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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. 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. Daniel J. 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 prime number 2^ - 19, and it uses the base point x = 9. This point generates a cyclic subgroup whose order is the prime 2^ + 27742317777372353535851937790883648493, this subgroup has a co-factor of 8, meaning the number of elements in the subgroup is 1/8 that of the elliptic cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve448
In cryptography, Curve448 or Curve448-Goldilocks is an elliptic curve cryptography, elliptic curve potentially offering 224 bits of security and designed for use with the elliptic-curve Diffie–Hellman (ECDH) key agreement scheme. 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. A 2019 draft oFIPS 186-5confirms this claim. Both are described in . The name X448 is used for the DH function. Mathematical properties Hamburg chose the Solinas prime, Solinas trinom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EdDSA
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] |
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 function ... [...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 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 , s, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DKIM
DomainKeys Identified Mail (DKIM) is an email authentication method designed to detect forged sender addresses in email (email spoofing), a technique often used in phishing and email spam. DKIM allows the receiver to check that an email 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 RFC 8463. Overview The need for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GnuPG
GNU Privacy Guard (GnuPG or GPG) is a free-software replacement for Symantec's PGP cryptographic software suite. The software is compliant with RFC 4880, the IETF standards-track specification of OpenPGP. Modern versions of PGP are interoperable with GnuPG and other OpenPGP-compliant systems. 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 public key to encrypt a session key which is used only once. This mode of operation is part of the OpenPGP standard and has been part of PGP from its first version. The GnuPG 1.x series uses an integrated cryptographic library, while the GnuPG 2.x series replaces this with Libgcrypt. GnuPG encrypts messages using asymmetric key pairs individually ge ... [...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 ''K'' (for example, over a finite field of elements, ) with characteristic different from 2 and with and , but they are also considered over the rationals with the same restrictions for and . Montgomery arithmetic It is possible to do some "operations" between the points of an elliptic curve: "adding" two points P, Q consists of finding a third one R such that R=P+Q; "doubling" a point consists of computing =P+P (For more information about operations see The group law) and below. A point P=(x,y) on the elliptic curve in the Montgomery form By^2 = x^3 + A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X25519
X, or x, is the twenty-fourth and third-to-last letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''"ex"'' (pronounced ), plural ''exes''."X", ''Oxford English Dictionary'', 2nd edition (1989); ''Merriam-Webster's Third New International Dictionary of the English Language, Unabridged'' (1993); "ex", ''op. cit''. X is regularly pronounced as "ks". History In Ancient Greek, ' Χ' and ' Ψ' were among several variants of the same letter, used originally for and later, in western areas such as Arcadia, as a simplification of the digraph 'ΧΣ' for . In the end, more conservative eastern forms became the standard of Classical Greek, and thus 'Χ' ''( Chi)'' stood for (later ; palatalized to in Modern Greek before front vowels). However, the Etruscans had taken over 'Χ' from western Greek, and it therefore stands for in Etruscan and Latin. The letter 'Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transport Layer Security
Transport Layer Security (TLS) is a cryptographic protocol designed to provide communications security over a computer network. The protocol is widely used in applications such as email, instant messaging, and voice over IP, but its use in securing HTTPS remains the most publicly visible. The TLS protocol aims primarily to provide security, including privacy (confidentiality), integrity, and authenticity through the use of cryptography, such as the use of certificates, between two or more communicating computer applications. It runs in the presentation layer and is itself composed of two layers: the TLS record and the TLS handshake protocols. The closely related Datagram Transport Layer Security (DTLS) is a communications protocol providing security to datagram-based applications. In technical writing you often you will see references to (D)TLS when it applies to both versions. TLS is a proposed Internet Engineering Task Force (IETF) standard, first defined in 1999, and the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Engineering Task Force
The Internet Engineering Task Force (IETF) is a standards organization for the Internet and is responsible for the technical standards that make up the Internet protocol suite (TCP/IP). It has no formal membership roster or requirements and all its participants are volunteers. Their work is usually funded by employers or other sponsors. The IETF was initially supported by the federal government of the United States but since 1993 has operated under the auspices of the Internet Society, an international non-profit organization. Organization The IETF is organized into a large number of working groups and birds of a feather informal discussion groups, each dealing with a specific topic. The IETF operates in a bottom-up task creation mode, largely driven by these working groups. Each working group has an appointed chairperson (or sometimes several co-chairs); a charter that describes its focus; and what it is expected to produce, and when. It is open to all who want to particip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenSSH
OpenSSH (also known as OpenBSD Secure Shell) is a suite of secure networking utilities based on the Secure Shell (SSH) protocol, which provides a secure channel over an unsecured network in a client–server architecture. Network Working Group of the IETF, January 2006, RFC 4252, The Secure Shell (SSH) Authentication Protocol. OpenSSH started as a fork of the free SSH program developed by Tatu Ylönen; later versions of Ylönen's SSH were proprietary software offered by SSH Communications Security. OpenSSH was first released in 1999 and is currently developed as part of the OpenBSD operating system. OpenSSH is not a single computer program, but rather a suite of programs that serve as alternatives to unencrypted protocols like Telnet and FTP. OpenSSH is integrated into several operating systems, namely Microsoft Windows, macOS and most Linux operating systems, while the portable version is available as a package in other systems. History OpenBSD Secure Shell was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
