ENCRYPTION

NTRU is an open source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data. It consists of two algorithms: NTRUEncrypt, which is used for encryption, and NTRUSign, which is used for digital signatures. Unlike other popular public-key cryptosystems, it is resistant to attacks using Shor's algorithm. NTRUEncrypt was patented, but it was placed in the public domain in 2017. NTRUSign is patented, but it can be used by software under the GPL.

NTRU is an abbreviation for "Nth degree truncated polynomial ring units."

NTRU - Wikipedia

1996 by Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman
2016, Daniel Bernstein, Chitchanok Chuengsatiansup, Tanja Lange and Christine van Vredendaal released NTRU Prime

XTR encryption

XTR is an algorithm for public-key encryption, relying on the difficulty of the DLP. XTR stands for 'ECSTR', which is an abbreviation for Efficient and Compact Subgroup Trace Representation. It relies on the difficulty of solving Discrete Logarithm related problems in the full multiplicative group of a finite field. Unlike many cryptographic protocols that are based on the generator of the full multiplicative group of a finite field, XTR uses the generator g of a relatively small subgroup of some prime order q of a subgroup.

XTR - WikipediaLenstra Verheul

Authenticated encryption

Authenticated encryption (AE) and authenticated encryption with associated data (AEAD) are forms of encryption which simultaneously assure the confidentiality and authenticity of data.

Six different authenticated encryption modes (namely OCB 2.0, Key Wrap, CCM, EAX, Encrypt-then-MAC (EtM), and GCM) have been standardized in ISO/IEC 19772:2009. More authenticated encryption methods were developed in response to NIST solicitation.

Basics

Homomorphic encryption

Homomorphic encryption is a form of encryption that allows computation on ciphertexts, generating an encrypted result which, when decrypted, matches the result of the operations as if they had been performed on the plaintext.

Basics

Homomorphic encryption - Wikipedia
Homomorphic encryption consortium - a consortium of industry, government and academia to standardise homomorphic encryption

Systems

Paillier - Wikipedia

Invented by and named after Pascal Paillier in 1999
Is a probabilistic asymmetric algorithm for public key cryptography
Based on the problem of computing n-th residue classes, i.e. the decisional composite residuosity assumption
Is an additive homomorphic cryptosystem; this means that, given only the public key and the encryption of m₁ and m₂ , one can compute the encryption of m₁ + m₂.

MPC

Secure multi-party computation (also known as secure computation, multi-party computation (MPC), or privacy-preserving computation) is a subfield of cryptography with the goal of creating methods for parties to jointly compute a function over their inputs while keeping those inputs private. Unlike traditional cryptographic tasks, where cryptography assures security and integrity of communication or storage and the adversary is outside the system of participants (an eavesdropper on the sender and receiver), the cryptography in this model protects participants' privacy from each other.

Related to Shamir's 'How to share a secret'.