Discrete Mathematics - Vol 3 | 17. More Applications of Groups by Abraham | Learn Smarter
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17. More Applications of Groups

The chapter delves into the concept of discrete logarithms within cyclic groups and their cryptographic implications, particularly in relation to key exchange protocols like those of Diffie and Hellman. It emphasizes the difficulty in computing discrete logarithms and reviews their foundational role in secure communications protocols.

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Sections

  • 17.1

    Discrete Mathematics

    This section introduces the discrete logarithm and its applications in cryptography, focusing on the discrete logarithm problem and the Diffie-Hellman key exchange protocol.

    Learning Practice

  • 17.2

    More Applications Of Groups

    This section explores the concept of discrete logarithms and their crucial applications in cryptography, including the Diffie-Hellman key exchange protocol.

    Learning Practice

  • 17.2.1

    Discrete Logarithm And The Discrete Logarithm Problem

    This section introduces the concept of discrete logarithms and the discrete logarithm problem, emphasizing their applications in cryptography.

    Learning Practice

  • 17.2.2

    Definition Of Discrete Logarithm

    This section introduces the concept of discrete logarithm within cyclic groups and its significance in cryptography, particularly in key exchange protocols.

    Learning Practice

  • 17.2.3

    Computational Difficulty Of Discrete Logarithm

    This section delves into the concept of discrete logarithms, their computational difficulty, and their importance in cryptographic applications.

    Learning Practice

  • 17.2.4

    Easy Computation In Certain Cyclic Groups

    This section introduces discrete logarithms in cyclic groups and their significance in cryptographic applications.

    Learning Practice

  • 17.2.5

    Difficult Computation In Certain Cyclic Groups

    This section introduces the concept of discrete logarithms within cyclic groups and explores the complexity of computing discrete logarithms, as well as their cryptographic implications.

    Learning Practice

  • 17.2.6

    Applications Of Discrete Log Problem In Cryptography

    The discrete logarithm problem is foundational in cryptography, enabling secure key exchanges such as the Diffie-Hellman protocol.

    Learning Practice

  • 17.2.7

    Key Agreement Problem

    The Key Agreement Problem discusses the discrete logarithm and its significance in cryptography, particularly in the Diffie-Hellman key exchange protocol.

    Learning Practice

References

ch66 - part A.pdf

Class Notes

Memorization

What we have learnt

  • The discrete logarithm is d...
  • The difficulty of computing...
  • Cryptography utilizes discr...

Final Test

Revision Tests