RD-flatness and RD-injectivity

It is proved that every commutative ring whose RD-injective modules are $\Sigma$-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively the RD-relativization of flat modules and fp-injective modules. It is also shown that a commutative ring is perfect if and only if each RD-flat module is RD-projective.Comment: A new section is added to the version published in Communications in Algebra where a complete proof of Theorem 3.1 is give

FP-injectivity of factors of injective modules

International audienceIt is shown that a ring is left semihereditary if and only each homomorphic image of its injective hull as left module is FP-injective. It is also proven that a commutative ring R is reduced and arithmetical if and only if E/U if FP-injective for any FP-injective R-module E and for any submodule U of finite Goldie dimension. A characterization of commutative rings for which each module of finite Goldie dimension is of injective dimension at most one is given. Let R be a chain ring and Z its subset of zerodivisors. It is proven that E/U is FP-injective for each FP-injective R-module E and each pure polyserial submodule U of E if R/I is complete in its f.c. topology for each ideal I whose the top prime ideal is Z. The converse holds if each indecomposable injective module whose the bottom prime ideal is Z contains a pure uniserial submodule. For some chain ring R we show that E/U is FP-injective for any FP-injective module E and any its submodule U of finite Goldie dimension, even if R is not coherent. It follows that any Archimedean chain ring is either coherent or maximal if and only if each factor of any injective module of finite Goldie dimension modulo a pure submodule is injective

Graph Based Reduction of Program Verification Conditions

Increasing the automaticity of proofs in deductive verification of C programs is a challenging task. When applied to industrial C programs known heuristics to generate simpler verification conditions are not efficient enough. This is mainly due to their size and a high number of irrelevant hypotheses. This work presents a strategy to reduce program verification conditions by selecting their relevant hypotheses. The relevance of a hypothesis is determined by the combination of a syntactic analysis and two graph traversals. The first graph is labeled by constants and the second one by the predicates in the axioms. The approach is applied on a benchmark arising in industrial program verification

Steganography: a Class of Algorithms having Secure Properties

Chaos-based approaches are frequently proposed in information hiding, but without obvious justification. Indeed, the reason why chaos is useful to tackle with discretion, robustness, or security, is rarely elucidated. This research work presents a new class of non-blind information hidingalgorithms based on some finite domains iterations that are Devaney's topologically chaotic. The approach is entirely formalized and reasons to take place into the mathematical theory of chaos are explained. Finally, stego-security and chaos security are consequently proven for a large class of algorithms.Comment: 4 pages, published in Seventh International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP 2011, Dalian, China, October 14-16, 201

Steganography: a class of secure and robust algorithms

This research work presents a new class of non-blind information hiding algorithms that are stego-secure and robust. They are based on some finite domains iterations having the Devaney's topological chaos property. Thanks to a complete formalization of the approach we prove security against watermark-only attacks of a large class of steganographic algorithms. Finally a complete study of robustness is given in frequency DWT and DCT domains.Comment: Published in The Computer Journal special issue about steganograph

Application of Steganography for Anonymity through the Internet

In this paper, a novel steganographic scheme based on chaotic iterations is proposed. This research work takes place into the information hiding security framework. The applications for anonymity and privacy through the Internet are regarded too. To guarantee such an anonymity, it should be possible to set up a secret communication channel into a web page, being both secure and robust. To achieve this goal, we propose an information hiding scheme being stego-secure, which is the highest level of security in a well defined and studied category of attacks called "watermark-only attack". This category of attacks is the best context to study steganography-based anonymity through the Internet. The steganalysis of our steganographic process is also studied in order to show it security in a real test framework.Comment: 14 page

The lambda-dimension of commutative arithmetic rings

It is shown that every commutative arithmetic ring $R$ has $lambda$-dimension $leq 3$. An example of a commutative Kaplansky ring with $lambda$-dimension 3 is given. If $R$ satisfies an additional condition then $lambda$-dim($R$