Rabin cryptosystem - History

To decode the ciphertext, the private keys are necessary. The process follows: If c and r are known, the plaintext is then with . For a composite r (that is, like the Rabin algorithm's ) there is no efficient method known for the finding of m. If, however (as are p and q in the Rabin algorithm), the Chinese remainder theorem can be applied to solve for m. Thus the square roots and ...

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Rabin cryptosystem, Rabin cryptosystem - History, Rabin cryptosystem - Key generation, Rabin cryptosystem - Encryption, Rabin cryptosystem - Decryption, Rabin cryptosystem - Computing square roots, Rabin cryptosystem - Evaluation of the algorithm, Rabin cryptosystem - Effectiveness, Rabin cryptosystem - Efficiency, Rabin cryptosystem - Security

Read more here: » Rabin cryptosystem: Encyclopedia II - Rabin cryptosystem - Decryption

The decryption requires to compute square roots of the ciphertext c modulo the primes p and q. Choosing p≡q≡3 (mod 4) allows to compute square roots by and . We can show that this method works for p as follows. First p≡3 (mod 4) implies that (p+1)/4 is an integer. The assumption is trival for c≡0 (mod p). Thus we may assume that p does not divide c. Then where is a Legendre symbol. From follows that c is a ...

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Rabin cryptosystem, Rabin cryptosystem - History, Rabin cryptosystem - Key generation, Rabin cryptosystem - Encryption, Rabin cryptosystem - Decryption, Rabin cryptosystem - Computing square roots, Rabin cryptosystem - Evaluation of the algorithm, Rabin cryptosystem - Effectiveness, Rabin cryptosystem - Efficiency, Rabin cryptosystem - Security

Read more here: » Rabin cryptosystem: Encyclopedia II - Rabin cryptosystem - Computing square roots

For the encryption, only the public key n is used, thus producing a ciphertext out of the plaintext. The process follows: Let P = {0,...,n − 1} be the plaintext space (consisting of numbers) and be the plaintext. Now the ciphertext c is determined by . That is, c is the quadratic remainder of the square of the plaintext, modulo the key-number nSee also:

Rabin cryptosystem, Rabin cryptosystem - History, Rabin cryptosystem - Key generation, Rabin cryptosystem - Encryption, Rabin cryptosystem - Decryption, Rabin cryptosystem - Computing square roots, Rabin cryptosystem - Evaluation of the algorithm, Rabin cryptosystem - Effectiveness, Rabin cryptosystem - Efficiency, Rabin cryptosystem - Security

Read more here: » Rabin cryptosystem: Encyclopedia II - Rabin cryptosystem - Encryption

As with all asymmetric cryptosystems, the Rabin system uses both a public and a private key. The public key is necessary for later encoding and can be published, while the private key must be possessed only by the recipient of the message. The precise key-generation process follows: Choose two large distinct primes p and q. One may choose p≡q≡3 (mod 4) to simplify the computation of square roots modulo p and q (see below). But the scheme works with any primes. Let n=p*q. Then n is the public key. The pri ...

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Rabin cryptosystem, Rabin cryptosystem - History, Rabin cryptosystem - Key generation, Rabin cryptosystem - Encryption, Rabin cryptosystem - Decryption, Rabin cryptosystem - Computing square roots, Rabin cryptosystem - Evaluation of the algorithm, Rabin cryptosystem - Effectiveness, Rabin cryptosystem - Efficiency, Rabin cryptosystem - Security

Read more here: » Rabin cryptosystem: Encyclopedia II - Rabin cryptosystem - Key generation