Revisiting Randomness Extraction and Key Derivation Using the CBC and Cascade Modes

Abstract

In this paper, we revisit a celebrated result by Dodis et al. from CRYPTO 2004, in relation with the suitability of CBC-MAC and cascade construction for randomness extraction. We first observe that the proof of three key sub-results are missing in the paper, which makes it difficult to verify the authors’ claims. Then, using a detailed and thorough analysis of the collision probability for both the CBC function and the cascade construction, we provide the missing proofs, thereby establishing the veracity of this old result. As a side-effect, we have made a significant advancement in the characterization of graph-based analysis of CBC and cascade construction, which could be of independent interest.

Keywords

• CBC-MAC
• cascade construction
• tight bound
• missing proofs