Exploring fields with shift registers
| dc.contributor.advisor | Dinolt, George | |
| dc.contributor.advisor | Fredricksen, Harold | |
| dc.contributor.author | Radowicz, Jody L. | |
| dc.contributor.corporate | Naval Postgraduate School (U.S.) | |
| dc.contributor.department | Computer Science (CS) | |
| dc.date.accessioned | 2012-03-14T17:35:41Z | |
| dc.date.available | 2012-03-14T17:35:41Z | |
| dc.date.issued | 2006-09 | |
| dc.description.abstract | The S-Boxes used in the AES algorithm are generated by field extensions of the Galois field over two elements, called GF(2). Therefore, understanding the field extensions provides a method of analysis, potentially efficient implementation, and efficient attacks. Different polynomials can be used to generate the fields, and we explore the set of polynomials x^ 2 + x + a^J over GF(2^n) where a is a primitive element of GF(2^n). The results of this work are the first steps towards a full understanding of the field that AES computation occurs in-GF(2^8). The charts created with the data we gathered detail which power of the current primitive root is equal to previous primitive roots for fields up through GF(2^16) created by polynomials of the form x^2 + x + a^i for a primitive element a. Currently, a C++ program will also provide all the primitive polynomials of the form x^2 + x+ a^i for a primitive element a over the fields through GF(2^32). This work also led to a deeper understanding of certain elements of a field and their equivalent shift register state. In addition, given an irreducible polynomial 2 f(x) = x^2 + a^i x + a^j over GF(2^n), the period (and therefore the primitivity) can be determined by a new theorem without running the shift register generated by f(x). | en_US |
| dc.description.distributionstatement | Approved for public release; distribution is unlimited. | |
| dc.description.uri | http://archive.org/details/exploringfieldsw109452603 | |
| dc.format.extent | xiv, 83 p. : ill. ; | en_US |
| dc.identifier.oclc | 73174933 | |
| dc.identifier.uri | https://hdl.handle.net/10945/2603 | |
| dc.publisher | Monterey, CA; Naval Postgraduate School | en_US |
| dc.subject.lcsh | Computer science | en_US |
| dc.subject.lcsh | Polynomials | en_US |
| dc.subject.lcsh | Exponential functions | en_US |
| dc.subject.lcsh | Algorithms | en_US |
| dc.title | Exploring fields with shift registers | en_US |
| dc.type | Thesis | en_US |
| dspace.entity.type | Publication | |
| etd.thesisdegree.discipline | Computer Science | en_US |
| etd.thesisdegree.grantor | Naval Postgraduate School | en_US |
| etd.thesisdegree.level | Masters | en_US |
| etd.thesisdegree.name | M.S. | en_US |
| etd.verified | no | en_US |
| relation.isDepartmentOfPublication | 67864e54-711d-4c0a-a6d4-439a011f2bd1 | |
| relation.isDepartmentOfPublication.latestForDiscovery | 67864e54-711d-4c0a-a6d4-439a011f2bd1 |
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