Cryptography: Block Cipher

 

In general, in a block cipher, we replace N bits from the plaintext with N bits of ciphertext. What defines an ideal block cipher?


An ideal block cipher is a type of block cipher in which it allows for the maximum for the maximum number of possible encryption mapping from plain text block. Ideal block cipher is defined by its encryption key which is its codebook itself, meaning that the table shows relation between the input and the output blocks and the relation between output and input block is random.



What makes ideal block cipher impractical?

The key size. The key size of the encryption key of ideal block cipher is given by n2^n. if n=64 key size is 10^21 bits. This is impractical for real time implementation.

Cryptography: Ideal Block Cipher

•In an ideal block cipher, the relationship between the input blocks and the output block is completely random. But it must be invertible for decryption to work.

–Therefore, it has to be one-to- one, meaning that each input block is mapped to a unique output block.

•The mapping from the input bit blocks to the output bit blocks can also be construed as a mapping from the integers corresponding to the input bit blocks to the integers corresponding to the output bit blocks.

•The encryption key for the ideal block cipher is the codebook itself, meaning the table that shows the relationship between the input blocks and the output blocks. 

Problems with Ideal Block Cipher

•There is a practical problem with the ideal block cipher.

•If a small block size, such as n = 4, is used, then the system is equivalent to a classical substitution cipher.

–Such systems are vulnerable to a statistical analysis of the plaintext.

–This weakness is not inherent in the use of a substitution cipher but rather results from the use of a small block size.

•If n is sufficiently large and an arbitrary reversible substitution between plaintext and ciphertext is allowed, then the statistical characteristics of the source plaintext are masked to such an extent that this type of cryptanalysis is infeasible.

•However, an arbitrary reversible substitution cipher (the ideal block cipher) for a large block size is not practical from an implementation and performance point of view.

–Why?

•n=4, required key length: (4 bits)*(16 rows) = 64 bits.

–In general, for an n-bit ideal block cipher, the length of the key defined in this fashion is n * 2n bits.

•For a 64-bit block, which is a desirable length to thwart statistical attacks, the required key length is 64 * 264 = 270 = 1021 bits.

•The size of the encryption key would make the ideal block cipher an impractical idea.

–Think of the logistical issues related to the transmission, storage, and processing of such large keys.

•Considering these difficulties, what we need to do is make an approximation for large value of n so that it is easily realizable.