

New Attacks on Prime Power N = Prq Using Good Approximation of Φ(N)





نویسنده

Shehu S. ,Ariffin M.R.K.

منبع

Malaysian Journal Of Mathematical Sciences  2017  دوره : 11  شماره : S  صفحه:121 138



چکیده

This paper proposes three new attacks. our first attack is based on the rsa key equation ed  kϕ(n) = 1 where ϕ(n) = pr1(p  1)(q  1). let q < p < 2q. if δ < 1γ/2 we shows that k/d can be recov ered among the convergents of the continued fractions expansions of we furthered our analysis on j prime power moduli ni = pi rqi satisfying a variant of the above mentioned condition. we utilized the lll algorithm on j prime power public keys (ni,ei) with ni = pi rqi and we were able to factorize the j prime power moduli ni = pi rqi simultaneously in polynomial time.

کلیدواژه

Continued Fractions; Factorization; Lll Algorithm; Prime Power; Simultaneous Diophantine Approximations

آدرس

AlKindi Cryptography Research Laboratory,Institute For Mathematical Research,Universiti Putra Malaysia (Upm),Selangor, Malaysia, Department Of Mathematics,Faculty Of Science,Universiti Putra Malaysia (Upm),Selangor, Malaysia














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