic algorithm (such as a cipher).

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## Knapsack problem

The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

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## Lagrange's theorem (group theory)

Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G. The theorem is named after Joseph-Louis Lagrange.

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## Least common multiple

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.

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## Leonard Adleman

Leonard Adleman (born December 31, 1945) is an American computer scientist.

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## Manischewitz

Manischewitz (מנישביץ) is a leading brand of kosher products based in the United States, best known for their matzo and kosher wine.

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## Martin Hellman

Martin Edward Hellman (born October 2, 1945) is an American cryptologist, best known for his invention of public key cryptography in cooperation with Whitfield Diffie and Ralph Merkle.

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## Masaryk University

Masaryk University (Masarykova univerzita; Universitas Masarykiana Brunensis) is the second largest university in the Czech Republic, a member of the Compostela Group and the Utrecht Network.

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## Massachusetts Institute of Technology

The Massachusetts Institute of Technology (MIT) is a private research university located in Cambridge, Massachusetts, United States.

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## Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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## Modular exponentiation

Modular exponentiation is a type of exponentiation performed over a modulus.

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## Modular multiplicative inverse

In mathematics, in particular the area of number theory, a modular multiplicative inverse of an integer is an integer such that the product is congruent to 1 with respect to the modulus.

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## Multiplicative group of integers modulo n

In modular arithmetic, the integers coprime (relatively prime) to n from the set \ of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n. Hence another name is the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. Here units refers to elements with a multiplicative inverse, which in this ring are exactly those coprime to n. This group, usually denoted (\mathbb/n\mathbb)^\times, is fundamental in number theory.

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## Neal Koblitz

Neal I. Koblitz (born December 24, 1948) is a Professor of Mathematics at the University of Washington.

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## Notices of the American Mathematical Society

Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.

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## OpenSSL

OpenSSL is a software library for applications that secure communications over computer networks against eavesdropping or need to identify the party at the other end.

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## Optimal asymmetric encryption padding

In cryptography, Optimal Asymmetric Encryption Padding (OAEP) is a padding scheme often used together with RSA encryption.

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## Padding (cryptography)

In cryptography, padding refers to a number of distinct practices.

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## Passover

Passover or Pesach (from Hebrew Pesah, Pesakh) is a major, biblically derived Jewish holiday.

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## Patent

A patent is a set of exclusive rights granted by a sovereign state or intergovernmental organization to an inventor or assignee for a limited period of time in exchange for detailed public disclosure of an invention.

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## Patent application

A patent application is a request pending at a patent office for the grant of a patent for the invention described and claimed by that application.

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## Paul Kocher

Paul Carl Kocher (born June 11, 1973) is an American cryptographer and cryptography consultant, currently the president and chief scientist of Cryptography Research, Inc.

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## Personal computer

A personal computer (PC) is a multi-purpose computer whose size, capabilities, and price make it feasible for individual use.

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## Peter Shor

Peter Williston Shor (born August 14, 1959) is an American professor of applied mathematics at MIT.

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## PKCS

In cryptography, PKCS stands for "Public Key Cryptography Standards".

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## PKCS 1

In cryptography, PKCS #1 is the first of a family of standards called Public-Key Cryptography Standards (PKCS), published by RSA Laboratories.

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## Plaintext

In cryptography, plaintext or cleartext is unencrypted information, as opposed to information encrypted for storage or transmission.

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## Pollard's p − 1 algorithm

Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974.

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## Primality test

A primality test is an algorithm for determining whether an input number is prime.

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## Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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## Primitive data type

In computer science, primitive data type is either of the following.

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## Probabilistic signature scheme

Probabilistic Signature Scheme (PSS) is a cryptographic signature scheme designed by Mihir Bellare and Phillip Rogaway.

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## Public-key cryptography

Public-key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner.

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## Quantum computing

Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.

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## Random number generation

Random number generation is the generation of a sequence of numbers or symbols that cannot be reasonably predicted better than by a random chance, usually through a hardware random-number generator (RNG).

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## ROCA vulnerability

The ROCA vulnerability is a cryptographic weakness that allows the private key of a key pair to be recovered from the public key in keys generated by devices with the vulnerability.

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## Ron Rivest

Ronald Linn Rivest (born May 6, 1947) is a cryptographer and an Institute Professor at MIT.

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## RSA numbers

In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that are part of the RSA Factoring Challenge.

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## RSA problem

In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key.

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## RSA Security

RSA Security LLC, formerly RSA Security, Inc. and doing business as RSA, is an American computer and network security company.

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## Semantic security

In cryptography, a semantically secure cryptosystem is one where only negligible information about the plaintext can be feasibly extracted from the ciphertext.

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## Shafi Goldwasser

Shafrira Goldwasser (שפרירה גולדווסר; born 1959) is an American-Israeli computer scientist and winner of the Turing Award in 2012.

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## Shor's algorithm

Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm (an algorithm that runs on a quantum computer) for integer factorization formulated in 1994.

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## Silvio Micali

Silvio Micali (born October 13, 1954) is an Italian computer scientist at MIT Computer Science and Artificial Intelligence Laboratory and a professor of computer science in MIT's Department of Electrical Engineering and Computer Science since 1983.

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## Simultaneous multithreading

Simultaneous multithreading (SMT) is a technique for improving the overall efficiency of superscalar CPUs with hardware multithreading.

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## Standardization

Standardization or standardisation is the process of implementing and developing technical standards based on the consensus of different parties that include firms, users, interest groups, standards organizations and governments Standardization can help to maximize compatibility, interoperability, safety, repeatability, or quality.

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## Symmetric-key algorithm

Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext.

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## Term of patent

The term of a patent is the maximum period during which it can be maintained in force.

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## The New York Times

The New York Times (sometimes abbreviated as The NYT or The Times) is an American newspaper based in New York City with worldwide influence and readership.

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## Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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## Transport Layer Security

Transport Layer Security (TLS) – and its predecessor, Secure Sockets Layer (SSL), which is now deprecated by the Internet Engineering Task Force (IETF) – are cryptographic protocols that provide communications security over a computer network.

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## Trapdoor function

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".

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## TWIRL

In cryptography and number theory, TWIRL (The Weizmann Institute Relation Locator) is a hypothetical hardware device designed to speed up the sieving step of the general number field sieve integer factorization algorithm.

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## United Kingdom

The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain,Usage is mixed with some organisations, including the and preferring to use Britain as shorthand for Great Britain is a sovereign country in western Europe.

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## United States

The United States of America (USA), commonly known as the United States (U.S.) or America, is a federal republic composed of 50 states, a federal district, five major self-governing territories, and various possessions.

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## University of Bristol

The University of Bristol (simply referred to as Bristol University and abbreviated as Bris. in post-nominal letters, or UoB) is a red brick research university located in Bristol, United Kingdom.

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## Whitfield Diffie

Bailey Whitfield 'Whit' Diffie (born June 5, 1944) is an American cryptographer and one of the pioneers of public-key cryptography along with Martin Hellman and Ralph Merkle.

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## .NET Framework

.NET Framework (pronounced dot net) is a software framework developed by Microsoft that runs primarily on Microsoft Windows.

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## 65,537

65537 is the integer after 65536 and before 65538.

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## Redirects here:

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## References

[1] https://en.wikipedia.org/wiki/RSA_(cryptosystem)