Review
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/809594e5ad477f6eab818bf68b4f30066c353feffc94863b16680c49b386e634.png)
OPT是一次性密碼本,僅密文無法得到任何資訊
Stream Ciphers
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/974a031c3e3590886ae379f760aec6c4e1eb63b5e7a1b6790a224f77dbf10078.png)
PRG:是一個方法,G:透過s位種子輸出一個n位的偽隨機序列,n>>s
用偽隨機代替隨機,使得OPT的使用更實際
為了使演算法更高效,G的輸出使用決定性演算法
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/7a369399e1349d0ac63399e0df310f03615c34cb1d3b5700851913f429c766e8.png)
k透過G生成G(k),然後使用OPT
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/4e3c4633fb590a17ad17adb02f6707eba4bf9249af6fcb08768849caf379a41a.png)
沒有完美保密性,因為k比m短
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/d2dbc39422e98e6587c7205951af033497863bfc5b1883035d2073f4c6940d4a.png)
安全依賴特殊的PRG
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/c108c7cdf032bd7380481949a764413e7c804a6a114ce4993bc3db240f4fc7a3.png)
PRG最好不可預測,不然猜測的m的字首與c異或得到輸出序列字首,將提出整個輸出序列
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/c9c0ba197880c222c3996b41da8b4d2a9037a6e0413cda3f993affdec4813a06.png)
PRG是不可預測=>不存在有效演算法,在知道i位時,能有一個不可忽略的機率得出i+1位
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/828767c68baafdd94681f426f0757d86ecb16e3a0ff30a54b3c5e8ebc86aee61.png)
G(k)全部異或得1,也不符合不可預測
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/0330bd9c4fec39e7a95f0383bc222a38219e5537cb45064e934eb97b17ccd8a9.png)
線性生成器不可靠,隨機數生成器也不可靠
Negligible and non-negligible 可忽略和不可忽略
negligible 微不足道的 scalar 標量
![Cipher006__史丹佛密碼學__Stream ciphers](https://i.iter01.com/images/3ce8b497f377abb91d7746ea1112385c30184d3540a243baf0aef516f215f133.png)
指數級可忽略,多項式級不可忽略