The amethyst you see above and to the right is a 1st century B.C. signet or intaglio depicting the goddess Demeter. It’s an engraved gemstone embedded in a gold ring. In the ancient world, and up until a few centuries ago, signets were deeply important security devices for both personal and official use. They were something like written signatures, but much much more.
Signets created (more or less) copy-proof impressions in wax or clay called seals; to the left of the signet in the banner you see a clay seal it produced. Seals could authenticate documents and enable detection of theft of or tampering with valuables. They validated and protected countless things: Financial ledgers, contracts, wills, private letters, state proclamations, and so forth. The Roman poet Horace even mentions the use of seals by a neighbor to detect when his slaves were drinking his wine.
For millennia, signets were the answer to one of the world’s oldest security challenges:
How can someone mark a document or object with a symbol that is easy to identify but hard to forge?
The mathematical notation you see beside the seal and signet describe a world-changing mathematical solution to this very problem called digital signatures. These algorithms are now a staple of cryptography and computer and internet security more generally.
In a digital signature scheme, a signer holds a numerical value sk, called a private key, that is kept secret and a corresponding public key pk, that may be made known to anyone. The signer applies the private key to a digital document m. The output of this operation is a digital signature on m, denoted by σsk[m]. Anyone who knows pk can verify that the signature is correct. But without knowledge of the secret sk, no one can feasibly forge a signature!
This idea, first advanced in practical form in 1977 in the famous RSA algorithm, is used in nearly every web browser and in countless other places. It’s a near-magical solution to the ancient security challenge of marking documents, and a contemporary answer to the signet. The physical beauty of the engraved gemstones in signets and the conceptual beauty of digital signatures nicely convey the deep importance and exciting ideas underlying computer security.