Hatem M. Bahig

Learn More
An addition chain for a natural number n is a sequence 1=a 0<a 1< . . . <a r =n of numbers such that for each 0<i≤r, a i =a j +a k for some 0≤k≤j<i. An improvement by a factor of 2 in the generation of all minimal (or one) addition chains is achieved by finding sufficient conditions for star steps, computing what we will call nonstar lower bound in a(More)
Let (n = pq, e) be an RSA public key with private exponent d = n<sup>delta</sup>, where p and q are large primes of the same bit size. Suppose that p<sub>o</sub> ges radicn be an approximation of p with |p - po| les 1/8n<sup>alpha</sup>, alpha les 1/2. Using continued fractions, we show that the system is insecure if delta &lt; 1-alpha/2. Our result is(More)
An addition chain for a natural number n is a sequence $${1=a_0 < a_1 < \cdots < a_r=n}$$ of numbers such that for each 0 < i ≤ r, a i  = a j  + a k for some 0 ≤ k ≤ j < i. The minimal length of an addition chain for n is denoted by ℓ(n). If j = i − 1, then step i is called a star step. We show that there is a minimal length addition chain for n such that(More)