# math代写 – MATH/CSCI 4116

### MATH/CSCI 4116

math代写 – 这是值得参考的math代写的题目

``````Cryptography
``````
`````` assignment 7
``````
1. Which of the following polynomials are irreducible in (Z/ 2 Z)[x]?
``````x
``````

#### 5

``````+x
``````

#### 3

``````+x
``````

#### + 1,

``````x
``````

#### 5

``````+x
``````

#### + 1,

``````x
``````

#### 5

``````+x
``````

#### + 1.

1. (a) Show that, in (Z/ 2 Z)[x],
``````x
``````

#### 4

``````x+ 1 (modx
``````

#### 4

``````+x+ 1),
``````
``````x
``````

#### 8

``````x
``````

#### 2

``````+ 1 (modx
``````

#### 4

``````+x+ 1),
``````
``````x
``````

#### 16

``````x (mod x
``````

#### 4

``````+x+ 1).
``````

(b) Show thatx

#### 15

``````1 (modx
``````

#### 4

``````+x+ 1) in (Z/ 2 Z)[x].
``````
1. The finite field GF(

#### 5

``````) can be constructed as (Z/ 2 Z)[x]/(x
``````

#### 5

``````+x
``````

#### + 1).

``````Compute (x
``````

#### 4

``````+x
``````

#### 3

``````)(x
``````

#### 3

``````+x
``````

#### 2

``````+ 1) in this field.
``````
1. Multiply the following elements of GF(

#### 8

``````), represented as bytes:
``````

#### 00000111 10101011.

(Use the standard Rijndael irreducible polynomial. This question should

only be done after the class of Thursday, March 9).

1. (a) Show thatx

#### 2

``````+ 1 is irredubible in (Z/ 3 Z)[x].
``````

(b) Use this to construct the finite field GF(

#### 2

``````) with its addition and
``````

multiplication tables.

``````(Careful: Here we havep= 3, and notp= 2 as usual.)
``````
``````Due: Thursday, March 16, 2023
``````