Cryptographic Machine

Definition

A machine is a Triple $\mu =(\text{ID},c,\tilde{\mu }$ with:

• An identity element $c\in \mathbb{N}$ that is visible to $\mu$ and constant
• Interaction tapes $c=\mathbb{N}\times \{\text{input, sub-output, backdoor}\}$ that is a Commutative set:
  • Inputs
  • Subroutine outputs
  • Backdoor (comes from adversary)
• A code $\tilde{\mu }$ - a Turing Machine that represents what the machine can do Has properties:
• Polynomial-Time-ness - there are finite interaction tapes

Example Secure Channel

${\mu }_1=(1,\{2,\text{input},(A,\text{backdoor}),{\tilde{\mu }}_1\}$ ${\mu }_2=(2,\{1,\text{subroutine-output},(A,\text{backdoor}),\widetilde{{\mu }_2}\}$