Secure Computation

Overview

Secure multi-party computation allows a network of mutually distrustful players, each holding a secret input, to run an interactive protocol in order to evaluate a function on their joint inputs in a secure way, i.e. without revealing anything more than what the output of the function might reveal. 

Secure computation is an abstraction of several important applications, including electronic voting, digital auctions, zero knowledge, and more. The course is thought as an introduction to secure computation,  and will cover both its theoretical foundations and its applications to practical settings such as distributed ledgers and cryptographic currencies.

Syllabus

• Computing over encrypted data: Equivalence between semantic security and CPA security. Fully-homomorphic encryption (FHE) and somewhat-homomorphic encryption (SHE). The Learning with Errors (LWE) assumption.  Constructing SHE from LWE.  Bootstrapping theorems.

• Secure two-party computation (2PC): Two-party protocols and definitions for passive and active security. Sequential composition theorem. Zero knowledge for NP. Coin tossing by telephone. Oblivious transfer. Yao's garbled circuits protocol and its optimizations.

• Secure multi-party computation (MPC): Multi-party protocols and definitions for passive and active security. Secret sharing schemes. MPC with honest majority. The SPDZ protocol.

• Cryptocurrencies: The Bitcoin protocol. Distributed ledgers, smart contracts, and altcoins. Applications to secure computation.

Teaching Material

The slides for the course can be downloaded from here. 

The following books are also suggested as further references:

• [1] Yehuda Lindell (Editor). Tutorials on the Foundations of Cryptography (dedicated to Oded Goldreich). Springer, 2017.

• [2] Carmit Hazay and Yehuda Lindell. Efficient Secure Two-Party Protocols, Springer, 2010.

• [3] Ronald Cramer, Ivan Bjerre Damgård, Jesper Buus Nielsen. Secure Multiparty Computation and Secret Sharing. Cambridge University Press, 2015.

Logistics

Lectures time: 

• Monday 10:00 - 13:00. 

• Thursday 10:00 - 12:00. 

Location: Aula Alfa, Via Salaria 113, 00198 Rome. 

Blended Learning: Due to the COVID-19 pandemic the lectures will be offered both in person and online using the rules established by Sapienza University. The lectures will be streamed live using Zoom with the credentials below. The recordings of the lectures will be made available on this page.

Meeting ID: 843 0863 7495 Passcode: 771882

Twitter: @SapienzaCrypto

Classroom (class code: ynf6ysa): https://classroom.google.com/c/NDY3MDE2MTcxMzY3?cjc=ynf6ysa

Grading

Oral exam. Optionally, students may select a project involving some coding (to be chosen together with the istructors), which will be evaluated along with the oral exam.

Announcements

• 04/02/2022: The course will start on February 21, 2022.

• 21/02/2022: The recording of the lecture on 21/02/2022 can be found here. The passcode is: yzH#W!t9. The link expires after 7 days.

• 24/02/2022: The recording of the lecture on 24/02/2022 can be found here. The passcode is: .@.mD19Q. The link expires after 7 days.

• 28/02/2022: The recording of the lecture on 28/02/2022 can be found here. The passcode is: Eh0F4%CZ. The link expires after 7 days.

• 03/03/2022: The recording of the lecture on 03/03/2022 can be found here. The passcode is: #1R1.gP3. The link expires after 7 day.

• 07/03/2022: The recording of the lecture on 07/03/2022 can be found here. The passcode is: ez3VWsD#. The link expires after 7 day.

• 10/03/2022: The recording of the lecture on 10/03/2022 can be found here. The passcode is: 5%uZYM4J. The link expires after 7 day.

• 14/03/2022: The recording of the lecture on 14/03/2022 can be found here. The passcode is: =L8$FCc2. The link expires after 7 day.

• 17/03/2022: The recording of the lecture on 17/03/2022 can be found here. The passcode is: bv@@8f%*. The link expires after 7 day.

• 21/03/2022: The recording of the lecture on 21/03/2022 can be found here. The passcode is: a4j@gJ6r. The link expires after 7 day.

• 24/03/2022: The recording of the lecture on 24/03/2022 can be found here. The passcode is: GkqX!x7*. The link expires after 7 day.

• 27/03/2022: The lesson of 28/03/2022 will be held completely online due to covid reasons.

• 28/03/2022: The recording of the lecture on 28/03/2022 can be found here. The passcode is: ?*L70zbZ. The link expires after 7 day.

• 30/03/2022:  As already said, also the classes of 31/3 and 4/4 will be online due to covid reasons.

• 31/03/2022: The recording of the lecture on 31/03/2022 can be found here. The passcode is: gGCwYt7%. The link expires after 7 day.

• 05/04/2022: The recording of the lecture on 04/04/2022 can be found here. The passcode is: CJ2XPc?1. The link expires after 7 day.

• 05/04/2022: The classes are returning in presence since 07/04/2022. Next lesson will start at 10.30 because Prof.  Lazzeretti is involved in an exam up to 10 AM.

• 07/04/2022: The recording of the lecture on 07/04/2022 can be found here. The passcode is: ^$a7F50n. The link expires after 7 day.

• 11/04/2022: The recording of the lecture on 11/04/2022 can be found here. The passcode is: W*X4uice. The link expires after 7 day.

• 21/04/2022: The recording of the lecture on 21/04/2022 can be found here. The passcode is: ^#1WgcR6. The link expires after 7 day.

• 28/04/2022: The recording of the lecture on 28/04/2022 can be found here. The passcode is: W&+.aT$0. The link expires after 7 day.

• 02/05/2022: The recording of the lecture on 02/05/2022 can be found here. The passcode is: i5AEuX3^. The link expires after 7 day.

• 05/05/2022: The recording of the lecture on 05/05/2022 can be found here. The passcode is: cw6Z@41x. The link expires after 7 day.

• 09/05/2022: The recording of the lecture on 09/05/2022 can be found here. The passcode is: 3Z!QxN.7. The link expires after 7 day.

• 12/05/2022: The recording of the lecture on 12/05/2022 can be found here. The passcode is: #r4*hEsx. The link expires after 7 day.

• 16/05/2022: The recording of the lecture on 16/05/2022 can be found here. The passcode is: 9hiSx=Sy. The link expires after 7 day.

• 19/05/2022: The recording of the lecture on 19/05/2022 can be found here. The passcode is: t#+Gqx9!. The link expires after 7 day.

• 23/05/2022: The recording of the lecture on 23/05/2022 can be found here. The passcode is: S5yq69^=. The link expires after 7 day.

• 26/05/2022: The recording of the lecture on 26/05/2022 can be found here. The passcode is: 8V!ISdmu. The link expires after 7 day.