Public key infrastructure is a system that uses mathematical permutations to encrypt and decrypt data. This article will discuss the three most popular permutations used in public key infrastructure: RSA, elliptic curve cryptography, and Diffie-Hellman. We will explain the advantages of asymmetric cryptography, how each works, and why they are essential for secure communication.
What Is PKI
PKI is an acronym for Public Key Infrastructure. It is a system of digital certificates, Certificate Authorities (CAs), and other registration authorities that verify and authenticate the identity of individuals and devices. PKI is used to secure communications over networks such as the Internet.
A PKI certificate contains a public key and a private key. The public key is used to encrypt data, and the private key is used to decrypt it. PKI enables users to securely exchange data over insecure channels by using a combination of cryptographic algorithms.
Mathematical Permutations
PKI is a system that uses math to encrypt and decrypt data. This means that it is very hard for people to hack into your computer or steal your information. Three kinds of math are used in PKI: RSA, elliptic curve cryptography, and Diffie-Hellman. Each is special in its own way, and they are all important for keeping your information safe.
RSA
RSA is an algorithm for public-key cryptography widely used in electronic commerce protocols. It is based on the factoring of large integers. The security of RSA rests on the difficulty of factoring large integers. The acronym RSA comes from the initials of the three inventors: Ron Rivest, Adi Shamir, and Len Adleman. RSA keys are used in software programs to encrypt and decrypt messages. They are also used to digitally sign documents, authenticate users, and establish secure communications channels.
The RSA algorithm can be used for both symmetric-key and asymmetric-key cryptography. In symmetric-key cryptography, the same key is used for encryption and decryption. In asymmetric-key cryptography, two keys are used: a public key for encryption and a private key for decryption. The RSA algorithm is commonly used with other algorithms, such as the AES (Advanced Encryption Standard) and the SHA (Secure Hash Algorithm).
ECC
In cryptography, an elliptic curve cryptosystem (ECC) is a public-key cryptosystem that employs pairs of points on an elliptic curve over a finite field Fp or finite field F2m to implement encryption and decryption. The basic idea is to use the algebraic structure of the elliptic curve group, like a generalization of the integers with some unique properties, to design secure protocols against attacks.
ECC is used in many applications, including TLS/SSL, PGP, VPNs, and Wi-Fi. It is also used in many cryptographic schemes such as Diffie–Hellman key exchange, ElGamal encryption, and digital signatures. ECC is based on the algebraic structure of elliptic curves over finite fields and their group properties. A significant advantage of ECC is that it can be used to create much smaller keys than other methods, which is especially important in constrained environments such as smartcards and embedded systems.
In addition, ECC has resistance against quantum computing attacks because most quantum computers cannot efficiently solve the Elliptic Curve Discrete Logarithm Problem (ECDLP). The security of ECC is derived from two algorithms: Elliptic Curve Diffie–Hellman (ECDH) and Elliptic Curve Digital Signature Algorithm (ECDSA). These algorithms are used for key exchange and digital signing, respectively.
No known quantum algorithms can efficiently solve the ECDLP unless the group order is minimal. New schemes such as quantum-resistant elliptic curve cryptography have been proposed to avoid these vulnerabilities.
Diffie-Hellmann
In cryptography, the Diffie–Hellman key exchange method allows two parties with no pre-shared information to jointly establish a shared secret key over an insecure communications channel. This key can then encrypt subsequent communications using a symmetric key cipher.
The Diffie–Hellman key exchange is named after Whitfield Diffie and Martin Hellman, who published this method in 1976. It is a specific method of exchanging keys that uses asymmetric encryption. Asymmetric encryption is a technique that allows anyone to send encrypted messages without having prior access to a secret key. In other words, it will enable two individuals to generate identical keys for symmetric encryption, which uses the same key for encrypting and decrypting data.
Diffie–Hellman is one of the earliest public-key protocols and is widely used in various protocols such as Secure Sockets Layer (SSL), Transport Layer Security (TLS), Pretty Good Privacy (PGP), Internet Protocol Security (IPsec), and Signal protocol. It is also used in some Quantum Key Distribution (QKD) protocol variants.
Final Thoughts
There are many advantages of asymmetric cryptography regarding securing essential data. Public key cryptography is a powerful tool used in many different applications. The three most popular public key cryptography methods are the RSA algorithm, Elliptic Curve Cryptography (ECC), and Diffie–Hellman key exchange.
All three of these methods are essential to the world of cryptography, and each has its place in the world of public key cryptography. Choose the proper method for the correct application, and you’ll be able to keep your data safe from quantum attacks.
