One way of defining cryptography is as the study of the limits of computing (under adversarial conditions): what can and cannot be computed? During the last decade functionalities that were previously considered unattainable have been shown to be feasible: computing on encrypted data (fully homomorphic encryption, FHE), computing with encrypted programs (obfuscation, iO), associating secret keys to function evaluations on the plaintext (functional encryption, FE). Less generically, operations like private set intersection (PSI) have reached a level of maturity that they can be deployed in practice; secure multiparty computation (MPC) is being commercialised and building blocks (e.g. for PSI) like oblivious PRFs (OPRF) are being standardised.

This research area studies these advanced functionalities both as objects of theoretical computer science, i.e. without an immediate regard for practicality, and with a view of deploying them or variants thereof in practice. This involves studying the underlying hard (lattice) problems, devising techniques for realising certain functionalities efficiently, standards and implementations. For example, researchers in the ISG have been involved in all aspects of developing homomorphic encryption, including cryptanalysis, noise growth analysis, encoding, implementation, and investigating specific practical applications.

• Martin Albrecht
• Carlos Cid
• Rachel Player

• Hiroki Okada, Shinsaku Kiyomoto, Carlos Cid: Integerwise Functional Bootstrapping on TFHE. ISC 2020: 107-125 https://link.springer.com/chapter/10.1007/978-3-030-62974-8_7
• Martin R. Albrecht, Pooya Farshim, Shuai Han, Dennis Hofheinz, Enrique Larraia, Kenneth G. Paterson: Multilinear Maps from Obfuscation. J. Cryptol. 33(3): 1080-1113 (2020) https://ia.cr/2015/780
• Anamaria Costache, Kim Laine, Rachel Player: Evaluating the Effectiveness of Heuristic Worst-Case Noise Analysis in FHE. ESORICS (2) 2020: 546-565 https://ia.cr/2019/493
• Martin R. Albrecht, Alex Davidson, Amit Deo, Nigel P. Smart: Round-optimal Verifiable Oblivious Pseudorandom Functions From Ideal Lattices. PKC 2021: https://ia.cr/2019/1271
• Benjamin R. Curtis and Rachel Player. On the Feasibility and Impact of Standardising Sparse-secret LWE Parameter Sets for Homomorphic Encryption. WAHC'19: Proceedings of the 7th ACM Workshop on Encrypted Computing & Applied Homomorphic Cryptography: 1-10 https://ia.cr/2019/1148  
• Martin R. Albrecht, Melissa Chase, Hao Chen, Jintai Ding, Shafi Goldwasser, Sergey Gorbunov, Shai Halevi, Jeffrey Hoffstein, Kim Laine, Kristin E. Lauter, Satya Lokam, Daniele Micciancio, Dustin Moody, Travis Morrison, Amit Sahai, Vinod Vaikuntanathan: Homomorphic Encryption Standard. IACR Cryptol. ePrint Arch. 2019: 939 (2019) https://homomorphicencryption.org/standard/
• Hiroki Okada, Carlos Cid, Seira Hidano, Shinsaku Kiyomoto: Linear Depth Integer-Wise Homomorphic Division. WISTP 2018: 91-106 https://link.springer.com/chapter/10.1007/978-3-030-20074-9_8
• Hao Chen, Kim Laine, Rachel Player, Yuhou Xia: High-Precision Arithmetic in Homomorphic Encryption. CT-RSA 2018: 116-136 https://ia.cr/2017/809
• Hao Chen, Kim Laine, Rachel Player: Simple Encrypted Arithmetic Library - SEAL v2.1. Financial Cryptography Workshops 2017: 3-18 https://www.microsoft.com/en-us/research/project/microsoft-seal/
• Martin R. Albrecht: On Dual Lattice Attacks Against Small-Secret LWE and Parameter Choices in HElib and SEAL. EUROCRYPT (2) 2017: 103-129 https://ia.cr/2017/047
• Alex Davidson, Carlos Cid: An Efficient Toolkit for Computing Private Set Operations. ACISP (2) 2017: 261-278 https://ia.cr/2016/108
• Martin R. Albrecht, Shi Bai, Léo Ducas: A Subfield Lattice Attack on Overstretched NTRU Assumptions - Cryptanalysis of Some FHE and Graded Encoding Schemes. CRYPTO (1) 2016: 153-178 https://ia.cr/2016/127
• Martin R. Albrecht, Catalin Cocis, Fabien Laguillaumie, Adeline Langlois: Implementing Candidate Graded Encoding Schemes from Ideal Lattices. ASIACRYPT (2) 2015: 752-775 https://ia.cr/2014/928