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- Hatem M. Bahig
- Discrete Mathematics
- 2008

- Dalia B. Nasr, Hatem M. Bahig, Sameh S. Daoud
- AMT
- 2011

- Hatem M. Bahig
- Computing
- 2006

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)

- Hatem M. Bahig, Ken Nakamula
- J. Algorithms
- 2002

- Dieaa I. Nassr, Hatem M. Bahig, Ashraf Bhery, Sameh S. Daoud
- 2008 IEEE/ACS International Conference on…
- 2008

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 < 1-alpha/2. Our result is… (More)

- Hatem M. Bahig, Hazem M. Bahig
- Computing
- 2010

An addition sequence problem is given a set of numbers X = {n 1, n 2, . . . , n m }, what is the minimal number of additions needed to compute all m numbers starting from 1? This problem is NP-complete. In this paper, we present a branch and bound algorithm to generate an addition sequence with a minimal number of elements for a set X by using a new… (More)

- Hatem M. Bahig, Ashraf Bhery, Dieaa I. Nassr
- ICICS
- 2012

- Hatem M. Bahig
- Computing
- 2010

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)

- Khaled A. Fathy, Hazem M. Bahig, Hatem M. Bahig, A. A. Ragb
- ICA3PP
- 2011