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Curve25519
In cryptography, Curve25519 is an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security (256-bit key size) and designed for use with the Elliptic-curve Diffie–Hellman (ECDH) key agreement scheme, first described and implemented by Daniel J. Bernstein. It is one of the fastest curves in ECC, and is not covered by any known patents. The reference implementation is public domain software. The original Curve25519 paper defined it as a Diffie–Hellman (DH) function. Bernstein has since proposed that the name Curve25519 be used for the underlying curve, and the name X25519 for the DH function. Mathematical properties The curve used is y^2 = x^3 + 486662x^2 + x, a Montgomery curve, over the prime field defined by the pseudo-Mersenne prime number 2^ - 19 (hence the numeric "" in the name), and it uses the base point x = 9. This point generates a cyclic subgroup whose order is the prime 2^ + 27742317777372353535851937790883648493. This subgroup has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic-curve Diffie–Hellman
Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an Elliptic curve, elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to Key derivation function, derive another key. The key, or the derived key, can then be used to encrypt subsequent communications using a Symmetric-key algorithm, symmetric-key cipher. It is a variant of the Diffie–Hellman key exchange, Diffie–Hellman protocol using elliptic-curve cryptography. Key establishment protocol The following example illustrates how a shared key is established. Suppose Alice and Bob, Alice wants to establish a shared key with Alice and Bob, Bob, but the only channel available for them may be eavesdropped by a third party. Initially, the Elliptic curve cryptography#Domain parameters, domain parameters (that is, (p, a, b, G, n, h) in the prime case or (m, f(x), a, b, G, n, h) in the bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Montgomery Ladder
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). 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 by 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 discrete logarithm problem by analogy to othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve448
In cryptography, Curve448 or Curve448-Goldilocks is an elliptic curve potentially offering 224 bits of security and designed for use with the elliptic-curve Diffie–Hellman (ECDH) key agreement scheme. History Developed by Mike Hamburg of Rambus Cryptography Research, Curve448 allows fast performance compared with other proposed curves with comparable security. The reference implementation is available under an MIT license. The curve was favored by the Internet Research Task Force Crypto Forum Research Group (IRTF CFRG) for inclusion in Transport Layer Security (TLS) standards along with Curve25519. In 2017, NIST announced that Curve25519 and Curve448 would be added to "Special Publication 800-186", which specifies approved elliptic curves for use by the US Federal Government, and in 2023 it was approved for use in FIPS 186-5. Both are described in . The name X448 is used for the DH function. X448 support was added to OpenSSL in version 1.1.1 (released on 11 September 2018). Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ed25519
In public-key cryptography, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves. It is designed to be faster than existing digital signature schemes without sacrificing security. It was developed by a team including Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, and Bo-Yin Yang. The reference implementation is public-domain software. Summary The following is a simplified description of EdDSA, ignoring details of encoding integers and curve points as bit strings; the full details are in the papers and RFC. An EdDSA signature scheme is a choice: * of finite field \mathbb_q over odd prime power q; * of elliptic curve E over \mathbb_q whose group E(\mathbb_q) of \mathbb_q-rational points has order \#E(\mathbb_q) = 2^c \ell, where \ell is a large prime and 2^c is called the cofactor; * of base point B \in E(\mathbb_q) with order \ell; and * of cryptographic hash functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GnuPG
GNU Privacy Guard (GnuPG or GPG) is a free-software replacement for Symantec's cryptographic software suite PGP. The software is compliant with the now obsoleted , the IETF standards-track specification of OpenPGP. Modern versions of PGP are interoperable with GnuPG and other OpenPGP v4-compliant systems. November 2023 saw two drafts aiming to update the 2007 OpenPGP v4 specification (RFC4880), ultimately resulting in thRFC 9580standard in July 2024. The proposal from the GnuPG developers, which is called LibrePGP, was not taken up by the OpenPGP Working Group and future versions of GnuPG will not support the current version of OpenPGP. GnuPG is part of the GNU Project and received major funding from the German government in 1999. Overview GnuPG is a hybrid-encryption software program because it uses a combination of conventional symmetric-key cryptography for speed, and public-key cryptography for ease of secure key exchange, typically by using the recipient's publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic-curve Cryptography
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 to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGamal cryptosystem. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic-curve factorization. History The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor S. Miller in 1985. Elliptic curve cryptography algorithms entered wide use in 2004 to 2005. In 1999, NIST recommended fifteen elliptic curves. Specifically, FIPS 186 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bits Of Security
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 have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DKIM
DomainKeys Identified Mail (DKIM) is an email authentication method that permits a person, role, or organization that owns the signing domain to claim some responsibility for a message by associating the domain with the message. The receiver can check that an email that claimed to have come from a specific domain was indeed authorized by the owner of that domain. It achieves this by affixing a digital signature, linked to a domain name, to each outgoing email message. The recipient system can verify this by looking up the sender's public key published in the DNS. A valid signature also guarantees that some parts of the email (possibly including attachments) have not been modified since the signature was affixed. Usually, DKIM signatures are not visible to end-users, and are affixed or verified by the infrastructure rather than the message's authors and recipients. DKIM is an Internet Standard. It is defined in RFC 6376, dated September 2011, with updates in RFC 8301 and RF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Montgomery Curve
In mathematics, the Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form. It is used for certain computations, and in particular in different cryptography applications. Definition A Montgomery curve over a field is defined by the equation :M_: By^2 = x^3 + Ax^2 + x for certain and with . Generally this curve is considered over a finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), s ... ''K'' (for example, over a finite field of element (mathematics), elements, ) with characteristic (algebra), characteristic different from 2 and with and , but they are also considered over the rational number, rationals with the same restrictions for and . Montgomery arithmetic It is possible to do some "ope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual EC DRBG
Dual_EC_DRBG (Dual Elliptic Curve Deterministic Random Bit Generator) is an algorithm that was presented as a cryptographically secure pseudorandom number generator (CSPRNG) using methods in elliptic curve cryptography. Despite wide public criticism, including the public identification of the possibility that the National Security Agency put a backdoor (cryptography), backdoor into a recommended implementation, it was, for seven years, one of four CSPRNGs standardized in NIST SP 800-90A as originally published circa June 2006, until it was withdrawn in 2014. Weakness: a potential backdoor Weaknesses in the cryptographic security of the algorithm were known and publicly criticised well before the algorithm became part of a formal standard endorsed by the American National Standards Institute, ANSI, International Organization for Standardization, ISO, and formerly by the National Institute of Standards and Technology (NIST). One of the weaknesses publicly identified was the pote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruce Schneier
Bruce Schneier (; born January 15, 1963) is an American cryptographer, computer security professional, privacy specialist, and writer. Schneier is an Adjunct Lecturer in Public Policy at the Harvard Kennedy School and a Fellow at the Berkman Klein Center for Internet & Society as of November, 2013. He is a board member of the Electronic Frontier Foundation, Access Now, and The Tor Project; and an advisory board member of Electronic Privacy Information Center and VerifiedVoting.org. He is the author of several books on general security topics, computer security and cryptography and is a squid enthusiast. Early life and education Bruce Schneier is the son of Martin Schneier, a Brooklyn Supreme Court judge. He grew up in the Flatbush neighborhood of Brooklyn, New York, attending P.S. 139 and Hunter College High School. After receiving a physics bachelor's degree from the University of Rochester in 1984, he went to American University in Washington, D.C., and got his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
