There are two types of cryptosystems: secret-key and public-key cryptography (see Questions 2.1.2 and 2.1.1). In secret-key cryptography, also referred to as symmetric cryptography, the same key is used for both encryption and decryption. The most popular secret-key cryptosystem in use today is the Data Encryption Standard (DES; see Section 3.2).
In public-key cryptography, each user has a public key and a private key. The public key is made public while the private key remains secret. Encryption is performed with the public key while decryption is done with the private key. The RSA public-key cryptosystem (see Section 3.1) is the most popular form of public-key cryptography. RSA stands for Rivest, Shamir, and Adleman, the inventors of the RSA cryptosystem.
The Digital Signature Algorithm (DSA; see Section 3.4) is also a popular public-key technique, though it can only be used only for signatures, not encryption. Elliptic curve cryptosystems (ECCs; see Section 3.5) are cryptosystems based on mathematical objects known as elliptic curves (see Question 2.3.10). Elliptic curve cryptography has been gaining in popularity recently. Lastly, the Diffie-Hellman key agreement protocol (see Question 3.6.1) is a popular public-key technique for establishing secret keys over an insecure channel.