A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Computing Riemann---Roch spaces in algebraic function fields and related topics
Journal of Symbolic Computation
Computing the multiplicative group of residue class rings
Mathematics of Computation
On the List and Bounded Distance Decodability of Reed-Solomon Codes
SIAM Journal on Computing
Complexity of Decoding Positive-Rate Reed-Solomon Codes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
Optimal authenticated data structures with multilinear forms
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Arithmetic of generalized jacobians
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Hard Problems of Algebraic Geometry Codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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The use of generalised Jacobians in discrete logarithm based cryptosystems has so far been rather limited since they offer no advantage over traditional discrete logarithm based systems. In this paper we continue the search for possible applications in two directions. Firstly, we investigate pairings on generalised Jacobians and show that these are insecure. Secondly, generalising and extending prior work, we show how the discrete logarithm problem in generalised Jacobians can be reduced to the minimal non zero weight word and maximum likelihood decoding problems in generalised algebraic geometric codes.