On the public key cryptosystems over class semigroups of imaginary quadratic non-maximal orders
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In this paper we will propose the methods for finding thenon-invertible ideals corresponding to non-primitive quadraticforms and clarify the structures of class semigroups of imaginaryquadratic orders which were given by Zanardo and Zannier [8], andwe will give a general algorithm for calculating power ofideals/classes via the Dirichlet composition of quadratic formswhich is applicable to cryptography in the class semigroup ofimaginary quadratic non-maximal order and revisit the cryptosystemof Kim and Moon [5] using a Zanardo and Zannier [8]'s quantity astheir secret key,in order to analyze Jacobson [7]'s revised cryptosystem based on the class semigroupwhich is an alternative of Kim and Moon [5]'s.
Abstract
In this paper we will propose the methods for finding thenon-invertible ideals corresponding to non-primitive quadraticforms and clarify the structures of class semigroups of imaginaryquadratic orders which were given by Zanardo and Zannier [8], andwe will give a general algorithm for calculating power ofideals/classes via the Dirichlet composition of quadratic formswhich is applicable to cryptography in the class semigroup ofimaginary quadratic non-maximal order and revisit the cryptosystemof Kim and Moon [5] using a Zanardo and Zannier [8]'s quantity astheir secret key,in order to analyze Jacobson [7]'s revised cryptosystem based on the class semigroupwhich is an alternative of Kim and Moon [5]'s.
참고문헌 (8)
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- "Primes of the form x^2 + n y^2" (1989)
- "New directions in cryptography", pp.472~22 (1976)
- "Disquisitiones Arithmeticae" (1986)
- "Public-Key Cryptosystems based on ClassSemigroups of Imaginary Quadratic Non-maximal Orders" (2003)
- "On the structures of class semigroups of quadraticnon-maximal orders" (2004)
- "The security of cryptosystems based on classsemigroups of imaginary quadratic non-maximal ordersASISP 2004" (2004)
- "The class semigroup of orders in number fields" (1994)