# An overview on Fully Homomorphic Encryption, Multilinear Maps and Obfuscation

Università degli Studi Trento

38123 Povo (TN)

Tel +39 04 61/281508-1625-1701-3898-1980.

dept.math [at] unitn.it

**Luogo:** Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari **“**-1**” **

**Ore** 14:00

**Relatore: **

**Elena Pagnin**

**Abstract: **Can we do arbitrary computations on data while it remains encrypted? After more than 30 years of research we now know that this is achievable via Fully Homomorphic Encryption (FHE) and Multi-Linear Maps (MLM). Intuitively, FHE enables an untested party to compute on (someone else’s) encrypted data, and output a cipher-text which decrypts to the actual result of the desired computation on the corresponding plain-texts. Similarly to FHE, MLMs let us encode data in a manner that simultaneously hides it and permits processing on it. In addition, MLMs let us recover some limited information (such as equality testing) on the processed data without needing any secret key.

But, what if we are interested in hiding the computation itself (in the form of a program / algorithm), rather than the the data on which to compute? This is the aim of Obfuscation. Intuitively, Obfuscation makes a program unintelligible while preserving its functionality, i.e., while ensuring the same input-output behaviour as the original (unobfuscated) program.

In this talk, I will highlight similarities and differences between FHE, MLM and Obfuscation. In particular, I will explain the high-level intuition behind these three cryptographic primitives and present the explicit CRT13 candidate construction for MLM and a zeroing attack against it.

**Referente: Massimiliano Sala**