arXiv subjects

Dongdai Lin

Publications and source records attributed to Dongdai Lin.

26 records · Page 2Linked to original sources

arXiv2014

Distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers

Let $\underline{a}$ and $\underline{b}$ be primitive sequences over $\mathbb{Z}/(p^e)$ with odd prime $p$ and $e\ge 2$. For certain compressing maps, we consider the distribution properties of compressing sequences of $\underline{a}$ and $\underline{b}$, and prove that $\underline{a}=\underline{b}$ if the compressing sequences are equal at the times $t$ such that $α(t)=k$, where $\underlineα$ is a sequence related to $\underline{a}$. We also discuss the $s$-uniform distribution property of compressing sequences. For some compressing maps, we have that there exist different primitive sequences such that the compressing sequences are $s$-uniform. We also discuss that compressing sequences can be $s$-uniform for how many elements $s$.

cs.IT↗

arXiv2013

Complete permutation polynomials induced from complete permutations of subfields

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to construct complete permutations of certain extension fields with these techniques. The results generalize some recent work of several authors.

math.NT↗

arXiv2013

New constructions of quaternary bent functions

In this paper, a new construction of quaternary bent functions from quaternary quadratic forms over Galois rings of characteristic 4 is proposed. Based on this construction, several new classes of quaternary bent functions are obtained, and as a consequence, several new classes of quadratic binary bent and semi-bent functions in polynomial forms are derived. This work generalizes the recent work of N. Li, X. Tang and T. Helleseth.

cs.DM↗

arXiv2011

Linear Relation on General Ergodic T-Function

We find linear (as well as quadratic) relations in a very large class of T-functions. The relations may be used in analysis of T-function-based stream ciphers.

cs.CR↗

arXiv2011

Ergodic Theory Over ${\F}_2[[T]]$

In cryptography and coding theory, it is important to study the pseudo-random sequences and the ergodic transformations. We already have the 1-Lipshitz ergodic theory over ${\Z}_2$ established by V. Anashin and others. In this paper we present an ergodic theory over ${\F}_2[[T]]$ and some ideas which might be very useful in applications.

math.CO↗

arXiv2009

Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

Algebraic and fast algebraic attacks are power tools to analyze stream ciphers. A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the notion of AAR (algebraic attack resistant) functions was introduced as a unified measure of protection against both classical algebraic and fast algebraic attacks. In this correspondence, we first give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks, and we also prove that no symmetric Boolean functions are AAR functions. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.

cs.CR↗

arXiv2006

Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model

We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks. In an effort to reduce the setup assumptions required for efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks, we consider a model, which we call the Authenticated Public-Key (APK) model. The APK model seems to significantly reduce the setup assumptions made by the CRS model (as no trusted party or honest execution of a centralized algorithm are required), and can be seen as a slightly stronger variation of the Bare Public-Key (BPK) model from \cite{CGGM,MR}, and a weaker variation of the registered public-key model used in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK model. Our main result is a constant-round concurrent non-malleable zero-knowledge argument of knowledge for any polynomial-time relation (associated to a language in $\mathcal{NP}$), under the (minimal) assumption of the existence of a one-way function family. Furthermore,We show time-efficient instantiations of our protocol based on known number-theoretic assumptions. We also note a negative result with respect to further reducing the setup assumptions of our protocol to those in the (unauthenticated) BPK model, by showing that concurrently non-malleable zero-knowledge arguments of knowledge in the BPK model are only possible for trivial languages.

cs.CR↗

arXiv2006

Resettable Zero Knowledge in the Bare Public-Key Model under Standard Assumption

In this paper we resolve an open problem regarding resettable zero knowledge in the bare public-key (BPK for short) model: Does there exist constant round resettable zero knowledge argument with concurrent soundness for $\mathcal{NP}$ in BPK model without assuming \emph{sub-exponential hardness}? We give a positive answer to this question by presenting such a protocol for any language in $\mathcal{NP}$ in the bare public-key model assuming only collision-resistant hash functions against \emph{polynomial-time} adversaries.

cs.CR↗