quartz/content/notes/06-hashing-binary-public-key-cryptography.md

title	aliases	tags	sr-due	sr-interval	sr-ease
06-hashing-binary-public-key-cryptography		lecture comp210	2022-08-19	3	250

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news

• pegasus project
• cutting internet cables

Hash function

• yields a small, districtive value (hash or digest) from an arbitrarily sized input.
• one way function
  • non-invertable
• uniform size (each ouput eqaully likely)
• deterministic (same input maps to same output)
• possibility of collisions (b-day paradox, potential attacks)

message => hash() => hash

also

• can be used for data structures
  • hash-map
  • lots of theory
  • often use modular arithmetic
  • usually have more complicated algorithms than mod

in crypto

• needs to be
  • impossible to reverse
  • difficult to find collision
  • uniform length output (tunable)
  • must account for every bit of information in a message
  • must be sensitive to changes input (avalancge effect)
  • ouput should no contain apparent iinformation (appears random)
  • easily computed (usually)
    • for passowords should be slow
    • makes brute force attacks take time
    • key strechting (repeated application of hash)
    • use complex memory access patterns to defeat esp

effectively a digital fingerprint;

collision probability

v = a^l

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can also be used to compare complexity of passwords

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• should have about 80 bits of entropy

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uses of hashing

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good algorithms

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One-time-pads

• basic idea
  • generate single-use truly-random key they is at least as long as the plaintext
  • combine the key with the plaintext using XOR one bit at a time
  • resulting ciphertext looks like random noise
  • decryption must use same key (symmetric)

limitations

impossible to crack, if properly implemented.

• but key must be shared
• key distribution problem
• need long, truly random, one time keys
  • must be used only once

assymetric cryptography

uses different but mathematically related keys for encrption and decryption

digital signatures

encryption + signing. signing verfies authenticity of sender

stream ciphers vs block ciphers

one bit at a time vs chunks

reciprocal cipher