How to cryptography 101

As many people have asked Omina how can they be good at cryptography like her, she prepared this post for everyone to get a solid start!

Cryptography? can I eat it?

Cryptography is the beautiful art and study of techniques used for secure communication in the presence of adversarial behavior! which helps Omnia keeps her secrets away from Sora:)

What do I need to know about cryptography?

MATH!MATH, and even more MATH, some computer science and cybersecurity is also required.

What fields do i exactly need to know?

ABSTRACT ALGEBRA! ABSTRACT ALGEBRA!, and even more ABSTRACT ALGEBRA!

Also we use a lot of number theory, and a knowledge of linear algebra is also extensively used in specific aspects of cryptography. In addition, some discrete math is a good to know too.

As for your computer science, you need good understanding of logical computation, at least one scripting language (use python, just python) and some “computer science common sense”.

Topics to read?

Ciphers	Post Quantum cryptography	Groups
Applied Cryptography	What does it mean to say that a cryptosystem is secure?	Rings
Historical cryptography	Proofs of Security	Fields
Modern cryptography	Threat Models	Greatest Common Divisor
Encoding and decoding	Adversary Goals	Chinese Remainder Theorem
Encryption and decryption	Perfect Secrecy	Fermat’s little theorem
Keys	Perfect Indistinguishability	Bits & Bytes
Spaces	Adversarial Indistinguishability	Binary system
Oracles	The definition of a key	Decimal & Octal & Hexadecimal systems
Hashes	Keys vs passwords	ASCII
Signatures	Characteristics of keys and common requirements	Hex
Zero knowledge proof	Types of keys	Base64
Random Number Generators	True Random Number Generators (TRNG)	Data formats
Pseudo Random Number Generators (PRNG)	Cryptographically Secure Pseudo Random Number Generators (CSPRNG)	The modulus operator
Python	Pycryptodome	Sage
Z3	The XOR operator	Properties of XOR
One Time Pad (OTP)	Symmetric encryption	Block ciphers
Modes of operations	How AES works	Attacks against AES
What is a stream	Padding	RC4
Salsa20 & ChaCha20	Textbook RSA	Padded RSA
Attacks against RSA	Discrete logarithm problem	Diffie-hellman key exchange
Elliptic Curves Cryptography	Signatures	Signature scheme’s security
Common signatures	One way functions	Hashes
Hash collision	Examples	Attacks
Zero knowledge proof	Cryptanalysis

This is very very short list and learning all of these concepts will make you “not beginner”

Reading where?

These are the books that Omnia have used to be good at cryptography.

1. Understanding cryptography by Christof Paar , Jan Pelzl , Tim Güneysu

This is the ultimate cryptography book, Omnia uses it all the time and it is really good at explaining everything, and is specially good at introducing new concepts.

2. Crypto 101 by Laurens Van Houten

Very good beginner’s book, sadly it has many incomplete sections, but it is very good at visually explaining concepts.

3. Algebra for Cryptologists by Alko R. Meijer

This book is a MUST for any advanced cryptography, skip reading the rest of this, go read it NOW.

4. Handbook of Applied Cryptography by A.J. Menezes et al.

Very good “what was that again” book. lives up to it’s name as “Handbook”.

5. Privacy and Authentication: An Introduction to Cryptography by Whitfield Diffie and Martin Hellman

Did I see these names before? Yes! these are the guys behind the Diffie-Hellman key exchange. It is very hard to read though tho(Omnia’s eyes were hurt reading this 90’s font)

6. Finite Fields by Tanja Lange

Very good sheet explaining group theory and finite fields, the author also has a YouTube channel that explains many concepts in cryptography.

7. Number Theory and Algebra by Tanja Lange

Same as above for number theory.

8. A Graduate Course in Applied Cryptography by Dan Boneh and Victor Shoup

Another “celebrity” book by Boneh, known for his Boneh-Durfee Attack in RSA, didn’t complete it but it is very good.

Honorable mention

These are books that Omina didn’t read but her friends say that they are good.

Lecture Notes on Cryptography by Szabolcs Tengely.
A Course in Cryptography by Rafael Pass and Abhi Shelat.
Fundamentals of Cryptology by Henk van Tilborg.
Mathematics of Public Key Cryptography by Steven Galbraith.
A Tutorial on Linear and Differential Cryptanalysis by Howard Heys.

Vidoes where?

Dirty hands where?

Omnia once spent too much time looking at books, but then she couldn’t solve any challenge because she wasn’t practicing, so she decided that she needs to always apply the knowledge she has to and play with the mud!