## NCTUCS 2013-Fall Introduction to Cryptography ...

# NCTUCS 2013-Fall Introduction to Cryptography by Professor Rong-Jaye Chen.

# LFSR == Linear Feedback Shift Register

## FSR

Feedback shift register

**connection polynomial:**

```
C(x) = 1 + C_{1}x + C_{2}x^{2} + \cdots + C_{L}x^{L}
```

## LFSR

If the feedback function is linear, the FSR is called LFSR

i.e.

```
S_{L} = C_{1}S_{L-1} + C_{2}S_{L-2} + \cdots + C_{L}S_0{}
```

is linear.

```
\begin{align}
& \text{If } C(x) \text{ is primitive and the initial state } \\
& (S_{0}, S_{1}, \cdots , S_{L-1}) \text{ is not zero, } \text{the period is } 2^{L} - 1
\end{align}
```

A stream cipher constructed by a LFSR alone is not secure.

## Nonlinear combination generators

- Geff Generator (1973)

## Nonlinear filter generators

## Clcok-controlled generators

- Stop-and-Go Generators (1987)
- The Shrinking Generator (1993)
- A5 (the GSM standard)
- E0 (Bluetooth's standard encryption)

## GSM A5/1

### Share

### Donation

如果覺得這篇文章對你有幫助， 除了留言讓我知道外， 或許也可以考慮請我喝杯咖啡， 不論金額多寡我都會非常感激且能鼓勵我繼續寫出對你有幫助的文章。

If this blog post happens to be helpful to you, besides of leaving a reply, you may consider buy me a cup of coffee to support me. It would help me write more articles helpful to you in the future and I would really appreciate it.

### Related Posts

- ITC week10 - Key Management and Distribution
- ITC Hw2
- ITC week9 - Hash
- ITC - week7
- 資訊工程研討 - 台灣資安防護及技術發展現況