JP Journal of Algebra, Number Theory and Applications
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Abstract: Let
be an RSA modulus, i.e., the product
of two large unknown primes of equal bit-size. We consider the class of the
public exponents satisfying an equation with (here denotes the nearest integer to x)
and
and all prime factors
of are less than Using the continued fraction
algorithm and the Elliptic Curve Method of factorization, we show that such
exponents yield the factorization of the RSA modulus. Further, we show that the
number of such weak keys is at least Thus, our attack applies to a
relatively large class of weak keys in RSA.
Keywords and phrases: RSA, cryptanalysis, factorization, continued fraction.
