How does the Euclidean Algorithm work to find the greatest common divisor (GCD) of two integers, and why is it important in cryptographic protocols?
The Euclidean Algorithm is a classical method in number theory used to determine the greatest common divisor (GCD) of two integers. The GCD of two integers and is the largest integer that divides both and without leaving a remainder. This algorithm is foundational in various fields, including cryptography, due to its efficiency and simplicity. How
What is the public-key cryptography (asymmetric cryptography)?
Public-key cryptography, also known as asymmetric cryptography, is a fundamental concept in the field of cybersecurity that emerged due to the issue of key distribution in private-key cryptography (symmetric cryptography). While the key distribution is indeed a significant problem in classical symmetric cryptography, public-key cryptography offered a way to resolve this problem, but additionally introduced
What are the 5 basic steps for the RSA cipher?
The RSA cipher is a widely used public-key encryption algorithm that relies on the mathematical properties of prime numbers and modular arithmetic. It was developed in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman, and has since become one of the most important cryptographic algorithms in use today. The RSA cipher is based on
When was the RSA cryptosystem invented and patented?
The RSA cryptosystem, a cornerstone of modern public-key cryptography, was invented in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman. However, it is important to note that the RSA algorithm itself was not patented in the United States until 2020. The RSA algorithm is based on the mathematical problem of factoring large composite numbers,
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, The RSA cryptosystem and efficient exponentiation
Why in the RSA cipher the public key has one part, while the private key has two parts?
The RSA cipher, which is widely used in public-key cryptography, utilizes a pair of keys: a public key and a private key. These keys are used in modular algebra computations to encrypt and decrypt messages. The public key consists of one part, while the private key consists of two parts. To understand the role of
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, The RSA cryptosystem and efficient exponentiation
Can Euler’s theorem be used to simplify the reduction of large powers modulo n?
Euler's theorem can be indeed used to simplify reduction of large powers modulo n. Euler's theorem is a fundamental result in number theory that establishes a relationship between modular exponentiation and Euler's phi function. It provides a way to efficiently compute the remainder of a large power when divided by a positive integer. Euler's theorem
What is the role of the parameter t in the Extended Euclidean Algorithm (EEA)?
The parameter t of the Extended Euclidean Algorithm (EEA) plays a important role in the field of public-key cryptography, specifically in the context of classical cryptography fundamentals. The EEA is a mathematical algorithm used to find the greatest common divisor (GCD) of two integers and to express it as a linear combination of the two