226 research outputs found
A Public Key Cryptosystem Based on Singular Cubic Curve
An efficient and semantically secure public key cryptosystem based on singular cubic curve is proposed in this paper. It is about two times faster than the cryptosystem of David at the same security label and more efficient than the Koyama scheme at high security level. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those are not possible in the proposed scheme
An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics
We define an isomorphism between the group of points of a conic and the set
of integers modulo a prime equipped with a non-standard product. This product
can be efficiently evaluated through the use of R\'edei rational functions. We
then exploit the isomorphism to construct a novel RSA-like scheme. We compare
our scheme with classic RSA and with RSA-like schemes based on the cubic or
conic equation. The decryption operation of the proposed scheme turns to be two
times faster than RSA, and involves the lowest number of modular inversions
with respect to other RSA-like schemes based on curves. Our solution offers the
same security as RSA in a one-to-one communication and more security in
broadcast applications.Comment: 18 pages, 1 figur
09221 Abstracts Collection -- Algorithms and NumberTheory
From 24.05. to 29.05.2009, the Dagstuhl Seminar 09221 ``Algorithms and Number Theory \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Some cryptographic algorithms
Cryptography is the practice and study of techniques for secure communication in the presence of third parties, called adversaries. Modern cryptography is heavily based on mathematical theory and computer science practice. Cryptographic algorithms are designed so that in practice they are hard to break by any adversary. In the present thesis consisting of two chapters first we have given a brief review of some important number theoretic concepts and results. Then we have discussed S-DES and DES algorithms for Secret key cryptography, RSA and DSA algorithms for Public key cryptography and at last a brief introduction of elliptic curves and their use in Cryptography is given
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