A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient strong reason to believe that the message was created by a known sender, that the message was not altered in transit. Digital signatures are a standard element of most cryptographic protocol suites, are used for software distribution, financial transactions, contract management software, in other cases where it is important to detect forgery or tampering. Digital signatures are used to implement electronic signatures, which includes any electronic data that carries the intent of a signature, but not all electronic signatures use digital signatures. In some countries, including South Africa, the United States, Turkey, Brazil, Mexico, Saudi Arabia, Switzerland and the countries of the European Union, electronic signatures have legal significance. Digital signatures employ asymmetric cryptography. In many instances they provide a layer of validation and security to messages sent through a non-secure channel: Properly implemented, a digital signature gives the receiver reason to believe the message was sent by the claimed sender.

Digital seals and signatures are equivalent to stamped seals. Digital signatures are equivalent to traditional handwritten signatures in many respects, but properly implemented digital signatures are more difficult to forge than the handwritten type. Digital signature schemes, in the sense used here, are cryptographically based, must be implemented properly to be effective. Digital signatures can provide non-repudiation, meaning that the signer cannot claim they did not sign a message, while claiming their private key remains secret. Further, some non-repudiation schemes offer a time stamp for the digital signature, so that if the private key is exposed, the signature is valid. Digitally signed messages may be anything representable as a bitstring: examples include electronic mail, contracts, or a message sent via some other cryptographic protocol. A digital signature scheme consists of three algorithms; the algorithm outputs a corresponding public key. A signing algorithm that, given a private key, produces a signature.

A signature verifying algorithm that, given the message, public key and signature, either accepts or rejects the message's claim to authenticity. Two main properties are required. First, the authenticity of a signature generated from a fixed message and fixed private key can be verified by using the corresponding public key. Secondly, it should be computationally infeasible to generate a valid signature for a party without knowing that party's private key. A digital signature is an authentication mechanism that enables the creator of the message to attach a code that acts as a signature; the Digital Signature Algorithm, developed by the National Institute of Standards and Technology, is one of many examples of a signing algorithm. In the following discussion, 1n refers to a unary number. Formally, a digital signature scheme is a triple of probabilistic polynomial time algorithms, satisfying: G generates a public key, a corresponding private key, on input 1n, where n is the security parameter.

S returns a tag, t, on the inputs: the private key, a string. V outputs accepted or rejected on the inputs: the public key, a string, a tag. For correctness, S and V must satisfy Pr = 1. A digital signature scheme is secure if for every non-uniform probabilistic polynomial time adversary, A Pr < negl,where AS denotes that A has access to the oracle, S, Q denotes the set of the queries on S made by A, which knows the public key, pk, the security parameter, n, x ∉ Q denotes that the adversary may not directly query the string, x, on S. In 1976, Whitfield Diffie and Martin Hellman first described the notion of a digital signature scheme, although they only conjectured that such schemes existed based on functions that are trapdoor one-way permutations. Soon afterwards, Ronald Rivest, Adi Shamir, Len Adleman invented the RSA algorithm, which could be used to produce primitive digital signatures; the first marketed software package to offer digital signature was Lotus Notes 1.0, released in 1989, which used the RSA algorithm.

Other digital signature schemes were soon developed after RSA, the earliest being Lamport signatures, Merkle signatures, Rabin signatures. In 1988, Shafi Goldwasser, Silvio Micali, Ronald Rivest became the first to rigorously define the security requirements of digital signature schemes, they described a hierarchy of attack models for signature schemes, presented the GMR signature scheme, the first that could be proved to prevent an existential forgery against a chosen message attack, the accepted security definition for signature schemes. The first such scheme, not built on trapdoor functions but rather on a family of function with a much weaker required property of one-way permutation was presented by Moni Naor and Moti Yung. One digital signature scheme is based on RSA. To create signature keys, generate a RSA key pair containing a modulus, N, the product of two random secret distin

Samsung DeX is a feature included on some Samsung handheld devices that enables users to extend their device into a desktop-like experience by connecting a keyboard and monitor. The name "DeX" is a contraction of "Desktop eXperience". Samsung first included the DeX feature on Samsung's Galaxy S8 and S8+ smartphones, has continued to support the feature on all of its latest flagship smartphones, including the Galaxy S9, S10, Note8, Note9 and Note10 throughout Android Pie The Galaxy A90 5G is the first Galaxy A phone with DeX support, it has been introduced on several high-end tablets, including the Galaxy Tab S4, S5e and Tab S6. The original version of DeX required; this provided ethernet, HDMI 2.0 output and two USB 2.0 ports. With the launch of the Note 9 in August 2018, Samsung introduced the DeX HDMI adapter and multiport adapter, eliminating the need for the previous docking accessories. Whilst connected to a display, the device itself can function as a touchpad or continue being used in its usual fashion whilst DeX is operating.

With the Note 10 and Galaxy Fold, DeX can now be launched via a direct cable connection to a physical computer using the existing charging cable, eliminating the need for any docking accessories. DeX has been used in the public safety setting to replace in-vehicle laptops. Samsung announced "Linux on Galaxy" which allows use of a compatible Linux distribution rather than the default Android OS giving full personal computer capabilities; the DeX Desktop can be accessed with a downloadable app for Windows and Mac OS or through third party accessories like the Melopow Dock. Samsung DeX devices can be managed by Samsung Knox to allow or restrict access using the Knox platform for added control and security. In October 2019 Samsung announced that Linux on DeX will not be available for Android 10 and warned users that after upgrade to Android 10 they will not be able to downgrade back, permanently losing the ability to use full Linux applications. Easy Projection, a similar desktop mode found on the Huawei Mate 10 and Mate 20 phones.

Docking station Webtop, a similar feature of the Motorola Atrix series, which required specialized hardware. "Samsung DeX: Desktop Dock for Galaxy Phones"

Phanindranath Rangarajan Kumaramangalam was a prominent politician of the Indian National Congress and the Bharatiya Janata Party and a Member of parliament, Lok Sabha from the Salem constituency from 1984 to 1996 and Tiruchirapalli constituency from 1998 to 2000. He served as the Minister of State for Law and Company Affairs in the P. V. Narasimha Rao government from July 1991 to December 1993 and as the Union Minister for Power in the Vajpayee Government from 1998 to 2000, he was the grandson of former Chief Minister of Madras, P. Subbarayan and the nephew of former Indian Chief of Army, General P. P. Kumaramangalam. Rangarajan was born on 12 May 1952 in a family of Zamindars of Thiruchengode, his grandfather Paramasiva Subbarayan was the Chief Minister of Madras province from 1925 to 1926 and a Cabinet Minister under Governments. His uncle, General P. P. Kumaramangalam was a former Chief of Army Staff. Rangarajan's father Mohan Kumaramangalam was an important theorist and organiser of the undivided Communist Party of India.

His mother Kalyani Mukherjee was the niece of Ajoy Mukherjee, sometime Chief Minister of West Bengal, of Biswanath Mukherjee, husband of the communist ideologue and parliamentarian Geeta Mukherjee. Ranga was involved in student politics right from the earliest stages, as one of the founding members and the first president of the National Students Union of India, it was no less a person than Prime Minister Indira Gandhi, whose great personal favourite he was, who called him to take up this post after going through due process. By 1973, he had been elected a member of the All India Congress Committee. In 1977, on obtaining a degree from Kirori Mal College, Delhi University, he moved to Madras to practice in labour law; when the Congress was re-elected in 1980, Rangarajan was asked by his dear friend, soon-to-be-Prime Minister Rajiv Gandhi, to play an active role in politics. He won the 1984 elections from Salem Lok Sabha constituency. P. V. Narasimha Rao appointed him Minister of State for Law and Company Affairs in July 1991.

Despite his personal sense of loyalty to Narasimha Rao, Ranga was unable to support him in what was being seen as a corrupt Congress regime. In a letter to the President he raised several issues with regards to corruption perpetrated by the Prime Minister, based on documents he had in his possession and that formed the basis of the Vohra Committee report. In this letter he asked the President to ask the Prime Minister to step down and face an investigation against the charges. In late 1993, Rangarajan resigned as Cabinet Minister. In May 1995, Rangarajan resigned from the primary membership of the Indian National Congress and along with Arjun Singh, N. D. Tiwari, Sheila Dikshit and others, founded the Congress. However, Rangarajan lost his seat in the 1996 Parliamentary elections during which his new party suffered a crushing defeat. In December 1997, Rangarajan joined the Bharatiya Janata Party, he won from the Tiruchirapalli Lok Sabha constituency in 1998 and 1999 and became one of the torch-bearers of the BJP in Tamil Nadu.

He served with distinction as the Union Minister for Power and Parliamentary Affairs, holding additional charge of Law and Company Affairs, Mines, in the Second Vajpayee Ministry from 1998 to 1999 and in the Third Vajpayee Ministry from 1999 until his death in 2000. One of the most charismatic and brilliant leaders in post independent India, Ranga was loved and respected across party lines, his capacity to get bills passed in parliament was unmatched. Additionally, he was one of that rare breed of Indian leaders who delivered on his promises, never forgetting the welfare of the common rural Indian, the farmer, while propelling mega power projects forward with matchless administrative and managerial capability. Rangarajan died on 23 August 2000 at the All India Institute of Medical Sciences at the age of 48 as a result of acute myeloid leukaemia. At the time of his death, he was the Power Minister in the A. B. Vajpayee ministry, he was cremated with full state honours on the same day. Political Families of The World Ranga cremated with full state honours, Rediff.com, 23 August 2000 Politician with a hearth of Gold, Tribute by K.

Srinivasan, Rediff.com, 23 August 2000'I think some poison had entered his body, was eating up his body' Rediff.com interview with Kitty Kumaramangalam, wife of Rangarajan Kumaramangalam on 22 September 2000* BJP fields Lalitha Kumaramangalam from Pondicherry, Yahoo News, 21 February 2004 The Hindu