New approaches to formalizing security Seminar report for Research Seminar in Cryptography

Recently the frameworks of abstract and constructive cryptography have been proposed by Maurer et al [MR11, Mau11, Mau10, Mau09]. These aim to redefine the common view of cryptographic security proofs and definitions. However, in a sense these ideas can be seen both as a protest and a generalisation of the current state of the art. First, a protest because current definitions and proofs are built from the very low details of the computation model, such as the Turing machine, but often rely on the general understanding of these models rather than actual details. These make the corresponding results less formal than we could desire. Secondly, a generalisation because an important observation behind the abstract cryptography is that different specification of low level details may still lead to more or less equivalent high level results. Hence, maybe it is actually reasonable to enable well formalised cryptographic arguments on a higher abstraction level to achieve general results that apply for all lower level specifications. This work is mostly based on the theory of abstract cryptography [MR11] and also uses the constructive cryptography [Mau10, Mau11] which is an application of abstract cryptography. This overview is intended to introduce these theories and offer some additional comments and insights. In addition, additional examples are given for the numerous definitions, that hopefully make understanding these ideas simpler. Firstly, Section 2 recalls some of the main challenges of cryptographic protocol design and uses them as motivation for the abstract and constructive cryptography frameworks. Secondly, Section 3 gives an overview of the abstract cryptography definitions with several examples of the introduced concepts. Section 4 continues the discussion about abstract cryptography by introducing some examples of using this theory as well as highlighting some open questions. Following Section 5 gives a subcase of abstract cryptography called the constructive cryptography. Finally, Section 6 concludes this report.