56 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
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
On differential uniformity of maps that may hide an algebraic trapdoor
We investigate some differential properties for permutations in the affine
group, of a vector space V over the binary field, with respect to a new group
operation , inducing an alternative vector space structure on .Comment: arXiv admin note: text overlap with arXiv:1411.768
Algebraic properties of generalized Rijndael-like ciphers
We provide conditions under which the set of Rijndael functions considered as
permutations of the state space and based on operations of the finite field
\GF (p^k) ( a prime number) is not closed under functional
composition. These conditions justify using a sequential multiple encryption to
strengthen the AES (Rijndael block cipher with specific block sizes) in case
AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R.
Wernsdorf provided conditions under which the group generated by the
Rijndael-like round functions based on operations of the finite field \GF
(2^k) is equal to the alternating group on the state space. In this paper we
provide conditions under which the group generated by the Rijndael-like round
functions based on operations of the finite field \GF (p^k) () is
equal to the symmetric group or the alternating group on the state space.Comment: 22 pages; Prelim0
Some group-theoretical results on Feistel Networks in a long-key scenario
The study of the trapdoors that can be hidden in a block cipher is and has
always been a high-interest topic in symmetric cryptography. In this paper we
focus on Feistel-network-like ciphers in a classical long-key scenario and we
investigate some conditions which make such a construction immune to the
partition-based attack introduced recently by Bannier et al.Comment: Accepted for publication in Advances in Mathematics of Communication
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
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