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Computer Security Algorithms

Problems related to computer security. Algorithms written in Python. Follow the Tutorial

Main topics (Tags)

  • RSA: RSA stands for Rivest-Shamir-Adleman. Is a widely used public-key cryptosystem "based on the practical difficulty of factoring the product of two large prime numbers" (RSA cryptosystem)

  • PublicKey-Crypto:

  • Hashing: A hash function maps data of arbitrary size to data of fixed size. An ideal hash function maps randomly, avoid colissions and is impossible to invert.

  • Symmetric-Crypto:

  • Classical-Crypto:

  • Passwords:

  • AES:

  • Tutorial:

  • Bitcoin:

  • PGP: PGP stands for Pretty Good Privacy. Is a program used to facilitate encrypt and decrypt your mail. PGP "has proven itself quite capable of resisting even the most sophisticated forms of analysis" (PGP faqs)

  • ECC:

  • Factoring:

  • OpenSSL:

  • PRNG:

Solved Problems

  • Hello PGP Use PGP programatically. Recover the message encrypted with a single English word.

  • Hello Bitcoin Do you know how bitcoin addresses are constructed?

  • Hello OpenSSL Can you read and use an OpenSSL RSA key?

  • AES-CTR with Nonce Reuse Can you exploit a reused nonce?

  • Affine Cipher Can you brute force this classical cipher?

  • Double Strength Affine A slight security upgrade, is it enought?

  • Ps and Qs RSA keys generated with one critical weakness

  • Insufficient Key Size Are you running on all 8 cores? This small key is factorable on a PC with an efficient implementation

  • Elliptic Curve Private Key Recovery Given the public parameters of an elliptic curve, recover the poorly chosen private key

  • Håstad's Broadcast Attack RSA with a small exponent is fast to compute but it has a serious weakness

  • Monoalphabetic Cipher Monoalphabetic ciphers leak information. Can you recover it?

  • Playfair This bigram cipher is a bit trickier...

  • Factoring RSA With CRT Optimization Recover a RSA private key when an optimization goes wrong

  • Rainbow Table Hash Chain Can you use a rainbow table to recover a password?

  • ECDSA Nonce Recovery Nonce reuse leading to private key recovery, this time with elliptic curves

  • Intro to Hashing Hashing is a vital concept in cryptography

  • Intro to PGP Can you use PGP programatically?

  • Intro to RSA Learn the basics of a common public key cryptosystem

  • CBC Padding Attack CBC is one of the best modes of operation for block ciphers, but even leaking a tiny amount of information is enough to completely undermine its security

  • CCA on Textbook RSA Turns out padding is important

  • Fast Hashing Passwords Cryptographic hash functions shouldn't be used to hash passwords directly

  • Salt Alone Won't Save You Salting password hashes is important, but not enough on it's own

  • Cut and Paste Attack On AES-ECB Create a valid ciphertext without knowledge of the key using some copypaste

  • Insecure PRNG Using a PRNG that isn't proven to be cryptographically secure is a recipe for disaster

  • Bad Entropy It's easy to generate bad symmetric keys

  • Caesar Should probably stick to the salad

Unsolved Problems

  • Bleichenbacher's CCA2 on RSA 14

  • CRIMEs against TLS 20

  • CBC Padding Attack 22

  • Breaking PDF Passwords 29

  • Backdoored PRNG 31

  • Vigenère 33

  • Rail Fence 34

  • Vigenère + Rail Fence 35

  • Not So Safe Primes 37