| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2012: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
|---|
| Outline of Final Research Achievements |
In the cryptography theory,it is important to construct functions over finite fields which have hight non-linearities. Almost perfect nonlinear(APN) functions are one of them. APN functions are classified in EA-equivalent classes. In the study,I consider some permutation group (G,S) where G is the linear group of degree n over GF(2) and S is a set of subspaces of the alternative product of a finite field F with some properties. I proved the number of G-orbits on S equals to the namber of EA equivalent classes of quadratic APN functions on F.I obtained some conditions that a special linear equation over a finite field has exactly two solutions and as a application of the results, I constructed three APN functions and decided subspaces corresponding to these functions up to EA-equivalence. Moreover I obtained an effective expression of APN functions which are equivalent to Gold functions which are most interesting ones among APN functions.
|
