TY - JOUR
T1 - Construction of RSA Cryptosystem over the Algebraic Field Using Ideal Theory and Investigation of Its Security
AU - Takagi, Tsuyoshi
AU - Naito, Shozo
PY - 2000/1/1
Y1 - 2000/1/1
N2 - The RSA cryptosystem is extended to the algebraic field by using ideal theory. In this paper, we describe the generation algorithm of prime ideals, how to select a representative class using an ideal as modulus, and the algorithm to compute a representative element, for cyclotomic fields and quadratic fields. From here, an RSA cryptosystem can be constructed on cyclotomic fields and quadratic fields. To break completely the proposed cryptosystem, when the public key is a product of inert prime numbers, is the same as for the conventional RSA cryptosystem and its security is better against the Håstad attacks.
AB - The RSA cryptosystem is extended to the algebraic field by using ideal theory. In this paper, we describe the generation algorithm of prime ideals, how to select a representative class using an ideal as modulus, and the algorithm to compute a representative element, for cyclotomic fields and quadratic fields. From here, an RSA cryptosystem can be constructed on cyclotomic fields and quadratic fields. To break completely the proposed cryptosystem, when the public key is a product of inert prime numbers, is the same as for the conventional RSA cryptosystem and its security is better against the Håstad attacks.
UR - http://www.scopus.com/inward/record.url?scp=0042730598&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0042730598&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1520-6440(200008)83:8<19::AID-ECJC3>3.0.CO;2-0
DO - 10.1002/(SICI)1520-6440(200008)83:8<19::AID-ECJC3>3.0.CO;2-0
M3 - Article
AN - SCOPUS:0042730598
SN - 1042-0967
VL - 83
SP - 19
EP - 29
JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
IS - 8
ER -