Virtual logarithms |
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| Authors: | Oliver Schirokauer |
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| Institution: | Department of Mathematics, Oberlin College, Oberlin, OH 44074, USA |
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| Abstract: | The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal. |
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| Keywords: | Finite field Discrete logarithm Number field sieve |
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