Investigations in the design and analysis of key-stream generators

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Walsh-Hadamard Transform and Cryptographic Applications in Bias Computing

Walsh-Hadamard transform is used in a wide variety of scientific and engineering applications, including bent functions and cryptanalytic optimization techniques in cryptography. In linear cryptanalysis, it is a key question to find a good linear approximation, which holds with probability $(1+d)/2$ and the bias $d$ is large in absolute value. Lu and Desmedt (2011) take a step toward answering this key question in a more generalized setting and initiate the work on the generalized bias problem with linearly-dependent inputs. In this paper, we give fully extended results. Deep insights on assumptions behind the problem are given. We take an information-theoretic approach to show that our bias problem assumes the setting of the maximum input entropy subject to the input constraint. By means of Walsh transform, the bias can be expressed in a simple form. It incorporates Piling-up lemma as a special case. Secondly, as application, we answer a long-standing open problem in correlation attacks on combiners with memory. We give a closed-form exact solution for the correlation involving the multiple polynomial of any weight \emph{for the first time}. We also give Walsh analysis for numerical approximation. An interesting bias phenomenon is uncovered, i.e., for even and odd weight of the polynomial, the correlation behaves differently. Thirdly, we introduce the notion of weakly biased distribution, and study bias approximation for a more general case by Walsh analysis. We show that for weakly biased distribution, Piling-up lemma is still valid. Our work shows that Walsh analysis is useful and effective to a broad class of cryptanalysis problems

Quantum Simulation Logic, Oracles, and the Quantum Advantage

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor's algorithm for integer factorization.Comment: 48 pages, 46 figure

Contributions to Confidentiality and Integrity Algorithms for 5G

The confidentiality and integrity algorithms in cellular networks protect the transmission of user and signaling data over the air between users and the network, e.g., the base stations. There are three standardised cryptographic suites for confidentiality and integrity protection in 4G, which are based on the AES, SNOW 3G, and ZUC primitives, respectively. These primitives are used for providing a 128-bit security level and are usually implemented in hardware, e.g., using IP (intellectual property) cores, thus can be quite efficient. When we come to 5G, the innovative network architecture and high-performance demands pose new challenges to security. For the confidentiality and integrity protection, there are some new requirements on the underlying cryptographic algorithms. Specifically, these algorithms should: 1) provide 256 bits of security to protect against attackers equipped with quantum computing capabilities; and 2) provide at least 20 Gbps (Gigabits per second) speed in pure software environments, which is the downlink peak data rate in 5G. The reason for considering software environments is that the encryption in 5G will likely be moved to the cloud and implemented in software. Therefore, it is crucial to investigate existing algorithms in 4G, checking if they can satisfy the 5G requirements in terms of security and speed, and possibly propose new dedicated algorithms targeting these goals. This is the motivation of this thesis, which focuses on the confidentiality and integrity algorithms for 5G. The results can be summarised as follows.1. We investigate the security of SNOW 3G under 256-bit keys and propose two linear attacks against it with complexities 2172 and 2177, respectively. These cryptanalysis results indicate that SNOW 3G cannot provide the full 256-bit security level. 2. We design some spectral tools for linear cryptanalysis and apply these tools to investigate the security of ZUC-256, the 256-bit version of ZUC. We propose a distinguishing attack against ZUC-256 with complexity 2236, which is 220 faster than exhaustive key search. 3. We design a new stream cipher called SNOW-V in response to the new requirements for 5G confidentiality and integrity protection, in terms of security and speed. SNOW-V can provide a 256-bit security level and achieve a speed as high as 58 Gbps in software based on our extensive evaluation. The cipher is currently under evaluation in ETSI SAGE (Security Algorithms Group of Experts) as a promising candidate for 5G confidentiality and integrity algorithms. 4. We perform deeper cryptanalysis of SNOW-V to ensure that two common cryptanalysis techniques, guess-and-determine attacks and linear cryptanalysis, do not apply to SNOW-V faster than exhaustive key search. 5. We introduce two minor modifications in SNOW-V and propose an extreme performance variant, called SNOW-Vi, in response to the feedback about SNOW-V that some use cases are not fully covered. SNOW-Vi covers more use cases, especially some platforms with less capabilities. The speeds in software are increased by 50% in average over SNOW-V and can be up to 92 Gbps.Besides these works on 5G confidentiality and integrity algorithms, the thesis is also devoted to local pseudorandom generators (PRGs). 6. We investigate the security of local PRGs and propose two attacks against some constructions instantiated on the P5 predicate. The attacks improve existing results with a large gap and narrow down the secure parameter regime. We also extend the attacks to other local PRGs instantiated on general XOR-AND and XOR-MAJ predicates and provide some insight in the choice of safe parameters

A true random number generator based on gait data for the Internet of You

The Internet of Things (IoT) is more and more a reality, and every day the number of connected objects increases. The growth is practically exponential -there are currently about 8 billion and expected to reach 21 billion in 2025. The applications of these devices are very diverse and range from home automation, through traffic monitoring or pollution, to sensors to monitor our health or improve our performance. While the potential of their applications seems to be unlimited, the cyber-security of these devices and their communications is critical for a flourishing deployment. Random Number Generators (RNGs) are essential to many security tasks such as seeds for key-generation or nonces used in authentication protocols. Till now, True Random Number Generators (TRNGs) are mainly based on physical phenomena, but there is a new trend that uses signals from our body (e.g., electrocardiograms) as an entropy source. Inspired by the last wave, we propose a new TRNG based on gait data (six 3-axis gyroscopes and accelerometers sensors over the subjects). We test both the quality of the entropic source (NIST SP800-90B) and the quality of the random bits generated (ENT, DIEHARDER and NIST 800-22). From this in-depth analysis, we can conclude that: 1) the gait data is a good source of entropy for random bit generation; 2) our proposed TRNG outputs bits that behave like a random variable. All this confirms the feasibility and the excellent properties of the proposed generator.This work was supported in part by the Spanish Ministry of Economy and Competitiveness under Contract ESP2015-68245-C4-1-P, in part by the Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation under Grant P2019-CARDIOSEC, and in part bythe Comunidad de Madrid, Spain, under Project CYNAMON (P2018/TCS-4566), co-financed by the European Structural Funds (ESF andFEDER

A hybrid classical-quantum algorithm for solution of nonlinear ordinary differential equations

A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of arbitrary vectors, which is enabled in our framework using quantum Hadamard gates along with state preparation, shifting, scaling, and measurement operations. It is estimated that the proposed hybrid classical-quantum approach for the Walsh-Hadamard transform of an input vector of size N results in a considerably lower computational complexity (O(N) operations) compared to the Fast Walsh-Hadamard transform (O(N log2(N)) operations). This benefit will also be relevant in the context of the proposed hybrid classical-quantum approach for the solution of nonlinear differential equations. Comparisons of results corresponding to the proposed hybrid classical-quantum approach and a purely classical approach for the solution of nonlinear differential equations (for cases involving one and two dependent variables) were found to be satisfactory. Some new perspectives relevant to the natural ordering of Walsh functions (in the context of both classical and hybrid approaches for the solution of nonlinear differential equations) and representation theory of finite groups are also presented here.Comment: 29 pages, 10 figure

A quantum approach for digital signal processing

We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the sequency-ordered Walsh-Hadamard transform, as well as quantum circuits for low-pass, high-pass, and band-pass filtering. Additionally, we provide a proof of correctness for the quantum circuit designed to perform the sequency-ordered Walsh-Hadamard transform. The performance and accuracy of the proposed approach for signal filtering were illustrated using computational examples, along with corresponding quantum circuits, for DC, low-pass, high-pass, and band-pass filtering. Our proposed algorithm for signal filtering has a reduced gate complexity and circuit depth of $O (\log_2 N)$, compared to at least $O ((\log_2 N )^2)$ associated with Quantum Fourier Transform (QFT) based filtering (excluding state preparation and measurement costs). In contrast, classical Fast Fourier Transform (FFT) based filtering approaches have a complexity of $O (N \log_2 N )$. This shows that our proposed approach offers a significant improvement over QFT-based filtering methods and classical FFT-based filtering methods. Such enhanced efficiency of our proposed approach holds substantial promise across several signal processing applications by ensuring faster computations and efficient use of resources via reduced circuit depth and lower gate complexity.Comment: 29 page

On Some Symmetric Lightweight Cryptographic Designs

This dissertation presents cryptanalysis of several symmetric lightweight primitives, both stream ciphers and block ciphers. Further, some aspects of authentication in combination with a keystream generator is investigated, and a new member of the Grain family of stream ciphers, Grain-128a, with built-in support for authentication is presented. The first contribution is an investigation of how authentication can be provided at a low additional cost, assuming a synchronous stream cipher is already implemented and used for encryption. These findings are then used when presenting the latest addition to the Grain family of stream ciphers, Grain-128a. It uses a 128-bit key and a 96-bit initialization vector to generate keystream, and to possibly also authenticate the plaintext. Next, the stream cipher BEAN, superficially similar to Grain, but notably using a weak output function and two feedback with carry shift registers (FCSRs) rather than linear and (non-FCSR) nonlinear feedback shift registers, is cryptanalyzed. An efficient distinguisher and a state-recovery attack is given. It is shown how knowledge of the state can be used to recover the key in a straightforward way. The remainder of this dissertation then focuses on block ciphers. First, a related-key attack on KTANTAN is presented. The attack notably uses only a few related keys, runs in less than half a minute on a current computer, and directly contradicts the designers' claims. It is discussed why this is, and what can be learned from this. Next, PRINTcipher is subjected to linear cryptanalysis. Several weak key classes are identified and it is shown how several observations of the same statistical property can be made for each plaintext--ciphertext pair. Finally, the invariant subspace property, first observed for certain key classes in PRINTcipher, is investigated. In particular, its connection to large linear biases is studied through an eigenvector which arises inside the cipher and leads to trail clustering in the linear hull which, under reasonable assumptions, causes a significant number of large linear biases. Simulations on several versions of PRINTcipher are compared to the theoretical findings

Cybersecurity in implantable medical devices

Mención Internacional en el título de doctorImplantable Medical Devices (IMDs) are electronic devices implanted within the body to treat a medical condition, monitor the state or improve the functioning of some body part, or just to provide the patient with a capability that he did not possess before [86]. Current examples of IMDs include pacemakers and defibrillators to monitor and treat cardiac conditions; neurostimulators for deep brain stimulation in cases such as epilepsy or Parkinson; drug delivery systems in the form of infusion pumps; and a variety of biosensors to acquire and process different biosignals. Some of the newest IMDs have started to incorporate numerous communication and networking functions—usually known as “telemetry”—, as well as increasingly more sophisticated computing capabilities. This has provided implants with more intelligence and patients with more autonomy, as medical personnel can access data and reconfigure the implant remotely (i.e., without the patient being physically present in medical facilities). Apart from a significant cost reduction, telemetry and computing capabilities also allow healthcare providers to constantly monitor the patient’s condition and to develop new diagnostic techniques based on an Intra Body Network (IBN) of medical devices [25, 26, 201]. Evolving from a mere electromechanical IMD to one with more advanced computing and communication capabilities has many benefits but also entails numerous security and privacy risks for the patient. The majority of such risks are relatively well known in classical computing scenarios, though in many respects their repercussions are far more critical in the case of implants. Attacks against an IMD can put at risk the safety of the patient who carries it, with fatal consequences in certain cases. Causing an intentional malfunction of an implant can lead to death and, as recognized by the U.S. Food and Drug Administration (FDA), such deliberate attacks could be far more difficult to detect than accidental ones [61]. Furthermore, these devices store and transmit very sensitive medical information that requires protection, as dictated by European (e.g., Directive 95/46/ECC) and U.S. (e.g., CFR 164.312) Directives [94, 204]. The wireless communication capabilities present in many modern IMDs are a major source of security risks, particularly while the patient is in open (i.e., non-medical) environments. To begin with, the implant becomes no longer “invisible”, as its presence could be remotely detected [48]. Furthermore, it facilitates the access to transmitted data by eavesdroppers who simply listen to the (insecure) channel [83]. This could result in a major privacy breach, as IMDs store sensitive information such as vital signals, diagnosed conditions, therapies, and a variety of personal data (e.g., birth date, name, and other medically relevant identifiers). A vulnerable communication channel also makes it easier to attack the implant in ways similar to those used against more common computing devices [118, 129, 156], i.e., by forging, altering, or replying previously captured messages [82]. This could potentially allow an adversary to monitor and modify the implant without necessarily being close to the victim [164]. In this regard, the concerns of former U.S. vice-president Dick Cheney constitute an excellent example: he had his Implantable Cardioverter Defibrillator (ICD) replaced by another without WiFi capability [219]. While there are still no known real-world incidents, several attacks on IMDs have been successfully demonstrated in the lab [83, 133, 143]. These attacks have shown how an adversary can disable or reprogram therapies on an ICD with wireless connectivity, and even inducing a shock state to the patient [65]. Other attacks deplete the battery and render the device inoperative [91], which often implies that the patient must undergo a surgical procedure to have the IMD replaced. Moreover, in the case of cardiac implants, they have a switch that can be turned off merely by applying a magnetic field [149]. The existence of this mechanism is motivated by the need to shield ICDs to electromagnetic fields, for instance when the patient undergoes cardiac surgery using electrocautery devices [47]. However, this could be easily exploited by an attacker, since activating such a primitive mechanism does not require any kind of authentication. In order to prevent attacks, it is imperative that the new generation of IMDs will be equipped with strong mechanisms guaranteeing basic security properties such as confidentiality, integrity, and availability. For example, mutual authentication between the IMD and medical personnel is essential, as both parties must be confident that the other end is who claims to be. In the case of the IMD, only commands coming from authenticated parties should be considered, while medical personnel should not trust any message claiming to come from the IMD unless sufficient guarantees are given. Preserving the confidentiality of the information stored in and transmitted by the IMD is another mandatory aspect. The device must implement appropriate security policies that restrict what entities can reconfigure the IMD or get access to the information stored in it, ensuring that only authorized operations are executed. Similarly, security mechanisms have to be implemented to protect the content of messages exchanged through an insecure wireless channel. Integrity protection is equally important to ensure that information has not been modified in transit. For example, if the information sent by the implant to the Programmer is altered, the doctor might make a wrong decision. Conversely, if a command sent to the implant is forged, modified, or simply contains errors, its execution could result in a compromise of the patient’s physical integrity. Technical security mechanisms should be incorporated in the design phase and complemented with appropriate legal and administrative measures. Current legislation is rather permissive in this regard, allowing the use of implants like ICDs that do not incorporate any security mechanisms. Regulatory authorities like the FDA in the U.S or the EMA (European Medicines Agency) in Europe should promote metrics and frameworks for assessing the security of IMDs. These assessments should be mandatory by law, requiring an adequate security level for an implant before approving its use. Moreover, both the security measures supported on each IMD and the security assessment results should be made public. Prudent engineering practices well known in the safety and security domains should be followed in the design of IMDs. If hardware errors are detected, it often entails a replacement of the implant, with the associated risks linked to a surgery. One of the main sources of failure when treating or monitoring a patient is precisely malfunctions of the device itself. These failures are known as “recalls” or “advisories”, and it is estimated that they affect around 2.6% of patients carrying an implant. Furthermore, the software running on the device should strictly support the functionalities required to perform the medical and operational tasks for what it was designed, and no more [66, 134, 213]. In Chapter 1, we present a survey of security and privacy issues in IMDs, discuss the most relevant mechanisms proposed to address these challenges, and analyze their suitability, advantages, and main drawbacks. In Chapter 2, we show how the use of highly compressed electrocardiogram (ECG) signals (only 24 coefficients of Hadamard Transform) is enough to unequivocally identify individuals with a high performance (classification accuracy of 97% and with identification system errors in the order of 10−2). In Chapter 3 we introduce a new Continuous Authentication scheme that, contrarily to previous works in this area, considers ECG signals as continuous data streams. The proposed ECG-based CA system is intended for real-time applications and is able to offer an accuracy up to 96%, with an almost perfect system performance (kappa statistic > 80%). In Chapter 4, we propose a distance bounding protocol to manage access control of IMDs: ACIMD. ACIMD combines two features namely identity verification (authentication) and proximity verification (distance checking). The authentication mechanism we developed conforms to the ISO/IEC 9798-2 standard and is performed using the whole ECG signal of a device holder, which is hardly replicable by a distant attacker. We evaluate the performance of ACIMD using ECG signals of 199 individuals over 24 hours, considering three adversary strategies. Results show that an accuracy of 87.07% in authentication can be achieved. Finally, in Chapter 5 we extract some conclusions and summarize the published works (i.e., scientific journals with high impact factor and prestigious international conferences).Los Dispositivos Médicos Implantables (DMIs) son dispositivos electrónicos implantados dentro del cuerpo para tratar una enfermedad, controlar el estado o mejorar el funcionamiento de alguna parte del cuerpo, o simplemente para proporcionar al paciente una capacidad que no poseía antes [86]. Ejemplos actuales de DMI incluyen marcapasos y desfibriladores para monitorear y tratar afecciones cardíacas; neuroestimuladores para la estimulación cerebral profunda en casos como la epilepsia o el Parkinson; sistemas de administración de fármacos en forma de bombas de infusión; y una variedad de biosensores para adquirir y procesar diferentes bioseñales. Los DMIs más modernos han comenzado a incorporar numerosas funciones de comunicación y redes (generalmente conocidas como telemetría) así como capacidades de computación cada vez más sofisticadas. Esto ha propiciado implantes con mayor inteligencia y pacientes con más autonomía, ya que el personal médico puede acceder a los datos y reconfigurar el implante de forma remota (es decir, sin que el paciente esté físicamente presente en las instalaciones médicas). Aparte de una importante reducción de costos, las capacidades de telemetría y cómputo también permiten a los profesionales de la atención médica monitorear constantemente la condición del paciente y desarrollar nuevas técnicas de diagnóstico basadas en una Intra Body Network (IBN) de dispositivos médicos [25, 26, 201]. Evolucionar desde un DMI electromecánico a uno con capacidades de cómputo y de comunicación más avanzadas tiene muchos beneficios pero también conlleva numerosos riesgos de seguridad y privacidad para el paciente. La mayoría de estos riesgos son relativamente bien conocidos en los escenarios clásicos de comunicaciones entre dispositivos, aunque en muchos aspectos sus repercusiones son mucho más críticas en el caso de los implantes. Los ataques contra un DMI pueden poner en riesgo la seguridad del paciente que lo porta, con consecuencias fatales en ciertos casos. Causar un mal funcionamiento intencionado en un implante puede causar la muerte y, tal como lo reconoce la Food and Drug Administration (FDA) de EE.UU, tales ataques deliberados podrían ser mucho más difíciles de detectar que los ataques accidentales [61]. Además, estos dispositivos almacenan y transmiten información médica muy delicada que requiere se protegida, según lo dictado por las directivas europeas (por ejemplo, la Directiva 95/46/ECC) y estadunidenses (por ejemplo, la Directiva CFR 164.312) [94, 204]. Si bien todavía no se conocen incidentes reales, se han demostrado con éxito varios ataques contra DMIs en el laboratorio [83, 133, 143]. Estos ataques han demostrado cómo un adversario puede desactivar o reprogramar terapias en un marcapasos con conectividad inalámbrica e incluso inducir un estado de shock al paciente [65]. Otros ataques agotan la batería y dejan al dispositivo inoperativo [91], lo que a menudo implica que el paciente deba someterse a un procedimiento quirúrgico para reemplazar la batería del DMI. Además, en el caso de los implantes cardíacos, tienen un interruptor cuya posición de desconexión se consigue simplemente aplicando un campo magnético intenso [149]. La existencia de este mecanismo está motivada por la necesidad de proteger a los DMIs frete a posibles campos electromagnéticos, por ejemplo, cuando el paciente se somete a una cirugía cardíaca usando dispositivos de electrocauterización [47]. Sin embargo, esto podría ser explotado fácilmente por un atacante, ya que la activación de dicho mecanismo primitivo no requiere ningún tipo de autenticación. Garantizar la confidencialidad de la información almacenada y transmitida por el DMI es otro aspecto obligatorio. El dispositivo debe implementar políticas de seguridad apropiadas que restrinjan qué entidades pueden reconfigurar el DMI o acceder a la información almacenada en él, asegurando que sólo se ejecuten las operaciones autorizadas. De la misma manera, mecanismos de seguridad deben ser implementados para proteger el contenido de los mensajes intercambiados a través de un canal inalámbrico no seguro. La protección de la integridad es igualmente importante para garantizar que la información no se haya modificado durante el tránsito. Por ejemplo, si la información enviada por el implante al programador se altera, el médico podría tomar una decisión equivocada. Por el contrario, si un comando enviado al implante se falsifica, modifica o simplemente contiene errores, su ejecución podría comprometer la integridad física del paciente. Los mecanismos de seguridad deberían incorporarse en la fase de diseño y complementarse con medidas legales y administrativas apropiadas. La legislación actual es bastante permisiva a este respecto, lo que permite el uso de implantes como marcapasos que no incorporen ningún mecanismo de seguridad. Las autoridades reguladoras como la FDA en los Estados Unidos o la EMA (Agencia Europea de Medicamentos) en Europa deberían promover métricas y marcos para evaluar la seguridad de los DMIs. Estas evaluaciones deberían ser obligatorias por ley, requiriendo un nivel de seguridad adecuado para un implante antes de aprobar su uso. Además, tanto las medidas de seguridad implementadas en cada DMI como los resultados de la evaluación de su seguridad deberían hacerse públicos. Buenas prácticas de ingeniería en los dominios de la protección y la seguridad deberían seguirse en el diseño de los DMIs. Si se detectan errores de hardware, a menudo esto implica un reemplazo del implante, con los riesgos asociados y vinculados a una cirugía. Una de las principales fuentes de fallo al tratar o monitorear a un paciente es precisamente el mal funcionamiento del dispositivo. Estos fallos se conocen como “retiradas”, y se estima que afectan a aproximadamente el 2,6 % de los pacientes que llevan un implante. Además, el software que se ejecuta en el dispositivo debe soportar estrictamente las funcionalidades requeridas para realizar las tareas médicas y operativas para las que fue diseñado, y no más [66, 134, 213]. En el Capítulo 1, presentamos un estado de la cuestión sobre cuestiones de seguridad y privacidad en DMIs, discutimos los mecanismos más relevantes propuestos para abordar estos desafíos y analizamos su idoneidad, ventajas y principales inconvenientes. En el Capítulo 2, mostramos cómo el uso de señales electrocardiográficas (ECGs) altamente comprimidas (sólo 24 coeficientes de la Transformada Hadamard) es suficiente para identificar inequívocamente individuos con un alto rendimiento (precisión de clasificación del 97% y errores del sistema de identificación del orden de 10−2). En el Capítulo 3 presentamos un nuevo esquema de Autenticación Continua (AC) que, contrariamente a los trabajos previos en esta área, considera las señales ECG como flujos de datos continuos. El sistema propuesto de AC basado en señales cardíacas está diseñado para aplicaciones en tiempo real y puede ofrecer una precisión de hasta el 96%, con un rendimiento del sistema casi perfecto (estadístico kappa > 80 %). En el Capítulo 4, proponemos un protocolo de verificación de la distancia para gestionar el control de acceso al DMI: ACIMD. ACIMD combina dos características, verificación de identidad (autenticación) y verificación de la proximidad (comprobación de la distancia). El mecanismo de autenticación es compatible con el estándar ISO/IEC 9798-2 y se realiza utilizando la señal ECG con todas sus ondas, lo cual es difícilmente replicable por un atacante que se encuentre distante. Hemos evaluado el rendimiento de ACIMD usando señales ECG de 199 individuos durante 24 horas, y hemos considerando tres estrategias posibles para el adversario. Los resultados muestran que se puede lograr una precisión del 87.07% en la au tenticación. Finalmente, en el Capítulo 5 extraemos algunas conclusiones y resumimos los trabajos publicados (es decir, revistas científicas con alto factor de impacto y conferencias internacionales prestigiosas).Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: Arturo Ribagorda Garnacho.- Secretario: Jorge Blasco Alís.- Vocal: Jesús García López de Lacall