One-time pad

Description:

• A private-key encryption scheme
• $M=\{0,1{\}}^n,K=\{0,1{\}}^n$
  • The key, $k$, is required to be as long as the message
  • The entire key used to mask the plain-text → “perfectly hides” the plain-text

Gen:

• Generates a key $k=k_1{k}_2...k_n$ uniformly from $K=\{0,1{\}}^n$

Enc:

• ${\text{Enc}}_n(m_1{m}_2...m_n)=c_1{c}_2...c_n$, where $c_i=m_i+k_i\mathrm{mod}2$ (equivalently$c_i=m_i\oplus k_i$ where $\oplus$ denotes XOR)

Dec:

• $De{c}_k(c_1{c}_2...c_n)=m_1{m}_2...m_n$ where $m_i=c_i-k_i\mathrm{mod}2$ (it is equivalent to $m_i=c_i\oplus k_i$)