arXiv subjects

Emanuele Bellini

Publications and source records attributed to Emanuele Bellini.

23 records · Page 2Linked to original sources

arXiv2015

An Extension of Cook's Elastic Cipher

Given a block cipher of length L Cook's elastic cipher allows to encrypt messages of variable length from L to 2L. Given some conditions on the key schedule, Cook's elastic cipher is secure against any key recovery attack if the underlying block cipher is, and it achieves complete diffusion in at most q + 1 rounds if the underlying block cipher achieves it in q rounds. We extend Cook's construction inductively, obtaining an elastic cipher for any message length greater than L with the same properties of security as Cook's elastic cipher.

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arXiv2015

On the Griesmer bound for nonlinear codes

Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound, holds only in the linear case. In this paper we characterize a family of systematic nonlinear codes for which the Griesmer bound holds. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by showing explicit counterexamples. On the other hand, we are also able to provide (weaker) versions of the Griesmer bound holding for all systematic codes.

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arXiv2014

Yet another algorithm to compute the nonlinearity of a Boolean function

We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and computing its evaluation vector requires a worst-case complexity of $O(n2^n)$ integer operations. This way, with a different approach, we reach the same complexity of established algorithms, such as those based on the fast Walsh transform.

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arXiv2013

On the Griesmer Bound for Systematic Codes

We generalize the Griesmer bound in the case of systematic codes over a field of size q greater than the distance d of the code. We also generalize the Griesmer bound in the case of any systematic code of distance 2,3,4 and in the case of binary systematic codes of distance up to 6.

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arXiv2012

Some bounds on the size of codes

We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the Plotkin bound, and one of these is actually an improvement of a bound by Litsyn and Laihonen. Our experiments show that in some cases (the majority of cases for some q) our bounds provide the best value, compared to all other theoretical bounds.

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