A Public Key Cryptosystem Based on Pell Equation

RSA type public key cryptosystems based on the Pell’s equation are proposed in the honor of an Indian mathematician Brahmgupta who studied Pell’s equation long before European mathematicians came to know about it. Three RSA type schemes are proposed, first two are not semantically secure where as the other two schemes are semantically secure. The decryption speed of the proposed schemes is about two times as fast as RSA for a 2 log n-bit message. It is shown that the proposed schemes are more secure than the RSA scheme when purely common plaintexts are encrypted in the broadcast application and are as secure as the RSA scheme against ciphertext attack. In addition the proposed schemes are also secure against partially known plaintext attack. First two are not semantically secure but the third one is semantically secure.