Colorful stories such as that of the Beale ciphers are what most of us associate with cryptography. Yet, modern cryptography differs in at least four important ways from these types of historical examples.

First, historically cryptography has only been concerned with secrecy (or confidentiality). [3] Ciphertexts would be created to ensure that only certain parties could be privy to the information in the plaintexts, as in the case of the Beale ciphers. In order for an encryption scheme to serve this purpose well, decrypting the ciphertext should only be feasible if you have the key.

Modern cryptography is concerned with a wider range of themes than just secrecy. These themes include primarily (1) message integrity—that is, assuring that a message has not been changed; (2) message authenticity—that is, assuring that a message has really come from a particular sender; and (3) non-repudiation—that is, assuring that a sender cannot falsely deny later that she sent a message. [4]

An important distinction to keep in mind is, thus, between an encryption scheme and a cryptographic scheme. An encryption scheme is just concerned with secrecy. While an encryption scheme is a cryptographic scheme, the reverse is not true. A cryptographic scheme can also serve the other main themes of cryptography, including integrity, authenticity, and non-repudiation.

The themes of integrity and authenticity are just as important as secrecy. Our modern communications systems would not be able to function without guarantees regarding the integrity and authenticity of communications. Non-repudiation is also an important concern, such as for digital contracts, but less ubiquitously needed in cryptographic applications than secrecy, integrity, and authenticity.

Second, classical encryption schemes such as the Beale ciphers always involve one key that was shared among all the relevant parties. However, many modern cryptographic schemes involve not just one, but two keys: a private and a public key. While the former should remain private in any applications, the latter is typically public knowledge (hence, their respective names). Within the realm of encryption, the public key can be used to encrypt the message, while the private key can be used for decryption.

The branch of cryptography that deals with schemes where all parties share one key is known as symmetric cryptography. The single key in such a scheme is usually called the private key (or secret key). The branch of cryptography which deals with schemes that require a private-public key pair is known as asymmetric cryptography. These branches are sometimes also referred to as private key cryptography and public key cryptography, respectively (though this can raise confusion, as public key cryptographic schemes also have private keys).

The advent of asymmetric cryptography in the late 1970s has been one of the most important events in the history of cryptography. Without it, most of our modern communication systems, including Bitcoin, would not be possible, or at least very impractical.

Importantly, modern cryptography is not exclusively the study of symmetric and assymetric key cryptographic schemes (though that covers much of the field). For instance, cryptography is also concerned with hash functions and pseudorandom number generators, and you can build applications on these primitives that are not related to symmetric or assymetric key cryptography.

Third, classical encryption schemes, like those used in the Beale ciphers, were more art than science. Their perceived security was largely based on intuitions regarding their complexity. They would typically be patched when a new attack on them was learned, or dropped entirely if the attack was particularly severe. Modern cryptography, however, is a rigorous science with a formal, mathematical approach to both developing and analyzing cryptographic schemes. [5]

Specifically, modern cryptography centers on formal proofs of security. Any proof of security for a cryptographic scheme proceeds in three steps:

Fourth, whereas historically cryptography was primarily utilized in military settings, it has come to permeate our daily activities in the digital age. Whether you are banking online, posting on social media, buying a product from Amazon with your credit card, or tipping a friend bitcoin, cryptography is the sine qua non of our digital age.

Given these four aspects to modern cryptography, we might characterize modern cryptography as the science concerned with the formal development and analysis of cryptographic schemes to secure digital information against adversarial attacks. [6] Security here should be broadly understood as preventing attacks that damage secrecy, integrity, authentication, and/or non-repudiation in communications.

Cryptography is best seen as a subdiscipline of cybersecurity, which is concerned with preventing the theft, damaging, and misuse of computer systems. Note that many cybersecurity concerns have little or only a partial connection to cryptography.

For instance, if a company houses expensive servers locally, they may be concerned with securing this hardware from theft and damage. While this is a cybersecurity concern, it has little to do with cryptography.

For another example, phishing attacks are a common problem in our modern age. These attacks attempt to deceive people via an e-mail or some other message medium to relinquish sensitive information such as passwords or credit card numbers. While cryptography can help address phishing attacks to a certain degree, a comprehensive approach requires more than just using some cryptography.

[3] To be exact, the important applications of cryptographic schemes have been concerned with secrecy. Kids, for instance, frequently use simple cryptographic schemes for “fun”. Secrecy is not really a concern in those cases.

[4] Bruce Schneier, Applied Cryptography, 2nd edn, 2015 (Indianapolis, IN: John Wiley & Sons), p. 2.

[5] See Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, CRC Press (Boca Raton, FL: 2015), esp. pp. 16–23, for a good description.

[6] Cf. Katz and Lindell, ibid., p. 3. I think their characterization has some issues, so present a slightly different version of their statement here.