Private Key Encryption¶

links: AC1 TOC - Private Key Encryption - Index

Private-Key Encryption Scheme¶

Every private key encryption scheme / cipher consists of three different algorithms:

k = Gen(n):
    Gen(n) generates a key k given the security parameter n

c = Enc(k,m):
    Enc(k,m) encrypts a message m given with a given key k, which outputs a 
    ciphertext c

m = Dec(k,c):
    Dec(k,c) decrypts a ciphertext c with a given key k, which outputs decrypted 
    plaintext m

Goals of Private Key Encryption¶

Encrypting and decrypting messages in a safe way
CPA-Secure: Secure against Chosen Plaintext Attacks
EAV-Secure: EAV means "Secure Against Eavesdropping" (which is included in Chosen Plaintext Attacks)
PPT algorithms (Probabilistic Polynomial Time algorithms)
Indistinguishability

Constructing Private-Key Encryption Scheme¶

The idea of stream ciphers is to leverage a Pseudorandom Number Generator (PRNG) and generate a OneTimePad using a key. This pad is then XORed onto the plaintext. This gives a ciphertext. For decryption again take the key and the Pseudorandom Number Generator (PRNG) and create the one-time pad. XORing the pad with the ciphertext will result in the plaintext. The key must be generated using the Gen(n) primitive of the respective private-key encryption scheme.

Here a simple example (the lengths are chosen for the example and are not secure):

k = Gen(10)     : 0110010010

plaintext m     : 1010

PRNG(k, len(m)) : 0100

encrypt         : m XOR PRNG = 1010 XOR 0100 = 1110
ciphertext c    : 1110

PRNG(k, len(c)) : 0100

decrypt         : c XOR PRNG = 1110 XOR 0100 = 1010 = m

Algorithms / Building blocks¶

Gen(n) = k¶

The key must be generated effectively at random using correct techniques (leverage a TRNG). It is used as seed to the PRNG.

Enc(k, m) = c¶

The encryption primitive initializes a PRNG using the generated key k as seed. Then it consumes a len(m) bit-string of the PRNG to XOR the string with the plaintext m, which results in ciphertext c.

Dec(k, c) = m¶

The decryption primitive initializes a PRNG using the generated key k as seed. Then it consumes a len(c) bit-string of the PRNG to XOR the string with the ciphertext c, which results in plaintext m

links: AC1 TOC - Private Key Encryption - Index