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Cryptanalysis of RSA improved with the private key d

Title
Cryptanalysis of RSA improved with the private key d
Authors
홍현수
Issue Date
2001
Department/Major
대학원 수학과
Keywords
CryptanalysisRSAMathematicskey d
Publisher
The Graduate school of Ewha women university
Degree
Master
Abstract
Asiacrypt '99에서 Sun, Yang, Laih는 Boneh와 Durfee의 공격을 피할 수 있도록 balanced가 아닌 unbalanced한 소수 p와 q를 이용한 방법 3가지를 제시하였다. 그러나, Asiacrypt ‘00에서 Durfee와 Nguyen은 lattice에 기반을 둔 Coppersmith방법을 이용해서 이를 공격하였다. 그런데 Sun, Yang, Laih가 제시한 방법 1,3의 비밀키의 크기는 증가하였으나 방법 2의 비밀키는 충분히 증가하지 못하였다. 이 논문에서는 방법 2의 비밀키의 크기를 N^(0.483)에서 N^(0.486)까지 증가시켰다.;At Asiacrypt '99 Sun, Yang and Laih proposed three different schemes of RSA cryptosystem to avoid Boneh and Durfee's attack.' They used unbalanced primes p and q instead of balanced primes. At Asiacrypt '00, Durfee-Nguyen attacked these systems based on Coppersmith's lattice technique for finding small roots to trivariate modular polynomial equations. The bounds of private key for the first and third schemes were much improved, but the bound of the second scheme was not good enough. Our result improves Durfee-Nguyen's bound of private key d from N^(0.483) and N^(0.486) to in the second scheme i.e. e□ N^(0.55) and p□N^(0.4)
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