# CryptoBook

## CryptoBook

- [CryptoBook](https://cryptohack.gitbook.io/cryptobook/master.md)
- [Book Plan](https://cryptohack.gitbook.io/cryptobook/todo.md): A summary we plan to cover
- [Style Guide](https://cryptohack.gitbook.io/cryptobook/style-guide.md): Work in progress
- [Sample Page](https://cryptohack.gitbook.io/cryptobook/style-guide/sample-page.md): A rough guideline to a page
- [Contributors](https://cryptohack.gitbook.io/cryptobook/contributors.md): Optional space to say that you've worked on the book
- [Mathematical Notation](https://cryptohack.gitbook.io/cryptobook/fundamentals/notation.md)
- [Division and Greatest common divisor](https://cryptohack.gitbook.io/cryptobook/fundamentals/division-and-gcd.md): Author: Zademn
- [Euclidean Algorithm](https://cryptohack.gitbook.io/cryptobook/fundamentals/division-and-gcd/euclidean-algorithm.md)
- [Modular Arithmetic](https://cryptohack.gitbook.io/cryptobook/fundamentals/modular-arithmetic.md): Authors: A~Z, perhaps someone else but not yet (or they've decided to remain hidden like a ninja)
- [Theorems of Wilson, Euler, and Fermat](https://cryptohack.gitbook.io/cryptobook/fundamentals/modular-arithmetic/theorems-of-wilson-euler-and-fermat.md)
- [Fermat's Little Theorem in Detail](https://cryptohack.gitbook.io/cryptobook/fundamentals/modular-arithmetic/theorems-of-wilson-euler-and-fermat/fermat-euler-theorem.md): Would you like to be an author?
- [Euler's Theorem in Detail](https://cryptohack.gitbook.io/cryptobook/fundamentals/modular-arithmetic/theorems-of-wilson-euler-and-fermat/eulers-theorem-in-detail.md)
- [Quadratic Residues](https://cryptohack.gitbook.io/cryptobook/fundamentals/modular-arithmetic/quadratic-residues.md)
- [Continued Fractions](https://cryptohack.gitbook.io/cryptobook/fundamentals/continued-fractions.md)
- [Ideals](https://cryptohack.gitbook.io/cryptobook/ideals.md)
- [Polynomials With Shared Roots](https://cryptohack.gitbook.io/cryptobook/polynomials-with-shared-roots.md): Algorithmic Number Theory
- [Integer Factorization](https://cryptohack.gitbook.io/cryptobook/integer-factorization.md)
- [Pollard rho](https://cryptohack.gitbook.io/cryptobook/integer-factorization/pollard-rho.md)
- [Sieves](https://cryptohack.gitbook.io/cryptobook/integer-factorization/sieves.md)
- [Groups](https://cryptohack.gitbook.io/cryptobook/abstract-algebra/groups.md)
- [Another take on groups](https://cryptohack.gitbook.io/cryptobook/abstract-algebra/groups/another-take-on-groups.md)
- [Discrete Log Problem](https://cryptohack.gitbook.io/cryptobook/abstract-algebra/groups/untitled.md)
- [Rings](https://cryptohack.gitbook.io/cryptobook/abstract-algebra/rings.md)
- [Fields](https://cryptohack.gitbook.io/cryptobook/abstract-algebra/fields.md)
- [Polynomials](https://cryptohack.gitbook.io/cryptobook/abstract-algebra/polynomials.md)
- [Untitled](https://cryptohack.gitbook.io/cryptobook/elliptic-curves/untitled.md)
- [Introduction](https://cryptohack.gitbook.io/cryptobook/lattices/definitions.md)
- [LLL reduction](https://cryptohack.gitbook.io/cryptobook/lattices/lll-reduction.md)
- [Gram-Schmidt Orthogonalization](https://cryptohack.gitbook.io/cryptobook/lattices/lll-reduction/gram-schmidt-orthogonalization.md)
- [Lagrange's algorithm](https://cryptohack.gitbook.io/cryptobook/lattices/lll-reduction/gaussian-reduction.md)
- [LLL reduction](https://cryptohack.gitbook.io/cryptobook/lattices/lll-reduction/lll-reduced-basis.md)
- [Lattice reduction](https://cryptohack.gitbook.io/cryptobook/lattices/shortest-vector-problem.md)
- [Minkowski reduced](https://cryptohack.gitbook.io/cryptobook/lattices/shortest-vector-problem/minkowski-reduced.md)
- [HKZ reduced](https://cryptohack.gitbook.io/cryptobook/lattices/shortest-vector-problem/hkz-reduced.md)
- [LLL reduced](https://cryptohack.gitbook.io/cryptobook/lattices/shortest-vector-problem/lll-reduced.md)
- [Applications](https://cryptohack.gitbook.io/cryptobook/lattices/applications.md)
- [Coppersmith algorithm](https://cryptohack.gitbook.io/cryptobook/lattices/applications/coppersmith-algorithm.md)
- [Extensions of Coppersmith algorithm](https://cryptohack.gitbook.io/cryptobook/lattices/applications/extensions-of-coppersmith-algorithm.md)
- [Hard lattice problems](https://cryptohack.gitbook.io/cryptobook/lattices/hard-lattice-problems.md)
- [Lattices of interest](https://cryptohack.gitbook.io/cryptobook/lattices/lattices-of-interest.md)
- [Cryptographic lattice problems](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems.md)
- [Short integer solutions (SIS)](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/short-integer-solutions-sis.md)
- [Learning with errors (LWE)](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/learning-with-errors-lwe.md)
- [Ring-LWE](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/ring-lwe.md)
- [NTRU](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/ntru.md)
- [Interactive fun](https://cryptohack.gitbook.io/cryptobook/lattices/interactive-fun.md)
- [Resources and notations](https://cryptohack.gitbook.io/cryptobook/lattices/resources-and-notations.md)
- [RSA](https://cryptohack.gitbook.io/cryptobook/untitled.md): Will be introduced in this page the fundamentals of RSA, mathematical requirement and also some application with python and openSSL.
- [Proof of correctness](https://cryptohack.gitbook.io/cryptobook/untitled/proof-of-correctness.md)
- [RSA application](https://cryptohack.gitbook.io/cryptobook/untitled/rsa-application.md): Tutorial for application with RSA. We are going to use openSSL, openSSH and pycryptodome for key generation, key extraction and some implementation with python
- [Low Private Component Attacks](https://cryptohack.gitbook.io/cryptobook/untitled/low-private-component-attacks.md)
- [Wiener's Attack](https://cryptohack.gitbook.io/cryptobook/untitled/low-private-component-attacks/wieners-attack.md)
- [Boneh-Durfee Attack](https://cryptohack.gitbook.io/cryptobook/untitled/low-private-component-attacks/boneh-durfee-attack.md)
- [Common Modulus Attack](https://cryptohack.gitbook.io/cryptobook/untitled/common-modulus-attack.md): What to do when the same message is encrypted twice with the same modulus but a different public key?
- [Recovering the Modulus](https://cryptohack.gitbook.io/cryptobook/untitled/recovering-the-modulus.md): When you want to recover N given some (plaintext, ciphertext) pairings
- [Diffie-Hellman](https://cryptohack.gitbook.io/cryptobook/diffie-hellman.md)
- [MITM](https://cryptohack.gitbook.io/cryptobook/diffie-hellman/mitm.md): Explanation of the MITM (Man In The Middle) with the Diffie-Hellmann key exchange
- [Elliptic Curve Cryptography](https://cryptohack.gitbook.io/cryptobook/elliptic-curve-cryptography.md)
- [Encryption](https://cryptohack.gitbook.io/cryptobook/symmetric-cryptography/encryption.md): Author: Chuck\_bartwoski
- [The One Time Pad](https://cryptohack.gitbook.io/cryptobook/symmetric-cryptography/the-one-time-pad.md): Author: chuck\_bartowski
- [AES](https://cryptohack.gitbook.io/cryptobook/symmetric-cryptography/aes.md): Advanced Encryption Standard
- [Rijndael Finite Field](https://cryptohack.gitbook.io/cryptobook/symmetric-cryptography/aes/rijndael-finite-field.md)
- [Round Transformations](https://cryptohack.gitbook.io/cryptobook/symmetric-cryptography/aes/round-transformations.md)
- [Introduction / overview](https://cryptohack.gitbook.io/cryptobook/hashes/introduction-overview.md)
- [The Birthday paradox / attack](https://cryptohack.gitbook.io/cryptobook/hashes/the-birthday-paradox-attack.md)
- [Introduction to Isogeny Cryptography](https://cryptohack.gitbook.io/cryptobook/isogeny-based-cryptography/introduction-to-isogeny-cryptography.md)
- [Isogenies](https://cryptohack.gitbook.io/cryptobook/isogeny-based-cryptography/untitled.md)
- [Isogeny and Ramanujan Graphs](https://cryptohack.gitbook.io/cryptobook/isogeny-based-cryptography/isogeny-and-ramanujan-graphs.md)
- [Sets and Functions](https://cryptohack.gitbook.io/cryptobook/appendices/sets-and-functions.md)
- [Probability Theory](https://cryptohack.gitbook.io/cryptobook/appendices/probability-theory.md)