The ray attack, an inefficient trial to break RSA cryptosystems

Details The ray attack, an inefficient trial to break RSA cryptosystems The ray attack, an inefficient trial to break RSA cryptosystems

2003-07-11

arxiv.org/abs/cs/0307029v1

Computer Science

Cryptography and Security

18 pages, 4 figures

Scientific paper

The basic properties of RSA cryptosystems and some classical attacks on them are described. Derived from geometric properties of the Euler functions, the Euler function rays, a new ansatz to attack RSA cryptosystems is presented. A resulting, albeit inefficient, algorithm is given. It essentially consists of a loop with starting value determined by the Euler function ray and with step width given by a function $\omega_e(n)$ being a multiple of the order $\mathrm{ord}_n(e)$, where $e$ denotes the public key exponent and $n$ the RSA modulus. For $n=pq$ and an estimate $r<\sqrt{pq}$ for the smaller prime factor $p$, the running time is given by $T(e,n,r) = O((r-p)\ln e \ln n \ln r).$

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