A new RSA vulnerability using continued fractions

Let (n = pq, e) be an RSA public key with private exponent d = n
^delta
, where p and q are large primes of the same bit size. Suppose that p
_o
ges radicn be an approximation of p with |p - po| les 1/8n
^alpha
, alpha les 1/2. Using continued fractions, we show that the system is insecure if delta < 1-alpha/2. Our result is deterministic polynomial time and an extension of Coppersmith's result on a factorization.