### Backdoors in Block Ciphers, Theory and Practice

Description: The main question is that given a complex structure of some real-life cipher can we design an S-box which makes this cipher weaker than expected.

Prerequisites: Strong algebra required, COMPGA18 obligatory, matrices, polynomials, Boolean functions, ANF, Differential Linear and Generalized Linear Cryptanalysis, some scientific programming background with polynomials in C++ or SAGE maths, SAT solvers and other software tools for cryptanalysis.

### Cold War Cryptography and Modern Block Ciphers

##### Description

We will study how various historical ciphers such as East-German T-310, Russian GOST cipher etc. We will exploit correlation, LC, DC, self-similarity, fixed points, involutions, reflection attacks etc.

##### Prerequisites

Maths, good grade in all cryptography modules, maybe some programming.

### Cryptanalysis of T-310

We will study the T-310 stream cipher used by Eastern German government during the Cold War. We will study the applicability of all known classical attacks on block and stream ciphers.

**Prerequisites:** COMPGA18 obligatory, good maths, matrices, polynomials, Boolean functions, ANF.

### Recovery of Private Keys in Crypto Currency Wallet

Description: We are going to study how provate keys can be recovered in specific attacks scenarios and design optmized key recovery techniques based on graphs and linear algebra. We will study different types of digital signature schemes nad possibilities offered by new upgrades of bitcoin with Schnorr signatures etc. We will study key derivation BIP32/44/48 standards, RF6979, HMAC, SHA256 and SHA256 and OpenSSL rng, and see how exactly these are or can be implemented and see how these can be attacked by side channel attacks in theory and in practice.

Prerequisites: COMPGA18,maths, programming, algebra, digital signatures, elliptic curves.

### Segregated Witness Digital Signatures and Off-Chain Payments in Bitcoin

We will study possibilities offered by new upgrades of bitcoin with Schnorr signatures.

**Prerequisites:** COMPGA12, COMPGA03 intro to cryptography, good programming, maths.

### Efficient Algebraic Coding of ECC Problems

We will study some selected topics covered in this paper such as D73 Theorem page 61. The main problem is given a set of solutions defined by ECC relations and constraints what is the most efficient method to encode them as low degree polynomial equations mod P? Another problem is, can such systems of equations be solved by software at a reasonable cost? A key problem is how the complexity of algebraic coding can be reduced by using redundant expansions on the set of variables. We dispose of a ready

suite of software solutions which allows one to explore these problems.

**Prerequisites:** COMPGA12 ECC labs, COMPGA18 Cryptanalysis obligatory, maths/algebra, scientific programming with polynomials in C/C++ or SAGE maths.