Journal of Algebra, Number Theory: Advances and ApplicationsAuthor's: Muhammad Rezal Kamel Ariffin, Sadiq Shehu and M. A. Asbullah
Pages: [35] - [59]
Received Date: June 30, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100121854
This paper proposes three new attacks on RSA-Takagi cryptosystem. The
first attack is based on the equation 
for suitable positive integers 
We show that 
can be recovered among the convergents of the
continued fractions expansion of 
and leads to successful factorization of the
prime power modulus 
in polynomial time. The second and third attack
works upon j public keys 
when there exist j relations of the
shape 
or of the shape 
where the parameters 
are suitably small in terms of the prime
factors of the moduli. Applying the LLL algorithm, we show that our
strategy enable us to simultaneously factor the j public key
in polynomial time.
prime power modulo, factorization, LLL algorithm, simultaneous Diophantine approximations, continued fractions.
