What are the current and emerging trends and innovations in asymmetric cryptography and public key?

2 Post-quantum signatures

Another area of innovation in asymmetric cryptography is the development of post-quantum signatures, which are digital signatures that can be verified by classical computers, but cannot be forged by quantum computers. Post-quantum signatures are essential for ensuring the integrity and authenticity of data and transactions in a quantum world, especially for applications such as blockchain, IoT, and cloud computing. Some of the promising post-quantum signature schemes include XMSS, SPHINCS, and LMS, which are based on hash functions and Merkle trees.

3 Attribute-based encryption

Attribute-based encryption (ABE) is a novel form of asymmetric cryptography that allows users to encrypt and decrypt data based on their attributes, rather than their identities or keys. For example, a user can encrypt a file with a policy that specifies who can access it based on their roles, locations, or preferences. ABE enables fine-grained access control and data privacy for scenarios such as cloud storage, social networks, and healthcare. There are different types of ABE, such as key-policy ABE, ciphertext-policy ABE, and functional encryption, which vary in how the attributes and policies are defined and enforced.

4 Homomorphic encryption

Homomorphic encryption (HE) is a breakthrough technique that allows performing computations on encrypted data without decrypting it. This means that users can outsource their data and operations to untrusted parties, such as cloud providers or third-party services, without compromising their security or privacy. HE enables new possibilities for applications such as machine learning, data analytics, and voting systems, where sensitive data can be processed and analyzed without revealing its contents. However, HE also poses significant challenges in terms of efficiency, scalability, and usability, which require further research and development.

5 Threshold cryptography

Threshold cryptography (TC) is a method of distributing cryptographic functions among multiple parties, such that no single party can perform the function alone, but a certain number or threshold of parties can cooperate to do so. For example, a private key can be split into several shares, and a signature can be generated only if a majority of the shares are combined. TC enhances the security and resilience of asymmetric cryptography by preventing single points of failure, compromising, or loss. TC can be applied to various domains, such as distributed ledger technology, key management, and multi-factor authentication.

6 Zero-knowledge proofs

Zero-knowledge proofs (ZKPs) are a type of cryptographic protocol that allows one party to prove to another party that they know some information, without revealing the information itself or any other details. For example, a user can prove that they have a valid password, without disclosing the password or any hints. ZKPs enable verifiable and privacy-preserving computation for applications such as identity verification, anonymous credentials, and confidential transactions. Some of the emerging ZKP techniques include zk-SNARKs, zk-STARKs, and bulletproofs, which differ in their assumptions, efficiency, and scalability.