Abstract
Two variations of the McEliece cryptosystem are presented. The first is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed.
| Original language | English |
|---|---|
| Title of host publication | Association for Women in Mathematics Series |
| Pages | 129-150 |
| Number of pages | 22 |
| DOIs | |
| State | Published - 2017 |
Publication series
| Name | Association for Women in Mathematics Series |
|---|---|
| Volume | 9 |
| ISSN (Print) | 2364-5733 |
| ISSN (Electronic) | 2364-5741 |
Bibliographical note
Publisher Copyright:© 2017, The Author(s) and the Association for Women in Mathematics.
Funding
We would like to thank the organizers of the IPAM workshop on Algebraic Geometry for Coding Theory and Cryptography for inviting us to the event. Thanks also go to Mike O?Sullivan for helpful conversations and to the anonymous referee for kind suggestions. JB was supported by the US Department of Education GAANN Grant P200A120068. HGL was partially supported by the National Science Foundation Grant DMS-1210061 and by the grant #422479 from the Simons Foundation. BM was partially supported by the National Security Agency under grant H98230-16-1-0300. JR was partially supported by the Swiss National Science Foundation under grant #169510. Acknowledgements We would like to thank the organizers of the IPAM workshop on Algebraic Geometry for Coding Theory and Cryptography for inviting us to the event. Thanks also go to Mike O\u2019Sullivan for helpful conversations and to the anonymous referee for kind suggestions. JB was supported by the US Department of Education GAANN Grant P200A120068. HGL was partially supported by the National Science Foundation Grant DMS-1210061 and by the grant #422479 from the Simons Foundation. BM was partially supported by the National Security Agency under grant H98230-16-1-0300. JR was partially supported by the Swiss National Science Foundation under grant #169510.
| Funders | Funder number |
|---|---|
| Simons Foundation | |
| Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | 169510 |
| Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | |
| U.S. Department of Education, OSERS | P200A120068 |
| U.S. Department of Education, OSERS | |
| National Security Agency | H98230-16-1-0300 |
| National Security Agency | |
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | DMS-1210061, 422479 |
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China |
ASJC Scopus subject areas
- Gender Studies
- General Mathematics