The Basic Functionality of a Public-Key Cryptosystem

Let's learn how the public-key cryptosystems work and how digital signatures help to provide data integrity.

Key generation

The revolutionary proposal by Diffie and Hellman is based on the idea that Alice and Bob no longer use the same key, but two different keys. This happens with the use of an asymmetric cryptosystem, which consists of two pieces of a pair of complementary keys, namely a private key kprivk_{p r i v} and a public key kpubk_{p u b}. If any plaintext mm was encrypted into ciphertext cc with one of these keys, it can only be decrypted again into plaintext mm with the other key, and vice versa.

The figure below illustrates the basic scheme of the two corresponding keys kpriv k_{\text {priv }} and kpubk_{p u b}, where both of them can be used for encryption or decryption. If encryption of asymmetric keys in public-key cryptography plaintext into ciphertext happened by kpriv k_{\text {priv }}, then decryption back into plaintext can only happen by using kpubk_{p u b} and vice versa.

Hence, the key pair is mathematically related. We’ll outline in the following section how this key pair is to be used in a public-key cryptosystem.

Figure 1

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