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- W1633657204 abstract "A special group based on a linear recurrence equation plays an important role in modern cryptography. Its relation appeared differently in various cryptosystem. Some cryptosystems that use this linear recurrence propertyare LUC, LUCDIF, and LUCELG but the first practical Lucas function in a cryptosystem is LUC, presented by Peter Smith and Michael Lennon in 1993. Cramer-Shoup is a practical public key cryptosystem provably secure against adaptive chosen ciphertext attack that requires a universal one-way hash function. Based on LUCELG and Cramer-Shoup cryptosystems, a new public key cryptosystem is developed bygenerating the key generation, encryption and decryption algorithm. There are two types of security for the new cryptosystem that we are concerned which are the security of Lucas function and its security against an adaptive chosen ciphertext attack. Since the encryption anddecryption algorithm of a new cryptosystem is based on the defined Lucas function, it is believed that the security of Lucas function is polynomial-time equivalent to thegeneralized discrete logarithm problems. Moreover, thenew cryptosystem is secure against adaptive chosen ciphertext attack by assuming that the hash function ischosen from a universal one-way family and the Diffie-Hellman decision problem is hard in the finite field." @default.
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- W1633657204 date "2009-01-01" @default.
- W1633657204 modified "2023-09-28" @default.
- W1633657204 title "A new cryptosystem analogous to LUCELG and Cramer-Shoup" @default.
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