Groups from cyclic infrastructures and Pohlig-Hellman in certain infrastructures
Institut für Mathematik, Universität Zürich, CH-8057, Switzerland
We recall the Pohlig-Hellman method, define the concept of a cyclic infrastructure and briefly describe how to obtain such infrastructures from certain function fields of unit rank one. Then, we describe how to obtain cyclic groups from discrete cyclic infrastructures and how to apply the Pohlig-Hellman method to compute absolute distances, which is in general a computationally hard problem for cyclic infrastructures. Moreover, we give an algorithm which allows to test whether an infrastructure satisfies certain requirements needed for applying the Pohlig-Hellman method, and discuss whether the Pohlig-Hellman method is applicable in infrastructures obtained from number fields. Finally, we discuss how this influences cryptography based on cyclic infrastructures.
Laurent Imbert, Michael J. Jacobson, Jr., Arthur Schmidt. Fast ideal cubing in imaginary quadratic number and function fields. Advances in Mathematics of Communications, 2010, 4 (2) : 237-260. doi: 10.3934/amc.2010.4.237
Diego F. Aranha, Ricardo Dahab, Julio López, Leonardo B. Oliveira. Efficient implementation of elliptic curve cryptography in wireless sensors. Advances in Mathematics of Communications, 2010, 4 (2) : 169-187. doi: 10.3934/amc.2010.4.169
Lidong Chen, Dustin Moody. New mission and opportunity for mathematics researchers: Cryptography in the quantum era. Advances in Mathematics of Communications, 2020, 14 (1) : 161-169. doi: 10.3934/amc.2020013
Ken Ono. Parity of the partition function. Electronic Research Announcements, 1995, 1: 35-42.
2019 Impact Factor: 0.734
[Back to Top]