19 research outputs found
A note on some algebraic trapdoors for block ciphers
We provide sufficient conditions to guarantee that a translation based cipher
is not vulnerable with respect to the partition-based trapdoor. This trapdoor
has been introduced, recently, by Bannier et al. (2016) and it generalizes that
introduced by Paterson in 1999. Moreover, we discuss the fact that studying the
group generated by the round functions of a block cipher may not be sufficient
to guarantee security against these trapdoors for the cipher.Comment: to be published on Advances in Mathematics of Communication
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
On the primitivity of Lai-Massey schemes
In symmetric cryptography, the round functions used as building blocks for
iterated block ciphers are often obtained as the composition of different
layers providing confusion and diffusion. The study of the conditions on such
layers which make the group generated by the round functions of a block cipher
a primitive group has been addressed in the past years, both in the case of
Substitution Permutation Networks and Feistel Networks, giving to block cipher
designers the receipt to avoid the imprimitivity attack. In this paper a
similar study is proposed on the subject of the Lai-Massey scheme, a framework
which combines both Substitution Permutation Network and Feistel Network
features. Its resistance to the imprimitivity attack is obtained as a
consequence of a more general result in which the problem of proving the
primitivity of the Lai-Massey scheme is reduced to the simpler one of proving
the primitivity of the group generated by the round functions of a strictly
related Substitution Permutation Network
A note on some algebraic trapdoors for block ciphers
We provide sufficient conditions to guarantee that a translation based cipher is not vulnerable with respect to the partition-based trapdoor. This trapdoor has been introduced, recently, by Bannier et al. (2016) and it generalizes that introduced by Paterson in 1999. Moreover, we discuss the fact that studying the group generated by the round functions of a block cipher may not be sufficient to guarantee security against these trapdoors for the cipher.acceptedVersio
Wave-Shaped Round Functions and Primitive Groups
Round functions used as building blocks for iterated block ciphers, both in
the case of Substitution-Permutation Networks and Feistel Networks, are often
obtained as the composition of different layers which provide confusion and
diffusion, and key additions. The bijectivity of any encryption function,
crucial in order to make the decryption possible, is guaranteed by the use of
invertible layers or by the Feistel structure. In this work a new family of
ciphers, called wave ciphers, is introduced. In wave ciphers, round functions
feature wave functions, which are vectorial Boolean functions obtained as the
composition of non-invertible layers, where the confusion layer enlarges the
message which returns to its original size after the diffusion layer is
applied. This is motivated by the fact that relaxing the requirement that all
the layers are invertible allows to consider more functions which are optimal
with regard to non-linearity. In particular it allows to consider injective APN
S-boxes. In order to guarantee efficient decryption we propose to use wave
functions in Feistel Networks. With regard to security, the immunity from some
group-theoretical attacks is investigated. In particular, it is shown how to
avoid that the group generated by the round functions acts imprimitively, which
represent a serious flaw for the cipher