Discrete Mathematics - Vol 3 | Basics 23 by Abraham | Learn Smarter
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Basics 23

This chapter introduces the concept of secret sharing in cryptography, particularly focusing on Shamir's (n, t) secret sharing scheme. It explains the motivation behind secret sharing through real-world applications like banking and national security. The chapter discusses the mathematical foundation of secret sharing, including the use of polynomials over finite fields, and details the properties that make the scheme secure against unauthorized access.

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Sections

  • 1

    Foundations Of Cryptography

    This section introduces the concept of secret sharing in cryptography, discussing the (n, t) secret sharing scheme and its applications, particularly in enhancing security for sensitive operations.

    Learning Practice

  • 1.1

    Secret Sharing Problem Motivation

    The section introduces the concept of secret sharing, highlighting its importance through real-world applications and illustrating the (n, t) secret sharing framework.

    Learning Practice

  • 1.2

    General Problem Definition Of (N, T) Secret Sharing

    The section discusses the (n, t) secret sharing paradigm, where secrets are shared among parties with a threshold for reconstruction to ensure security.

    Learning Practice

  • 1.3

    Shamir's (N, T) Secret Sharing Scheme

    Shamir's (n, t) Secret Sharing Scheme offers a method for distributing a secret among a group of shareholders, enabling recovery only when a specified threshold of shareholders cooperate.

    Learning Practice

  • 1.4

    Description Of Finite Field And Polynomial Properties

    This section discusses the concept of finite fields, relevant properties of polynomials over such fields, and their applications in cryptography, particularly in secret sharing schemes.

    Learning Practice

  • 2

    Shamir’s Secret Sharing Protocol

    This section introduces Shamir's Secret Sharing Protocol, discussing its motivation, workings, and application in cryptography.

    Learning Practice

  • 2.1

    Setup Of Shamir’s Secret Sharing Scheme

    This section introduces Shamir's Secret Sharing Scheme, explaining its structure and fundamental concepts related to secret sharing problems in cryptography.

    Learning Practice

  • 2.2

    Proof Of Privacy In Shamir’s Secret Sharing

    This section delves into Shamir's Secret Sharing scheme, detailing its privacy guarantees and the theoretical background behind the (n, t) secret sharing model.

    Learning Practice

References

ch72.pdf

Class Notes

Memorization

What we have learnt

  • Secret sharing is a method ...
  • Shamir’s secret sharing sch...
  • The requirements of any val...

Final Test

Revision Tests