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RSA (cryptosystem)

RSA is one of the first public-key cryptosystems and is used for secure data transmission. In such a cryptosystem, the encryption key is public and it is different from the decryption key, kept secret. In RSA, this asymmetry is based on the practical difficulty of the factorization of the product of two large prime numbers, the "factoring problem"; the acronym RSA is made of the initial letters of the surnames of Ron Rivest, Adi Shamir, Leonard Adleman, who first publicly described the algorithm in 1977. Clifford Cocks, an English mathematician working for the British intelligence agency Government Communications Headquarters, had developed an equivalent system in 1973, but this was not declassified until 1997. A user of RSA creates and publishes a public key based on two large prime numbers, along with an auxiliary value; the prime numbers must be kept secret. Anyone can use the public key to encrypt a message, but only someone with knowledge of the prime numbers can decode the message. Breaking RSA encryption is known as the RSA problem.

Whether it is as difficult as the factoring problem remains an open question. There are no published methods to defeat the system if a large enough key is used. RSA is a slow algorithm, because of this, it is less used to directly encrypt user data. More RSA passes encrypted shared keys for symmetric key cryptography which in turn can perform bulk encryption-decryption operations at much higher speed; the idea of an asymmetric public-private key cryptosystem is attributed to Whitfield Diffie and Martin Hellman, who published this concept in 1976. They introduced digital signatures and attempted to apply number theory, their formulation used a shared-secret-key created from exponentiation of some number, modulo a prime number. However, they left open the problem of realizing a one-way function because the difficulty of factoring was not well-studied at the time. Ron Rivest, Adi Shamir, Leonard Adleman at the Massachusetts Institute of Technology, made several attempts over the course of a year to create a one-way function, hard to invert.

Rivest and Shamir, as computer scientists, proposed many potential functions, while Adleman, as a mathematician, was responsible for finding their weaknesses. They tried many approaches including "knapsack-based" and "permutation polynomials". For a time, they thought what they wanted to achieve was impossible due to contradictory requirements. In April 1977, they spent Passover at the house of a student and drank a good deal of Manischewitz wine before returning to their homes at around midnight. Rivest, unable to sleep, lay on the couch with a math textbook and started thinking about their one-way function, he spent the rest of the night formalizing his idea, he had much of the paper ready by daybreak. The algorithm is now known as RSA – the initials of their surnames in same order as their paper. Clifford Cocks, an English mathematician working for the British intelligence agency Government Communications Headquarters, described an equivalent system in an internal document in 1973. However, given the expensive computers needed to implement it at the time, RSA was considered to be a curiosity and, as far as is publicly known, was never deployed.

His discovery, was not revealed until 1997 due to its top-secret classification. Kid-RSA is a simplified public-key cipher published in 1997, designed for educational purposes; some people feel that learning Kid-RSA gives insight into RSA and other public-key ciphers, analogous to simplified DES. MIT was granted U. S. Patent 4,405,829 for a "Cryptographic communications system and method" that used the algorithm, on September 20, 1983. Though the patent was going to expire on September 21, 2000, the algorithm was released to the public domain by RSA Security on September 6, 2000, two weeks earlier. Since a detailed description of the algorithm had been published in the Mathematical Games column in the August 1977 issue of Scientific American, prior to the December 1977 filing date of the patent application, regulations in much of the rest of the world precluded patents elsewhere and only the US patent was granted. Had Cocks's work been publicly known, a patent in the United States would not have been legal either.

From the DWPI's abstract of the patent, The system includes a communications channel coupled to at least one terminal having an encoding device and to at least one terminal having a decoding device. A message-to-be-transferred is enciphered to ciphertext at the encoding terminal by encoding the message as a number M in a predetermined set; that number is raised to a first predetermined power and computed. The remainder or residue, C, is... computed when the exponentiated number is divided by the product of two predetermined prime numbers. The RSA algorithm involves four steps: key generation, key distribution and decryption. A basic principle behind RSA is the observation that it is practical to find three large positive integers e, d and n such that with modular exponentiation for all integers m: d ≡ m and that knowing e and n or m it can be difficult to find d; the triple bar here denotes modular congruence. In addition, for some operations it is convenient that the order of the two exponentiations can be changed and that this relation implies: e ≡

I Love...

I Love... is a British television and compilation album brand by the BBC, which looks back at a specific year in each episode. The programs consist of celebrities and public figures discussing and commenting on the pop culture of the time i.e. films, fashion, music etc. that relate to the program's overall topic. BBC made three series: I Love...the 1970s premiered on 22 July 2000 in the UK, with the final part I Love 1979 premiering on 23 September 2000. I Love...the 1980s premiered on 13 January 2001 in the UK, with the final part I Love 1989 premiering on 24 March 2001. I Love...the 1990s premiered on 18 August 2001 in the UK, with the final part I Love 1999 premiering on 3 November 2001. VH1 produced a USA version of the series of this show for American television, beginning in 2002 with I Love the'80s; the programs consist of celebrities discussing American pop culture that relate to the program's overall topic. The series continued with programs focusing on decades, such as I Love the'70s, as well as doing sequels to done decades, such as I Love the'80s Strikes Back.

2008 featured the premiere of I Love the New Millennium, the first series to be completed before the end of the decade presented. The series has so far released two programs that were not focused on decades, with I Love Toys and I Love the Holidays; the use of the word "love" instead of the heart symbol was to avoid a trademark dispute with the state of New York, owners of the ILove trademark in the United States. On 20 February 2010 VH1 aired six hours' worth of the "best of" specials for the Best of I Love the... series: Best of I Love the'70s, Best of I Love the'80s and Best of I Love the'90s. However, these episodes only featured clips. Music, used in the clips in the previous I Love... series were replaced with generic tracks. To deliver funny and memorable moments on the spot, the guests switched from famous celebrities to lesser-known people with comedic backgrounds. I Love the'80s I Love the'70s I Love the'80s Strikes Back I Love the'90s I Love the'90s: Part Deux I Love the'80s 3-D I Love the Holidays I Love Toys I Love the'70s: Volume 2 I Love the New Millennium Best of I Love the...

I Love the 2000s A number of I Love... tie-in albums were produced and released by EMI/Virgin. I Love 70s I Love 80s I Love Ibiza I Love 90s I Love 2 Party I Love Summer I Love 2 Party 2003 I Love U I Love ChristmasA number of VH1's I Love the... tie-in albums were produced and released by Rhino Records. VH1: I Love the'70s VH1: I Love the'80s VH1: I Love the'90s

Mango Dreams

Mango Dreams is a 2016 English-language drama film produced and directed by John Upchurch. As a child, Dr. Amit Singh survived the British partition of India. Since he has been running forward his whole life, running from the horrors of his past — his family murdered by Muslims and the personal guilt he feels for the death of his brother. Now, with the onset of dementia, Amit must return to his childhood home and confront the memories he has been trying to forget before dementia robs him of his last chance for peace, but before the journey home begins, Amit’s son Abhi arrives from America to commit his father to an old age home. Amit encounters Salim. Salim is a Muslim auto-rickshaw driver whose wife was burned to death by Hindu rioters. Amit had earlier saved the life of Salim’s son. Salim offers to drive the doctor anywhere, as a way of repaying his debt; when Amit asks to be taken home, Salim cannot imagine how far he will end up going for the doctor or where the journey will lead them. Along the way and Salim forge an unforgettable friendship and help each other discover the peace they have been longing for.

Ram Gopal Bajaj as Amit Pankaj Tripathi as Salim Samir Kochhar as Abhi Rohini Hattangadi as Padma S M Zaheer as Prashant Naseeruddin Shah as Abhay 2016 Arizona International Film Festival - Special Jury Award for Bridging Cultures 2016 Cebu International Film Festival - Humanity Award 2016 Full Bloom Film Festival - Best Narrative Feature 2017 London Asian Film Festival - Best Script 2017 Peace On Earth Film Festival - Best Narrative Feature 2017 Dada Saheb Phalke Film Festival Best Film - Jury: Mazahir Rahim, John Upchurch Best Actor: Ram Gopal Bajaj Best Supporting Actor: Pankaj Tripathi 2017 Telly Awards Cinematography: Nouman Ahsan, Amit Singh Directing: John Upchurch 2017 filmSPARK Best Feature: Mazahir Rahim, John Upchurch Mango Dreams on IMDb