1,697 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
Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations
In this paper we propose a definition and construction of a new family of
one-way candidate functions , where
is an alphabet with elements. Special instances of these functions can have
the additional property to be permutations (i.e. one-way permutations). These
one-way functions have the property that for achieving the security level of
computations in order to invert them, only bits of input are needed.
The construction is based on quasigroup string transformations. Since
quasigroups in general do not have algebraic properties such as associativity,
commutativity, neutral elements, inverting these functions seems to require
exponentially many readings from the lookup table that defines them (a Latin
Square) in order to check the satisfiability for the initial conditions, thus
making them natural candidates for one-way functions.Comment: Submitetd to conferenc
A CCA2 Secure Variant of the McEliece Cryptosystem
The McEliece public-key encryption scheme has become an interesting
alternative to cryptosystems based on number-theoretical problems. Differently
from RSA and ElGa- mal, McEliece PKC is not known to be broken by a quantum
computer. Moreover, even tough McEliece PKC has a relatively big key size,
encryption and decryption operations are rather efficient. In spite of all the
recent results in coding theory based cryptosystems, to the date, there are no
constructions secure against chosen ciphertext attacks in the standard model -
the de facto security notion for public-key cryptosystems. In this work, we
show the first construction of a McEliece based public-key cryptosystem secure
against chosen ciphertext attacks in the standard model. Our construction is
inspired by a recently proposed technique by Rosen and Segev
Codes, Cryptography, and the McEliece Cryptosystem
Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow for increased security. Finally, we develop a family of twisted Hermitian codes that meets the criteria set forth for security
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