Meri Leeworthy

Introduction to asymmetric cryptography

In the previous lessons, your focus has been on studying the aspects of symmetric encryption. While this technique is powerful and efficient, it relies on the utmost secrecy being maintained in respect to the key. Provided both communicating parties had access to the key, the encryption and decryption of messages was simple. However, despite all of these benefits, symmetric cryptosystems posed two main challenges:

Symmetric cryptosystems generally relied on permutation and substitution mechanisms to encipher and decipher messages. These mechanisms were not able to address the two main issues. This was resolved with the introduction of asymmetric cryptography or public key cryptosystems.

Asymmetric cryptosystems use a pair of related keys rather than a single key. Both keys were generated using a mathematical function which could easily be computed one way but the reverse was infeasible or extremely computationally intensive. The foundational premise of asymmetric cryptosystems is that since the key pair were paired, either could be used to perform one operation and the other could then be used for the inverse operation. This allowed users to maintain a private key, which they kept secret and a public key, which could be shared with anyone. Messages encrypted with the public key could then only be deciphered with the private key and vice versa. This technique revolutionised modern cryptography alleviating many of the challenges associated with symmetric cryptosystems.

As asymmetric cryptosystems use different keys for encryption and decryption, they need different algorithms in place as well to perform each function. In order to define such an algorithm, it must meet the following requirements:

public − PUb      private − PRb

C = E(PUb, M)C = E(PUb​, M)

M = D[PUb, E(PRb, M)] = D[PRb, E(PUb, M)]

A high level illustration of the asymmetric cryptosystem can be defined as shown in the image below.

Any asymmetric cryptosystem generally consists of the following six aspects:

It is important to note that for any two parties communicating both sender and receiver must use the sender’s keypair when transmitting a message.

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