**ETH Series in Information Security and
Cryptography
edited by Ueli Maurer
Volume 6**

**Krzysztof Pietrzak**

**Indistinguishability and Composition
of Random Systems**

1^{st}
edition/ 1. Auflage 2006, 172 pages/Seiten, € 64,00. ISBN 3-86628-063-7

Many
security proofs for cryptographic systems are achieved by showing that the
system at hand is indistinguishable from some ideal and thus trivially secure
system. For example an ideal block-cipher is a uniform random permutation and
an ideal authentication scheme is a uniform random function.

In this thesis we develop and apply techniques to prove the
indistinguishability of constructions, assuming some indistinguishability of
the underlying components. Maurer's framework from Eurocrypt'02 is the starting
point for this thesis.

For example we show that the sequential composition g(f(.)) of two
non-adaptively secure (meaning indistinguishable from a random function)
functions f(.) and g(.), is always adaptively secure in the information
theoretic setting, but in general not in the computational setting (i.e. for
pseudorandom systems).

**Keywords:
Cryptograhpy, Pseudorandomness, Quasirandomness, Indistinguishability, Random-systems,
Luby-Rackoff cipher, Minicrypt, Key-agreement.**

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ETH Series in Information Security and Cryptography