- Cryptographic Algorithms
- Introduction and notes on symmetric cryptography
- Algorithms and mathematical foundations for asymmetric cryptography
- The key exchange problem and Diffie and Hellman protocol
- Asymmetric algorithms and protocols for encryption: RSA, Rabin, ElGamal
- Digital signature, RSA algorithms, ElGamal, DSA
- Elliptic curves, properties of key exchange algorithms (ECDH) and digital signature (ECDSA)
- Discrete Mathematics
- Cardinality of sets. Sets with the same power. Finite and infinite sets. Discrete sets. Countable sets. The cardinality of continuum. Comparison of cardinalities: Cantor-Berstein theorem. Equivalence relations. Equivalence classes. Quotient sets. Partitions.
- The Euclidean division. The greatest common divisor: definition, existence and uniqueness. The Euclidean algorithm and computation of the GCD. Properties of the co-prime numbers and characterisation of prime numbers. The least common multiple. Solution of diophantine linear equations. The unique factorization theorem. Existence of infinite prime numbers.
- Congruence relation modulus a positive integer n. The set of the remainder classes mod. n and its operations. The Chinese theorem of the remainder. Linear congruences. The Euler function and the Euler-Fermat theorem. Public key cryptography methods RSA. Error corrector codes.
- Simple and repeating dispositions; permutations; simple and repeating combinations; permutations on a multiset. Sum and Product Principle. Inclusion/exclusion principle. Da Silva formula.
- Recursion: recursive definitions and recursive algorithms. Closed formulas. Homogenous and non-homogeneous linear recursion relations. Solution of the first-order linear recursive relations. "Divide et impera" type algorithms. Characteristic equation of a recursive relation. Solution of second-order linear homogeneous relations. Fibonacci numbers. The Hanoi tower problem. Some elements of generating functions.
- Special graphs. Graph isomorphisms. Walks; paths; cycles. Connected components. The incidence matrix. Degree of a vertex and graph score. Eulerian and Hamiltonian graphs. Trees and recovering trees. Colourings and chromatic number of a graph; Chromatic polynomial; Whitney theorem.
- Real-Time Embedded System
- Pthread programming: creation, join, scheduling, semaphores, mutexes, conditions.
- Real-Time Scheduling: tasks, jobs, preemptive/non-preemptive systems, latencies, worst-case execution time, mixed-critical systems, periodic/sporadic/aperiodic tasks, scheduling anomalies. Scheduling algorithms: FCFS, SJF, round robin, fixed/dynamic priorities, EDF (and related optimality).
- Schedulability Analysis: Rate Monotonic, Deadline Monotoniv, EDF, and related schedulability tests. Utilization, least upper bound, response time, processor demand.
- Critical instant and worst-case conditions
- Shared resource protocols: priority inversion, NPP, HLP, PIP, PCP, SRP.
- Automotive Connectivity
- Module 1: The first module takes care of the internal vehicle system (inter-vehicular communications). It studies the sensors type, the vehicle hardware architecture, and the application domains in which the sensors and each particular device operate. Together with the architecture, also the typical vehicular signal bus will be studied. We will investigate several protocols: CAN, CAN-FD, LIN, FlexRay, MOST and Automotive Ethernet
- Module 2: The second module takes care of inter-vehicular communications, i.e., the communications between the vehicle and the external world. It studies the protocol suite and the communication standards used to manage communications between vehicles and between a vehicle and the internet. Protocols studied: GPS, Bluetooth, LoRa, and IEEE 802.11p. Even in this case, the focus will be on the applications on top of the communication system, emphasizing the broadcast messages.
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