## 2, where |ρq − p | ≤

by
Subhamoy Maitra
,
Santanu Sarkar

### BibTeX

@MISC{Maitra_2,where,

author = {Subhamoy Maitra and Santanu Sarkar},

title = {2, where |ρq − p | ≤},

year = {}

}

### OpenURL

### Abstract

Abstract. In this paper we revisit Wiener’s method (IEEE-IT 1990) of continued fraction (CF) to find new weaknesses in RSA. We consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. Our motivation is to find out when RSA is insecure given d is O(N δ), where we are mostly interested in the range 0.3 ≤ δ ≤ 0.5. Given ρ (1 ≤ ρ ≤ 2) is known to the attacker, we show that the RSA keys are weak when d = N δ and δ < 1 2