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In cryptography the Rabin signature algorithm is a method of digital signature proposed by Michael O. Rabin in 1979; the Rabin signature algorithm was one of the first digital signature schemes proposed, it is the only one to relate the hardness of forgery directly to the problem of integer factorization. The Rabin signature algorithm is existentially unforgeable in the random oracle model assuming the integer factorization problem is intractable; the Rabin signature algorithm is closely related to the Rabin cryptosystem. But, the RSA cryptosystem has a prominent role in the early days of public key cryptography, the Rabin signature algorithm is not covered in most introductory courses on cryptography. If H is a collision resistant hash function, m the message to sign and H p − 1 2 mod p = 1 and H q − 1 2 mod q = 1 the signature S is given by the equation S = mod. Everybody can verify H = S. Key Generation The signer S chooses primes p, q each of size k/2 bits, computes the product n = p ⋅ q.

S chooses a random b in. The public key is; the private key is. Signing To sign a message m the signer S picks random padding U and calculates m ⋅ U mod n. S solves x mod n = m ⋅ U mod n. If there is no solution S tries again; the signature on m is the pair Verification Given a message m and a signature the verifier V calculates x mod n and m ⋅ U mod n and verifies that they are equal. The secure algorithm relies on a collision-resistant hash function H: ∗ → k. In most presentations the algorithm is simplified by choosing b = 0; the hash function H with k output bits is assumed to be a random oracle and the algorithm works as follows: Key generation Signing Verification In some treatments the random pad U is eliminated. Instead we can multiply the hash value with two numbers a or b with the properties = − = − 1 and = − = − 1, where denotes the legendre symbol. For any H modulo n one of the four numbers H, a H, b H, a b H will be a square modulo n, the signer chooses that one for his signature. More simple, we change the message m until the signature can be verified.

If the hash function H is a random oracle, i.e. its output is random in Z / n Z forging a signature on any message m is as hard as calculating the square root of a random element in Z / n Z. To prove that taking a random square root is as hard as factoring, we first note that in most cases there are four distinct square roots since n has two square roots modulo p and two square roots modulo q, each pair gives a square roo

This is a list of episodes of the anime series Kimi to Boku. The episodes in the anime are based from the manga series by Kiichi Hotta. An anime television adaption of Kimi to Boku was announced in the April 2011 issue of Monthly GFantasy; the series was produced by J. C. Staff under the direction of Mamoru Kanbe with scripts supervised by Reiko Yoshida and music by Elements Garden and began its broadcast run starting October 4, 2011; the series will be split into two 13-episode seasons. For the first season, the opening theme "Bye Bye" was performed by the Japanese rock band, Seven Oops, while the ending "Nakimushi" is by Miku Sawai. A second season was announced on the main site and started airing on April 2, 2012; the opening song "Zutto" is performed by a popular nico nico singer 少年T / 佐香智久. Official anime website Official Twitter website