Encoding

A <=> B

Binary

• bit vs byte
• 0 vs 1 is a representation
• 8bits = 1byte = 256 values (adding length multiplies the space : 7bits = 128 values, + 0 OR 1 is then 256)

Context needed

• "2018" : Hexa vs ASCII vs Base64
• Binary : number, text, raw data, ...
• UTF-8 vs Latin1 (with invalid codepoints)
• Double vs uint vs int

Different representation, same information

• Transferability (charset, base64 web vs normal)
• Lisibility (hashids, intercom names)
• Weight (hex as UTF8 : 1byte weights 2) 
• Encoding / decoding on interfaces
• URL Encoding

Encryption

A => B / B => A

Theorem

• n = modulo space
• if e.d  = 1 (mod ϕ(n))
• then M ^ (e.d) = M (mod n)
• since M ^ (e.d) = (M ^ e) ^ d = (M ^ d) ^ e (mod n)
• then C = M ^ e is decryptable by d, n 
• and C' = M ^ d is decryptable by e, n
• (d, n) is the private key
• (e, n) is the public key

Usage

• Actually symetric key
• Public/private is convention
• Key size can be controlled
• Always generated by pairs

Actual keypair generation

• choose large primes p, q
• n = p.q
• ϕ(n) = (p - 1).(q - 1)
• choose e < ϕ(n), coprime to ϕ(n)
• determine d / d.e = 1 (mod ϕ(n))
• done !

Hashing

A => B

1-way function

• to fixed length
• pseudo-random & well distributed
• deterministic & reproducible

hash("hello") => 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824

Crypto vs non-crypto

• SHA-2x family
• non-reversible
• non-generable
• still fast !

Applications

• Dicts
• Grouping w/ modulo (since pseudo-random)
• Payload verification

Application: Signature

2 goals

• Message integrity
• Sender identity

With hashes

• Shared secret
• hash (M, secret) => signature
• hash (M, timestamp, secret) => timed signature

With encryption

• No shared secret
• encrypt (hash(M), pubkey) => signature