 # Module description - Mathematics for Datacommunication (Mathematik für die Datenkommunikation)

 Number mada ECTS 3.0 Level basic Overview This course introduces the students into the fundamental mathematical notions and results of elementary number theory used in data communication, and gives some applications. ContentsA data communication modelProblems of data communicationNumber Theory for Public Key CryptographyArithmetic in ZModular arithmeticExtended euclidean algorithmLinear diophantic equations in two variablesSquare-and-multiply algorithmComplexityGroup TheoryProperties of groupsExamples of groups: Z/nZ, Z/nZ* etc.Subgroups and cosetsHomomorphisms of groupsRSA and Diffie-HellmanKey generationEncryption and decryptionKey-agreement protocolMan-in-the-middle attackCodesExamples of CodesError-recognizing and error-correcting codesLinear codesSyndrome decodingApplications(The order and emphasis of the topics are left to the lecturers.) Learning objectives Number TheoryThe students understand the fundamental notions of elementary number theory. They are able to compute with residue classes. They understand the extended euclidean algorithm and the square-and-multiply algorithm for modular exponentiation. They are able to apply these algorithms and to explain their complexities. They are able to solve linear diophantic equations in two variables.Group TheoryThe students are able to explain what a group is, know some examples of groups and can calculate in the groups Z/nZ und Z/nZ*. They understand the notions of cyclic groups, generating elements, the order of a group and the order of an element. They understand subgroups and cosets, and know that the order of a subgroup of a finite group always divides the order of the group. In simple cases, they are able to determine the subgroups of a group. They can explain what a group homomorphism is and know some examples.RSA and Diffie-Hellman The students are able to generate RSA-keys and to encrypt and decrypt messages. They know some precautions for the key generation. They know the Diffie-Hellman protocol and are able to use this protocol.They understand the man-in-the-middle attack CodesThe students know what (n,M,d)-codes are and can explain their parameters.They know some specific codes and are able to use these codes for error-correction. In simple cases, they are able to decode linear codes by syndrome decoding. Previous knowledge Number TheoryThe students understand the fundamental notions of elementary number theory. They are able to compute with residue classes. They understand the extended euclidean algorithm and the square-and-multiply algorithm for modular exponentiation. They are able to apply these algorithms and to explain their complexities. They are able to solve linear diophantic equations in two variables.Group TheoryThe students are able to explain what a group is, know some examples of groups and can calculate in the groups Z/nZ und Z/nZ*. They understand the notions of cyclic groups, generating elements, the order of a group and the order of an element. They understand subgroups and cosets, and know that the order of a subgroup of a finite group always divides the order of the group. In simple cases, they are able to determine the subgroups of a group. They can explain what a group homomorphism is and know some examples.RSA and Diffie-Hellman The students are able to generate RSA-keys and to encrypt and decrypt messages. They know some precautions for the key generation. They know the Diffie-Hellman protocol and are able to use this protocol.They understand the man-in-the-middle attack CodesThe students know what (n,M,d)-codes are and can explain their parameters.They know some specific codes and are able to use these codes for error-correction. In simple cases, they are able to decode linear codes by syndrome decoding. Exam format Continuous assessment grade with final written exam
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