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Old 2006-08-27, 15:32   #1

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Default Discrete logarithm mod Mersenne primes?

According to:

Show that there exists a natural number N such that whenever p is a Fermat prime or a Mersenne prime, discrete logarithm in F_p is computable in O((log^N)(p)) bit operations. Show that this implies that breaking the Diffie-Hellman Key Exchange Protocol is easy for Fermat primes and Mersenne primes.
Can someone please explain the fast discrete logarithm mod Mersenne primes or give pointers to papers on it?

Does the above quote mean that the smooth part of p+1 leaks information about the exponent in DL?

Thanks in advance.
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