The Beta Cryptosystem
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TLDR
The newly developed beta cryptosystem is efficient with respect to encryption and decryption and the validity of this algorithm is proven by applying to message that are text and returning the original message in numerical examples.Abstract:
This paper, we introduce mainly the concept of beta cryptosystem, whose security is based on generalized discrete logarithm problem and integer factorization problem in the multiplicative group of finite fields. We show that the proposed public key cryptosystem based on generalized discrete logarithm problem and integer factorization problem, provides more security because of double computation comparing with the generalized discrete logarithm problem and integer factorization problem. Hence the adversary has to solve distinct discrete logarithm problems and integer factorization problem simultaneously in the multiplicative group of finite fields in order to recover a corresponding plaintext from the received cipertext. Therefore, this scheme is expected to gain a higher level of security. We next show that, the newly developed scheme is efficient with respect to encryption and decryption and the validity of this algorithm is proven by applying to message that are text and returning the original message in numerical examples.read more
Citations
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A new public-key cryptosystem
David Naccache,Jacques Stern +1 more
TL;DR: This paper describes a new public-key cryptosystem where the ciphertext is obtained by multiplying the public-keys indexed by the message bits and the cleartext is recovered by factoring the cipher Text raised to a secret power.
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Factoring by electronic mail
Arjen K. Lenstra,Mark S. Manasse +1 more
TL;DR: The distributed implementation of two factoring algorithms, the elliptic curve method (ecm) and the multiple polynomial quadratic sieve algorithm (mpqs), shows that the enormous computational task of factoring 100 digit integers with the current algoritluns can be completed almost for free.