Was public-key cryptography introduced for use in encryption?
The question of whether public-key cryptography was introduced for the purpose of encryption requires an understanding of both the historical context and the foundational objectives of public-key cryptography, as well as the technical mechanisms underlying its most prominent early systems, such as RSA. Historically, cryptography was dominated by symmetric-key algorithms, where both parties shared a
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, The RSA cryptosystem and efficient exponentiation
Is the encryption function in the RSA cipher an exponential function modulo n and the decryption function an exponential function with a different exponent?
The RSA cryptosystem is a foundational public-key cryptographic scheme based on number-theoretic principles, specifically relying on the mathematical hardness of factoring large composite numbers. When examining the encryption and decryption functions in RSA, it is both accurate and instructive to characterize these operations as modular exponentiations, each employing a distinct exponent. Key Generation in RSA
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, The RSA cryptosystem and efficient exponentiation
What does Fermat’s Little Theorem state?
Fermat's Little Theorem is a foundational result in number theory and plays a significant role in the theoretical underpinnings of public-key cryptography, particularly in the context of algorithms such as RSA. Let us analyze the theorem, its statement, and its didactic value, specifically within the context of cryptography and number theory. Correct Statement of Fermat’s
What is EEA ?
In the field of cybersecurity, particularly within the domain of classical cryptography fundamentals and the introduction to public-key cryptography, the term "EEA" refers to the Extended Euclidean Algorithm. This algorithm is a vital tool in number theory and cryptographic applications, especially in the context of public-key cryptography systems such as RSA (Rivest-Shamir-Adleman). The Euclidean Algorithm
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, Number theory for PKC – Euclidean Algorithm, Euler’s Phi Function and Euler’s Theorem
In RSA cipher, does Alice need Bob’s public key to encrypt a message to Bob?
In the context of the RSA cryptosystem, Alice indeed requires Bob's public key to encrypt a message intended for Bob. The RSA algorithm is a form of public-key cryptography, which relies on a pair of keys: a public key and a private key. The public key is used for encryption, while the private key is
How many part does a public and private key has in RSA cipher
The RSA cryptosystem, named after its inventors Rivest, Shamir, and Adleman, is one of the most well-known public-key cryptographic systems. It is widely used for secure data transmission. RSA is based on the mathematical properties of large prime numbers and the computational difficulty of factoring the product of two large prime numbers. The system relies
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, The RSA cryptosystem and efficient exponentiation
Can public key be used for authentication if the asymmetric relation in terms of complexity in computing keys is reversed?
Public-key cryptography fundamentally relies on the asymmetric nature of key pairs for secure communication, encryption, and authentication. In this system, each participant possesses a pair of keys: a public key, which is openly distributed, and a private key, which is kept confidential. The security of this system hinges on the computational difficulty of deriving the
What are eulers theorem used for?
Euler's theorem is a fundamental result in number theory that has significant applications in the field of public-key cryptography. The theorem states that for any integer and a positive integer that are coprime (i.e., ), the following congruence holds: Here, represents Euler's totient function, which counts the positive integers up to that are
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, Number theory for PKC – Euclidean Algorithm, Euler’s Phi Function and Euler’s Theorem
What are eulers theorem used for?
Euler's Theorem is a fundamental result in number theory, which states that for any integer and a positive integer that are coprime (i.e., their greatest common divisor is 1), the following congruence relation holds: Here, is Euler's Totient Function, which counts the number of positive integers up to that are relatively prime to
What is the exponentiation function in the RSA cipher?
The RSA (Rivest-Shamir-Adleman) cryptosystem is a cornerstone of public-key cryptography, which is widely used for securing sensitive data transmission. One of the critical elements of the RSA algorithm is the exponentiation function, which plays a pivotal role in both the encryption and decryption processes. This function involves raising a number to a power, and then
- Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, Introduction to public-key cryptography, The RSA cryptosystem and efficient exponentiation