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完善保密性

完善保密性(perfect secrecy)是資訊理論安全性的一个特例,为香农提出的信息学观点,具有该性质的密文不应该透露任何明文的信息。在該觀點中達成這項性質的方法,是使用與明文空間相等或更大的密鑰空間。

严密定义

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密钥空间内任取一个密钥,加密方式为随机明文为随机密文则概率关系有

该处为相同文段。

也可定义为:

任意,有
即通过观察密文无法得到关于明文的任何信息。

或是: 一組在上的密碼系統滿足

其中 是由 K 當中以完全均等的機率隨機取樣

(註:某事件 表示該事件發生的機率, 各為密鑰、明文及密文空間, 為解密與加密函數)

性质

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由於密鑰空間等於或大於明文空間,所以對同一個密文以窮舉法破解時,將會獲得所有可能的明文,使得無法分辨何者為真正的訊息。因此若沒有密鑰,即使敌手拥有无穷的计算时间和存储空间,密文仍然不可能破解。

具有完善保密性的密钥长度不可短于被加密的密文。此性质造成实际应用的不便。[1]

为了消除这种不便,一般使用两种方法:

  • 流加密:使用种子(Seed),即初始密钥,和密钥生成器(Generator)生成和明文一样长的密钥,对明文字符进行对应加密。
  • 分组加密:将明文分割为固定长度的段,每一段使用一个密钥加密(密钥长度不定)。

只是這樣的改變會縮小密鑰空間,因而失去完善保密性。

参考文献

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  1. ^ "Cryptography Theory and Practice" Stinson. (2ed)

参见

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完善保密性
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