Measuring Diffusion in Stream Ciphers using Statistical Testing Methods

摘要

Confusion and diffusion suggested by Claude Shannon are two techniques that symmetric key ciphers should satisfy to prevent cryptanalysis. Diffusion dissipates the statistical properties of the plaintext over the whole ciphertext. For a block cipher, each bit of the output ciphertext block changes with probability one half for any flipped bit in the input plaintext block, implying the cipher to have good diffusion properties. This definition with slight modification can also be applied to stream ciphers but here it is enough to make sure the following: (ⅰ) to ensure an overall change in the output keystream with probability half for any flipped bit in the key-IV bit sequence, and (ⅱ) to verify that every bit in the output keystream changes with probability one half for any single bit flip in the key-IV bit sequence. Here we insist on using these tests together for measuring diffusion in stream ciphers. Based on this we have examined the level of diffusion exhibited by some of the eSTREAM candidates and the result is given in this paper.