Public key cryptography is a family of cryptographic techniques where a party, say Alice, initially sets up a secret decryption key that she keeps to herself. She also generates a corresponding public encryption key that anyone, say Bob, can use to encrypt data, such that only Alice can recover the data. Equally important are digital signatures, where a party holding a secret key can generate a signature on a message such that anyone knowing the corresponding public key can verify the signature. In this way one can make sure that a message really comes from a particular sender. 

Public key cryptography is the foundation of security on the Internet and is used millions of times every day. For instance, the nation-wide Danish MitID system uses digital signatures to verify user’s identities.

The Aarhus group has contributed new constructions of public key encryption with useful additional algebraic properties, enabling new applications, to secure voting. We have also worked on constructions of advanced digital signatures allowing authenticated off-the-record communication in a group of parties, where an external adversary cannot after the fact demand to be told what was sent. In addition, we have designed new post-quantum secure digital signature schemes, more on this can be found in the section on post-quantum cryptography.

Public key cryptography secures digital communication, protects user privacy, and enables trust in online services. From national ID systems like MitID to secure voting and private group chats, its real-world applications support digital democracy and safeguard civil liberties, both now and in a post-quantum future.