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- Abderrahmane Nitaj
- AFRICACRYPT
- 2012

In RSA, the public modulus N = pq is the product of two primes of the same bit-size, the public exponent e and the private exponent d satisfy ed â‰¡ 1 (mod (pâˆ’1)(qâˆ’1)). In many applications of RSA, dâ€¦ (More)

Introduction to Cryptography with Open-Source Software is a well written text book covering many aspects: an introduction to cryptography, a clever use of the open source algebra system Sage andâ€¦ (More)

- Abderrahmane Nitaj
- AFRICACRYPT
- 2008

A well-known attack on RSA with low secret-exponent d was given by Wiener in 1990. Wiener showed that using the equation ed âˆ’ (p âˆ’ 1)(q âˆ’ 1)k = 1 and continued fractions, one can efficiently recoverâ€¦ (More)

- Abderrahmane Nitaj, Muhammad Rezal Kamel Ariffin
- IACR Cryptology ePrint Archive
- 2014

Let N1 = p1q1 and N2 = p2q2 be two RSA moduli, not necessarily of the same bit-size. In 2009, May and Ritzenhofen proposed a method to factor N1 and N2 given the implicit information that p1 and p2â€¦ (More)

- Haoyu Li, Renzhang Liu, Abderrahmane Nitaj, Yanbin Pan
- ACISP
- 2018

In PKCâ€™08, Plantard, Susilo and Win proposed a latticebased signature scheme, whose security is based on the hardness of the closest vector problem with the infinity norm (CVPâˆž). This signatureâ€¦ (More)

- Abderrahmane Nitaj
- AFRICACRYPT
- 2009

Let N = pq be an RSA modulus, i.e. the product of two large unknown primes of equal bit-size. In the X9.31-1997 standard for public key cryptography, Section 4.1.2, there are a number ofâ€¦ (More)

- Abderrahmane Nitaj
- I. J. Network Security
- 2011

NTRU is a fast public key cryptosystem presented in 1996 by Hoffstein, Pipher and Silverman. It operates in the ring of truncated polynomials. In NTRU, a public key is a polynomial defined by theâ€¦ (More)

A conjecture of P. Erdos says that the diophantine equation x+y = z has infinitely many solutions with (x,y) â€” 1 and such that if a prime p divides xyz, then p divides xyz. In this paper, we give aâ€¦ (More)

In this paper, we analyze the security of the KMOV public key cryptosystem. KMOV is based on elliptic curves over the ring Zn where n = pq is the product of two large unknown primes of equal bitsize.â€¦ (More)

- Abderrahmane Nitaj
- IACR Cryptology ePrint Archive
- 2006

Let n = pq be an RSA modulus with unknown prime factors of equal bit-size. Let e be the public exponent and d be the secret exponent satisfying ed â‰¡ 1 (mod Ï†(n)) where Ï†(n) is the Euler totientâ€¦ (More)