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Elliptic-curve Discrete Logarithm Problem
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security.Commercial National Security Algorithm Suite and Quantum Computing FAQ U.S. National Security Agency, January 2016. Elliptic curves are applicable for key agreement, s, [...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] |
Elliptic Curve Point Multiplication
Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic curve cryptography (ECC) as a means of producing a one-way function. The literature presents this operation as scalar multiplication, as written in Hessian form of an elliptic curve. A widespread name for this operation is also elliptic curve point multiplication, but this can convey the wrong impression of being a multiplication between two points. Basics Given a curve, ''E'', defined along some equation in a finite field (such as ''E'': ), point multiplication is defined as the repeated addition of a point along that curve. Denote as for some scalar (integer) ''n'' and a point that lies on the curve, ''E''. This type of curve is known as a Weierstrass curve. The security of modern ECC depends on the intractability of determining ''n'' from given known values of ''Q'' and ''P'' if ''n'' is large (known as the elliptic curve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Security Level
In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level is usually expressed as a number of "bits of security" (also security strength), where ''n''-bit security means that the attacker would have to perform 2''n'' operations to break it, but other methods have been proposed that more closely model the costs for an attacker. This allows for convenient comparison between algorithms and is useful when combining multiple primitives in a hybrid cryptosystem, so there is no clear weakest link. For example, AES-128 (key size 128 bits) is designed to offer a 128-bit security level, which is considered roughly equivalent to a RSA using 3072-bit key. In this context, security claim or target security level is the security level that a primitive was initially designed to achieve, although "security level" is also sometimes used in those contexts. When attacks are found that hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Key Size
In cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest known attack against an algorithm), since the security of all algorithms can be violated by brute-force attacks. Ideally, the lower-bound on an algorithm's security is by design equal to the key length (that is, the security is determined entirely by the keylength, or in other words, the algorithm's design does not detract from the degree of security inherent in the key length). Indeed, most symmetric-key algorithms are designed to have security equal to their key length. However, after design, a new attack might be discovered. For instance, Triple DES was designed to have a 168-bit key, but an attack of complexity 2112 is now known (i.e. Triple DES now only has 112 bits of security, and of the 168 bits in the key the attack has rendered 5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel J
Daniel is a masculine given name and a surname of Hebrew origin. It means "God is my judge"Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 68. (cf. Gabriel—"God is my strength"), and derives from two early biblical figures, primary among them Daniel from the Book of Daniel. It is a common given name for males, and is also used as a surname. It is also the basis for various derived given names and surnames. Background The name evolved into over 100 different spellings in countries around the world. Nicknames (Dan, Danny) are common in both English and Hebrew; "Dan" may also be a complete given name rather than a nickname. The name "Daniil" (Даниил) is common in Russia. Feminine versions (Danielle, Danièle, Daniela, Daniella, Dani, Danitza) are prevalent as well. It has been particularly well-used in Ireland. The Dutch names "Daan" and "Daniël" are also variations of Daniel. A related surname developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA Security
RSA Security LLC, formerly RSA Security, Inc. and doing business as RSA, is an American computer and network security company with a focus on encryption and encryption standards. RSA was named after the initials of its co-founders, Ron Rivest, Adi Shamir and Leonard Adleman, after whom the RSA public key cryptography algorithm was also named. Among its products is the SecurID authentication token. The BSAFE cryptography libraries were also initially owned by RSA. RSA is known for incorporating backdoors developed by the NSA in its products. It also organizes the annual RSA Conference, an information security conference. Founded as an independent company in 1982, RSA Security was acquired by EMC Corporation in 2006 for US$2.1 billion and operated as a division within EMC. When EMC was acquired by Dell Technologies in 2016, RSA became part of the Dell Technologies family of brands. On 10 March 2020, Dell Technologies announced that they will be selling RSA Security to a consorti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Federal Government Of The United States
The federal government of the United States (U.S. federal government or U.S. government) is the national government of the United States, a federal republic located primarily in North America, composed of 50 states, a city within a federal district (the city of Washington in the District of Columbia, where most of the federal government is based), five major self-governing territories and several island possessions. The federal government, sometimes simply referred to as Washington, is composed of three distinct branches: legislative, executive, and judicial, whose powers are vested by the U.S. Constitution in the Congress, the president and the federal courts, respectively. The powers and duties of these branches are further defined by acts of Congress, including the creation of executive departments and courts inferior to the Supreme Court. Naming The full name of the republic is "United States of America". No other name appears in the Constitution, and this i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ECC Patents
Patent-related uncertainty around elliptic curve cryptography (ECC), or ECC patents, is one of the main factors limiting its wide acceptance. For example, the OpenSSL team accepted an ECC patch only in 2005 (in OpenSSL version 0.9.8), despite the fact that it was submitted in 2002. According to Bruce Schneier as of May 31, 2007, "Certicom certainly can claim ownership of ECC. The algorithm was developed and patented by the company's founders, and the patents are well written and strong. I don't like it, but they can claim ownership." Additionally, NSA has licensed MQV and other ECC patents from Certicom in a US$25 million deal for NSA Suite B algorithms. (ECMQV is no longer part of Suite B.) However, according to RSA Laboratories, "''in all of these cases, it is the implementation technique that is patented, not the prime or representation, and there are alternative, compatible implementation techniques that are not covered by the patents.''" Additionally, Daniel J. Bernstein h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or "qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 quantum s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classified Information In The United States
The United States government classification system is established under Executive Order 13526, the latest in a long series of executive orders on the topic beginning in 1951. Issued by President Barack Obama in 2009, Executive Order 13526 replaced earlier executive orders on the topic and modified the regulations codified to 32 C.F.R. 2001. It lays out the system of classification, declassification, and handling of national security information generated by the U.S. government and its employees and contractors, as well as information received from other governments. The desired degree of secrecy about such information is known as its sensitivity. Sensitivity is based upon a calculation of the damage to national security that the release of the information would cause. The United States has three levels of classification: Confidential, Secret, and Top Secret. Each level of classification indicates an increasing degree of sensitivity. Thus, if one holds a Top Secret security cle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Security Agency
The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collection, and processing of information and data for foreign and domestic intelligence and counterintelligence purposes, specializing in a discipline known as signals intelligence (SIGINT). The NSA is also tasked with the protection of U.S. communications networks and information systems. The NSA relies on a variety of measures to accomplish its mission, the majority of which are clandestine. The existence of the NSA was not revealed until 1975. The NSA has roughly 32,000 employees. Originating as a unit to decipher coded communications in World War II, it was officially formed as the NSA by President Harry S. Truman in 1952. Between then and the end of the Cold War, it became the largest of the U.S. intelligence organizations in terms of pers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Curve Digital Signature Algorithm
In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography. Key and signature-size As with elliptic-curve cryptography in general, the bit size of the private key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits—meaning an attacker requires a maximum of about 2^ operations to find the private key—the size of an ECDSA private key would be 160 bits. On the other hand, the signature size is the same for both DSA and ECDSA: approximately 4 t bits, where t is the security level measured in bits, that is, about 320 bits for a security level of 80 bits. Signature generation algorithm Suppose Alice wants to send a signed message to Bob. Initially, they must agree on the curve parameters (\textrm, G, n). In addition to the field and equation of the curve, we need G, a base point of pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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