## Elliptic Curves and their use in Cryptography (1997)

Venue: | DIMACS Workshop on Unusual Applications of Number Theory |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Miller97ellipticcurves,

author = {Victor S. Miller},

title = {Elliptic Curves and their use in Cryptography},

booktitle = {DIMACS Workshop on Unusual Applications of Number Theory},

year = {1997}

}

### OpenURL

### Abstract

The security of many cryptographic protocols depends on the difficulty of solving the so-called "discrete logarithm" problem, in the multiplicative group of a finite field. Although, in the general case, there are no polynomial time algorithms for this problem, constant improvements are being made -- with the result that the use of these protocols require much larger key sizes, for a given level of security, than may be convenient. An abstraction of these protocols shows that they have analogues in any group. The challenge presents itself: find some other groups for which there are no good attacks on the discrete logarithm, and for which the group operations are sufficiently economical. In 1985, the author suggested that the groups arising from a particular mathematical object known as an "elliptic curve" might fill the bill. In this paper I review the general cryptographic protocols which are involved, briefly describe elliptic curves and review the possible attacks again...