Public-key systems

Why RSA algorithm works?

N
# digits # operations
Factorize N computing time
with Cray
50 1.4x10¹⁰ 4 Hours
80 1.3x10¹³ 150 Days
100 2.3x10¹⁷ 74 Years
200 1.2x10²³ 3.8x10⁹ Years

N # digits	# operations Factorize N	computing time with Cray
50	1.4x10¹⁰	4 Hours
80	1.3x10¹³	150 Days
100	2.3x10¹⁷	74 Years
200	1.2x10²³	3.8x10⁹ Years

Digital Signature
(an application of public key systems)

Require:
1. D(E(M)) = E(D(M)) = M
2. i can't deny, j can't forge D_i(M)!!

Last modified: Mon Jun 22 11:17:37 CST 1998