ElGamal signature scheme The ElGamal signature scheme is a digital signature scheme which is based on the difficulty of computing discrete logarithms . It was described by Taher Elgamal in 1985. The ElGamal signature algorithm is rarely used in practice. A variant developed at the NSA and known as the Digital Signature Algorithm is much more widely used. There are several other variants. The ElGamal signature scheme must not be confused with ElGamal encryption which was also invented by Taher Elgamal.Overview The ElGamal signature scheme is a digital signature scheme based on the algebraic properties of modular exponentiation , together with the discrete logarithm problem . The algorithm uses a key pair consisting of a public key and a private key . The private key is used to generate a digital signature for a message, and such a signature can be verified by using the signer's corresponding public key. The digital signature provides message authentication , integrity and non-repudiation.History The ElGamal signature scheme was described by Tahir Elgamal in 1985.Operation The scheme involves four operations: key generation , key distribution , signing and signature verification.Key generation has two phases. The first phase is a choice of algorithm parameters which may be shared between different users of the system, while the second phase computes a single key pair for one user.Parameter generation The algorithm parameters are. These parameters may be shared between users of the system.Per-user keys Given a set of parameters, the second phase computes the key pair for a single user: Choose an integer randomly from. Compute. is the private key and is the public key.Key distribution The signer should send the public key to the receiver via a reliable, but not necessarily secret, mechanism. The signer should keep the private key secret.Signing A message is signed as follows: Choose an integer randomly from with relatively prime to. Compute. Compute. In the unlikely event that start again with a different random. The signature is.Verifying a signature One can verify that a signature is a valid signature for a message as follows: The algorithm is correct in the sense that a signature generated with the signing algorithm will always be accepted by the verifier. The computation of during signature generation implies Since is relatively prime to,Security A third party can forge signatures either by finding the signer's secret key x or by finding collisions in the hash function . Both problems are believed to be difficult. However, as of 2011 no tight reduction to a computational hardness assumption is known. The signer must be careful to choose a different k uniformly at random for each signature and to be certain that k , or even partial information about k , is not leaked. Otherwise, an attacker may be able to deduce the secret key x with reduced difficulty, perhaps enough to allow a practical attack. In particular, if two messages are sent using the same value of k and the same key, then an attacker can compute x directly.Existential forgery The original paper did not include a hash function as a system parameter. The message m was used directly in the algorithm instead of H . This enables an attack called existential forgery , as described in section IV of the paper. Pointcheval and Stern generalized that case and described two levels of forgeries: The one-parameter forgery. Select an such that. Set and. Then the tuple is a valid signature for the message. The two-parameters forgery. Select, and. Set and. Then the tuple is a valid signature for the message. The one-parameter forgery is a special case of the two-parameter forgery, when.
Popular articles Javier Milei - Argentine libertarian economist, author, radio conductor and public speaker sympathetic to the Austrian School of economic thought. He became widely known for his regular ...Jimmy Carter - American politician, philanthropist, and former farmer who served as the 39th president of the United States from 1977 to 1981. A member of the Democratic Party, he previ...UEFA Euro 2024 - The 2024 UEFA European Football Championship , commonly referred to as UEFA Euro 2024 or simply Euro 2024 , will be the 17th edition of the UEFA European Championship, the quadrennial internationa...Argentina - country located mostly in the southern half of South America. Sharing the bulk of the Southern Cone with Chile to the west, the country is also b...Sam Altman - American entrepreneur, investor, programmer, and blogger. He is the former president of Y Combinator and now the CEO of OpenAI. Early life and education. ...Rosalynn Carter - American who served as First Lady of the United States from 1977 to 1981 as the wife of President Jimmy Carter. For decades, she has been a leading advocate for numerou...Next Argentine presidential election - Next Argentine presidential election - presidential election in Argentina....Popular movies The Hunger Games (film) - 2012 American dystopian action thriller science fiction-adventure film directed by Gary Ross and based on Suzanne Collins’s 2008 novel of the same name. It is the first insta...untitled Captain Marvel sequel - part of Marvel Cinematic Universe....Killers of the Flower Moon (film project) - Killers of the Flower Moon - film project in United States of America. It was presented as drama, detective fiction, thriller. The film project starred Leonardo Dicaprio, Robert De Niro. Director of...Five Nights at Freddy's (film) - Five Nights at Freddy's - film published in 2017 in United States of America. Scenarist of the film - Scott Cawthon....Popular video games Minecraft - sandbox video game developed by Mojang Studios. Created by Markus "Notch" Persson in the Java programming language and released as a public alpha for personal computers in 2...Grand Theft Auto V - 2013 action-adventure game developed by Rockstar North and published by Rockstar Games. It is the first main entry in the Grand Theft Auto series since 2008's Grand Theft ...Roblox - online game platform and game creation system that allows users to program games and play games created by other users. Founded by David Baszucki and Erik Cassel in 2004 and released in...Baldur's Gate III - upcoming role-playing video game developed and published by Larian Studios for Microsoft Windows and the Stadia streaming service. It is the third main game in the Baldur's ...Alan Wake - action-adventure video game developed by Remedy Entertainment and published by Microsoft Studios, released for the Xbox 360 and Microsoft Windows. The story follows best-selling thri...Fortnite - online video game developed by Epic Games and released in 2017. It is available in three distinct game mode versions that otherwise share the same general gameplay and game engine: ...Super Mario RPG - is a role-playing video game developed by Square and published by Nintendo for the Super Nintendo Entertainment System in 1996. It was directed by Yoshihiko Maekawa and Chihiro Fujioka and produced by...Popular books Book of Revelation - The Book of Revelation is the final book of the New Testament, and consequently is also the final book of the Christian Bible. Its title is derived from the first word of the Koine Greek text: apok...Book of Genesis - account of the creation of the world, the early history of humanity, Israel's ancestors and the origins...Gospel of Matthew - The Gospel According to Matthew is the first book of the New Testament and one of the three synoptic gospels. It tells how Israel's Messiah, rejected and executed in Israel, pronounces judgement on ...Michelin Guide - Michelin Guides are a series of guide books published by the French tyre company Michelin for more than a century. The term normally refers to the annually published Michelin Red Guide , the oldest...Psalms - The Book of Psalms , commonly referred to simply as Psalms , the Psalter or "the Psalms", is the first book of the Ketuvim , the third section of the Hebrew Bible, and thus a book of th...Ecclesiastes - Ecclesiastes is one of 24 books of the Tanakh , where it is classified as one of the Ketuvim . Originally written c. 450–200 BCE, it is also among the canonical Wisdom literature of the Old Tes...The 48 Laws of Power - non-fiction book by American author Robert Greene. The book...Popular television series The Crown (TV series) - historical drama web television series about the reign of Queen Elizabeth II, created and principally written by Peter Morgan, and produced by Left Bank Pictures and Sony Pictures Tel...Friends - American sitcom television series, created by David Crane and Marta Kauffman, which aired on NBC from September 22, 1994, to May 6, 2004, lasting ten seasons. With an ensemble cast sta...Young Sheldon - spin-off prequel to The Big Bang Theory and begins with the character Sheldon...Modern Family - American television mockumentary family sitcom created by Christopher Lloyd and Steven Levitan for the American Broadcasting Company. It ran for eleven seasons, from September 23...Loki (TV series) - upcoming American web television miniseries created for Disney+ by Michael Waldron, based on the Marvel Comics character of the same name. It is set in the Marvel Cinematic Universe, shar...Game of Thrones - American fantasy drama television series created by David Benioff and D. B. Weiss for HBO. It...Shameless (American TV series) - American comedy-drama television series developed by John Wells which debuted on Showtime on January 9, 2011. It...
OWIKI.org . Text is available under the Creative Commons Attribution-ShareAlike License.