1,721,055 research outputs found
The group generated by the round functions of a GOST-like cipher
Get PDFWe define a cipher that is an extension of GOST, and study the permutation group generated by its round functions. We show that, under minimal assumptions on the components of the cipher, this group is the alternating group on the plaintext space. This we do by first showing that the group is primitive, and then applying the OâNan-Scott classification of primitive groups
A Survey on PoW-based Consensus
Get PDFWe provide a historical overview of proof-of-work techniques and the fields in which it plunges its roots. We are interested in PoW-techniques applied to blockchain technology and therefore we survey the state-of-the-art protocols employing these methods for consensus algorithms, emphasizing the differences between the efficient hashcash systems and the promising bread pudding protocols. Afterwards, the consensus mechanisms are discussed and some interesting known attacks to these algorithms are collected and classified according to their underlying ideas
Some security bounds for the key sizes of DGHV scheme
No full textThe correctness in decrypting a ciphertext after some operations in the DGVH scheme depends heavily on the dimension of the secret key. In this paper we compute two bounds on the size of the secret key for the DGHV scheme to decrypt correctly a ciphertext after a fixed number of additions and a fixed number of multiplication. Moreover we improve the original bound on the dimension of the secret key for a general circuit
HELP: a sparse error locator polynomial for BCH codes
Get PDFIn 1990 Cooper suggested to use Groebner bases’ computations to decode
cyclic codes and his idea gave rise to many research papers. In particular, as proved
by Sala-Orsini, once defined the polynomial ring whose variables are the syndromes,
the locations and the error values and considered the syndrome ideal, only one polynomial of a lexicographical Groebner basis for such ideal is necessary to decode (the
general error locator polynomial, a.k.a. GELP). The decoding procedure only consists
in evaluating this polynomial in the syndromes and computing its roots: the roots are
indeed the error locations. A possible bottleneck in this procedure may be the evaluation part, since a priori the GELP may be dense.
In this paper, focusing on binary cyclic codes with length n = 2^m − 1, correcting up to
two errors, we give a Groebner-free, sparse analog of the GELP, the half error locator polynomial (HELP). In particular, we show that it is not necessary to compute the
whole Groebner basis for getting such kind of locator polynomial and we construct
the HELP, studying the quotient algebra of the polynomial ring modulo the syndrome
ideal by a combinatorial point of view. The HELP turns out to be computable with
quadratic complexity and it has linear growth in the length n of the code: O( (n+1)/2)
Wave-shaped round functions and primitive groups
Get PDFRound functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks (SPN) and Feistel Networks (FN), are often obtained as the composition of different layers. The bijectivity of any encryption function 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. Efficient decryption is guaranteed by the use of wave functions in FNs. It is shown how to avoid that the group generated by the round functions acts imprimitively, a serious flaw for the cipher. The primitivity is a consequence of a more general result, which reduce the problem of proving that a given FN generates a primitive group to proving that an SPN, directly related to the given FN, generates a primitive group. Finally, a concrete instance of real-world size wave cipher is proposed as an example, and its resistance against differential and linear cryptanalyses is also established
On weak differential uniformity of vectorial Boolean functions as a cryptographic criterion
No full textWe study the relation among some security parameters for vectorial Boolean functions which prevent attacks on the related block cipher. We focus our study on a recently-introduced security criterion, called weak differential uniformity, which prevents the existence of an undetectable trapdoor based on imprimitive group action. We present some properties of functions with low weak differential uniformity, especially for the case of power functions and 4-bit S-Boxes
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