Guillermo Morales-Luna

FPGA implementation of an efficient multiplier over finite fields GF(2/sup m/)

Arithmetic operations over finite fields GF(2m) are widely used in cryptography, error-correcting codes and signal processing. In particular, multiplication is especially relevant since other arithmetic operators, such as division or exponentiation, which they usually utilize multipliers as building blocks. Hardware implementation of field multiplication may provide a great speedup in procedures performance, which easily exceeds the one observed in software platforms. In this paper we deal with an FPGA implementation of an efficient serial multiplier over the binary extension fields GF(2193) and GF(2239). Those extension fields are included among the ones recommended by NIST (National Institute of Standards and Technology) standards for Elliptic Curve Cryptography. Our multiplier is of type Serial/Parallel LSB-first and operates with a latency of m-clock cycles, where m is the length of the field word. We calculate the space complexity attending the number of slices used in the FPGA

Low-Complexity Bit-Parallel Square Root Computation over GF(2^{m}) for All Trinomials

In this contribution, we introduce a low-complexity bit-parallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied to any type of irreducible polynomials. We derive explicit formulas for the space and time complexities associated with the square root operator when working with binary extension fields generated using irreducible trinomials. We show that, for those finite fields, it is possible to compute the square root of an arbitrary field element with equal or better hardware efficiency than the one associated with the field squaring operation. Furthermore, a practical application of the square root operator in the domain of field exponentiation computation is presented.

Key Distribution Protocols Based on Noisy Channels in Presence of an Active Adversary: Conventional and New Versions With Parameter Optimization

In this paper, we consider the information-theoretic secure key distribution problem over noisy wiretap channels with public discussion and in the presence of an active adversary. There are several well-known versions of the protocols proposed by Maurer and Wolf to solve this problem. We describe several new versions of the key distribution protocols for the same channel model allowing to increase the key rate given a fixed key security and under an optimization of the protocol parameters. Both asymptotic and nonasymptotic cases are presented. It is shown that in some cases the nonasymptotic key rate is not so far from the asymptotic one whenever the lengths of the transmitted strings are of the order of thousands of bits.

Ontology-Based Knowledge Retrieval

We deal with knowledge retrieval within the context of Virtual Learning Environment (VLE). A good VLE should deliver relevant learning materials to the learner at the most appropriate time to facilitate knowledge acquisition by Problem-Based Learning (PBL). In PBL, students should retrieve information about a problem by working in small groups with the guidance of a learning facilitator providing materials required through the problem solving process. The use of ontologies to represent domain knowledge improves the information management in a VLE because it enables automatic reasoning and facilitates the processes of knowledge searching and retrieving needed to promote the interest in problem solving. We propose an ontology-based for searching, discovering and publishing relevant learning materials as Learning Objects to help students in the PBL approach.

On the existence of perfect stegosystems

There are several steganography techniques (e.g. linguistic or least significant bit embedding) that provide security but no robustness against an active adversary. On the other hand it is rather well known that the spread-spectrum based technique is robust against an active adversary but it seems to be insecure against a statistical detection of stegosignal. We prove in this paper that actually this is not the case and that there exists an stegosystem that is asymptotically both secure to statistical detection and robust against a jamming of stegosignal by an active adversary. We call such stegosystems quasiperfect whereas we call them perfect if in addition the data rate of secret information is asymptotically constant. We prove that perfect stegosystems do not exist for both blind and informed decoders. Some examples using the simplex and the Reed-Muller codes jointly with stegosystems are given.

Privacy Amplification Theorem for Noisy Main Channel

Secret key agreement protocol between legal parties based on reconciliation and privacy amplification procedure has been considered in [2]. The so called privacy amplification theorem is used to estimate the amount of Shannons information leaking to an illegal party (passive eavesdropper) about the final key. We consider a particular case where one of the legal parties (Alice) sends to another legal party (Bob) a random binary string x through a binary symmetric channel (BSC) with bit error probability ?m while an eavesdropper (Eve) receives this string through an independent BSC with bit error probability ?w. We assume that ?m < ?w and hence the main channel is superior to the wire-tap channel. To reconcile the strings between legal parties Alice sends to Bob through noiseless channel the check string y based on some good error correcting code. Since this transmission is completely public Eve can eavesdrop it and therefore this extra information has to be taken into account in an estimation of the information leaking to Eve about the final key. In [3] an inequality has been proved to upper bound the information of Eve in such scenario. The main contribution of the running paper is to improve this inequality and hence to enhance the privacy amplification theorem. We present also bounds for the probability of false reconciliation when the check symbols of the linear code are transmitted through noiseless channel. The presented results can be very useful when considering the non-asymptotic case.

Correlation analysis of complex network metrics on the topology of the Internet

We present an experimental study on the linear relationship between a rich set of complex network metrics, to methodologically select a subset of non-redundant and potentially independent metrics that explain different aspects of the topology of the Autonomous System view of the Internet. We followed a data-driven approach based on (1) a correlation study of different properties of evolving Internet networks, and (2) the validation of a non-redundant set of metrics by evaluating the performance of supervised and unsupervised machine learning techniques. We confirm pair-wise metric correlations observed in other types of networks and identify sets of highly correlated metrics that may reveal patterns specific to the topology of the Internet.

A parallel version of the Itoh-Tsujii multiplicative inversion algorithm

In this contribution, we derive a novel parallel formulation of the standard Itoh-Tsujii algorithm for multiplicative inverse computation over GF(2m). When implemented in a Virtex 3200E FPGA device, our design is able to compute multiplicative inversion over GF(2193) after 20 clock cycles in about 0.94µS.

Watermarking of binary messages in conditions of an additive binary noise attack

We consider a private watermarking system (WM) for binary cover messages (CMs). The goal of an attacker is to render unable the WM-owner of WM detection without noticeable corruption of CMs. Here, we restrict the attackers activity to modulo two addition of a binary noise sequence to the watermarked stegomessage (SM). The formulas for the probabilities of WM-missing and WM-false alarm are obtained. We prove that the WM procedure can be designed to be reliable without significant distortions and for medium length of CMs even in the case in which CMs are unknown by the WM detector.

Secret Key Agreement Over Multipath Channels Exploiting a Variable-Directional Antenna

We develop an approach of key distribution protocol(KDP) proposed recently by T.Aono et al., where the security of KDP is only partly estimated in terms of eavesdroppers key bit errors. Instead we calculate the Shannons information leaking to a wire tapper and also we apply the privacy amplification procedure from the side of the legal users. A more general mathematical model based on the use of Variable-Directional Antenna (VDA) under the condition of multipath wave propagation is proposed. The new method can effectively be used even in noiseless interception channels providing thus a widened area with respect to practical applications. Statistical characteristics of the VDA are investigated by simulation, allowing to specify the model parameters. We prove that the proposed KDP provides both security and reliability of the shared keys even for very short distances between legal users and eavesdroppers. Antenna diversity is proposed as a mean to enhance the KDP security. In order to provide a better performance evaluation of the KDP, it is investigated the use of error correcting codes.