Cryptography

There have been 4 completed talks and 2 topic suggestions tagged with cryptography.

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Completed Talks

Group Theoretic Attacks on the Enigma Cipher

Delivered by Laindon Burnett on Friday March 31, 2017

General Secure Multi-Party Computation from any Linear Secret-Sharing Scheme

Delivered by Zihao Zhu on Friday February 17, 2017

As more and more sensitive data gets digitized, there is a need to ensure privacy and reliability of the data, especially in the face of adversarial parties who attempt to corrupt or unwanted access to sensitive secrets.

In many instances such as online gambling, bidding, and even Google's targeted advertisements, a client wants to be able to take inputs from multiple sources (for example, auction bids) and produce an output (for example, the highest bidder) without revealing any information about the other inputs. We will use such scenarios as well as more cryptography related ones in order to motivate Multi-Party Computation as a method to compute on encrypted data. With MPC, we will quickly see it's limitations with unsecure channels and first develop secret sharing schemes (specifically linear secret sharing schemes) such as Shamir's scheme, and soon after, verifiable secret sharing schemes.

We will introduce the different types of adversarial structures and explore both the robustness and limitations of secret sharing schemes against them.

Finally, we will show that all Linear Secret Sharing Schemes can be constructed to be verifiable. We will explore the consequences of this and discuss techniques in their construction.

Prereqs: Math136 used in proofs

A summary of this talk is available here.

Bitcoin and the Blockchain

Delivered by Ben Zhang on Friday February 17, 2017

In this talk, we will learn about the principles behind the Double Spend Problem, the Blockchain, and explore the various ways this technology is being used today.

Transferring money in the physical world is easy. However, the transfer of virtual currency is not as easy to validate. The Double Spend Problem has long stood in the way of a free (libre et gratis) virtual currency, and the world found a need for a third party (usually in the form of large banks) to validate all virtual transactions.

In 2008, a mysterious individual known as Satoshi Nakamoto published a paper titled "Bitcoin: A Peer-to-Peer Electronic Cash System" which describes a system for virtual transactions to be validated through the distributed computing power of the community. The system, known as the Blockchain, uses hashing and non-deterministic mathematics to protect itself from Double Spending attacks. Nakamoto's paper led to the creation of free online currencies such Bitcoin, Litecoin, and Ethereum, which are used in marketplaces today.

Prerequisite Information: Middle school math.

Voting with Homomorphic Encryption

Delivered by Sidhant Saraogi on Friday December 2, 2016

In light of the recently concluded Elections or as John Oliver would call it “A horifying glimpse at Satan's Pinterest Board 2016”, “The One who must not be named” has repeatedly insinuated that the elections have been rigged. Our humble aim, present a voting scheme where:

each voter casts exactly one ballot.
voting is anonymous.

We delve into two areas on our way to prove our goal :

Blind Signatures, which allow for anonymous voting
Pallier Cryptosystem, which gives us the ability to sum up the votes even though they have been encrypted thus allowing the election to be “publically audited”.

We might also, if time permit, talk about more modern systems of enabling fair elections that have even been implemented in real life.

This talk is based off Ron Rivest’s lecture, of which a summary is available.

Talk Suggestions

Galois Field Arithmetic

A Galois field is a finite field and are used in a variety of applications, including in classical coding theory and cryptography algorithms. This topic studies how to efficiently optimize arithmetic in such fields.

Possible reference materials for this topic include

Quick links: Google search, arXiv.org search, propose to present a talk

algebra algorithm computer science cryptography efficiency field theory