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The asymptotically fastest algorithm to solve the
Discrete Logarithm Problem in finite fields is the
Number Field Sieve (NFS). This work presents a
summary of the Number Field Sieve and its practical
experimental implementation to solve the discrete
logarithm problem in finite fields of degree six.
This particular problem arises e.g. when one tries to
solve DLP in XTR cryptosystem. As shown, the degree
six instance of the DLP is practically more difficult
to solve with NFS as a classical DLP.
Also contained in this book are some specific remarks
to the related topic of the polynomial selection for
the NFS. A three dimensional adaptation of the line
sieving algorithm is described as well as the
parametrization choices for the sieve region,
contribution of small primes and exclusion of higher
degree ideals.
Although the results of this work are related to the
specific instance of NFS, they can influence also the
mainstream NFS applications (the factoring of
integers or the classical DLP).
Discrete Logarithm Problem in finite fields is the
Number Field Sieve (NFS). This work presents a
summary of the Number Field Sieve and its practical
experimental implementation to solve the discrete
logarithm problem in finite fields of degree six.
This particular problem arises e.g. when one tries to
solve DLP in XTR cryptosystem. As shown, the degree
six instance of the DLP is practically more difficult
to solve with NFS as a classical DLP.
Also contained in this book are some specific remarks
to the related topic of the polynomial selection for
the NFS. A three dimensional adaptation of the line
sieving algorithm is described as well as the
parametrization choices for the sieve region,
contribution of small primes and exclusion of higher
degree ideals.
Although the results of this work are related to the
specific instance of NFS, they can influence also the
mainstream NFS applications (the factoring of
integers or the classical DLP).