Abstract

Abstract. This paper considers the construction and analysis of pseudo-random functions (PRFs) with specific reference to modes of operations of a block cipher. In the context of message authentication codes (MACs), earlier independent work by Bernstein and Vaudenay show how to reduce the analysis of relevant PRFs to some probability calculations. In the first part of the paper, we revisit this result and use it to prove a general result on constructions which use a PRF with a “small ” domain to build a PRF with a “large ” domain. This result is used to analyse two new parallelizable PRFs which are suitable for use as MAC schemes. The first scheme, called iPMAC, is based on a block cipher and improves upon the well-known PMAC algorithm. The improvements consist in faster masking operations and the removal of a design stage discrete logarithm computation. The second scheme, called VPMAC, uses a keyed compression function rather than a block cipher. The only previously known compression function based parallelizable PRF is called the protected counter sum (PCS) and is due to Bernstein. VPMAC improves upon PCS by requiring lesser number of calls to the compression function. The second part of the paper takes a new look at the construction and analysis of modes of operations for authenticated encryption (AE) and for authenticated encryption with associated data (AEAD). Usually, the most complicated part in the security analysis of such modes is the analysis of authentication

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