Digital Signature Based on Conic Curve over Eisenstein Ring
LI Duan-duan · Jisuanji gongcheng · 2010
In order to make the cryptosystem over curves safe and efficient, this paper introduces Eisenstein ring Z [ω ]and introduces the conic curve C r( a ,b )over the residue class ring Z [ω ]/( r), where r is the product of two different impartibility numbers, which satisfies N (π 1 ) ≠ N(π2 ) over Z [ω ]. Conic analog of blind signature based on RSA over conic curve C r( a ,b )is presented and E-cash in the E-payment system is taken as an example to discuss the application of digital signature over C r( a ,b ). The security is based on the difficulty in factorizing large integer and computing discrete logarithm on Abel group C r( a ,b ). The digital signature based on the conic curve C r( a ,b )shows the merits on conic curve that it is easy to embed plaintext, and its computing speed is rapid and is easy to implement.