Public-Key Encryption Schemes: Benaloh Cryptosystem, Blum Goldwasser Cryptosystem, Boneh Franklin Scheme, Cayley Purser Algorithm, Ceilidh, Cramer Sh

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 31. Chapters: Benaloh cryptosystem, Blum Goldwasser cryptosystem, Boneh Franklin scheme, Cayley Purser algorithm, CEILIDH, Cramer Shoup cryptosystem, Damgard Jurik cryptosystem, Efficient Probabilistic Public-Key Encryption Scheme, ElGamal encryption, GGH encryption scheme, Goldwasser Micali cryptosystem, Hidden Field Equations, Key encapsulation, McEliece cryptosystem, Merkle Hellman knapsack cryptosystem, Naccache Stern cryptosystem, Naccache Stern knapsack cryptosystem, Niederreiter cryptosystem, NTRUEncrypt, Okamoto Uchiyama cryptosystem, Optimal asymmetric encryption padding, Paillier cryptosystem, Rabin cryptosystem, RSA (algorithm), Schmidt-Samoa cryptosystem. Excerpt: RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem. RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman, who first publicly described the algorithm in 1977. Clifford Cocks, an English mathematician, had developed an equivalent system in 1973, but it was classified until 1997. A user of RSA creates and then publishes the product of two large prime numbers, along with an auxiliary value, as their public key. The prime factors must be kept secret. Anyone can use the public key to encrypt a message, but with currently published methods, if the public key is large enough, only someone with knowledge of the prime factors can feasibly decode the message. Whether breaking RSA encryption is as hard as factoring is an open question known as the RSA problem. Adi Shamir, one of the authors of RSA: Rivest, Shamir and AdlemanThe RSA algorithm was publicly described in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman at MIT; the letters RSA are the initials of their surnames, listed in the same order as on the paper. MIT was granted for a "Cryptographic communications system and method" that used the algorithm in 1983. The patent would have expired on September 21, 2000 (the term of patent was 17 years at the time), but the algorithm was released to the public domain by RSA Security on September 6, 2000, two weeks earlier. Since a paper describing the algorithm had been published in August 1977, 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' work been publicly known, a patent in the US might not have been possible, 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