What Is Trapdoor Function

This section describes what is Trapdoor Function - An operation that is much easier to perform than its reverse operation.

Let's pause for a moment on the discussion of DLP and take a look at the definition of Trapdoor Function.

What Is Trapdoor Function? A Trapdoor Function is an operation that is much easier to perform than its reverse operation.

Multiplication of two large prime numbers is a trapdoor function because:

1. Performing the multiplication of two given large prime numbers is easy. For example, p=... and q=... are two prime number, f(p,q)=p*q=... can be easily calculated.

2. If f(p,q)=p*q=... is given, find p and q is called factoring an integer into prime numbers, and is difficult.

Of course, when p and q are very small, factoring p*q is not that difficult. So f(p,q)=p*q is a trapdoor function, only when p and q and large prime numbers.

By the way, f(p,q)=p*q, as a trapdoor function has been widely used in cryptography to generate public and private keys.

Trapdoor concept is also used build mouse traps (source: caramembuatkue.info). Easy to pass in one direction, and difficult to pass in the reverse direction.

Mouse Trap Device with Trapdoors
Mouse Trap Device with Trapdoors

Last update: 2019.

Table of Contents

 About This Book

 Geometric Introduction to Elliptic Curves

 Algebraic Introduction to Elliptic Curves

 Abelian Group and Elliptic Curves

Discrete Logarithm Problem (DLP)

 Doubling or Squaring in Abelian Group

 Scalar Multiplication or Exponentiation

 What Is Discrete Logarithm Problem (DLP)

 Examples of Discrete Logarithm Problem (DLP)

What Is Trapdoor Function

 DLP And Trapdoor Function

 Scalar Multiplication on Elliptic Curve as Trapdoor Function

 Finite Fields

 Generators and Cyclic Subgroups

 Reduced Elliptic Curve Groups

 Elliptic Curve Subgroups

 tinyec - Python Library for ECC

 EC (Elliptic Curve) Key Pair

 ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

 ECDSA (Elliptic Curve Digital Signature Algorithm)

 ECES (Elliptic Curve Encryption Scheme)

 Terminology

 References

 Full Version in PDF/EPUB