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Reusing a one-bit encryption pad — independent controls

Lax755887.ReusedKeyControls · concepts/Lax755887/ReusedKeyControls.lean · lax-755887

proven

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    Natural Language Statement

    Theorem

    These statements use only the background axioms. They record the actual behavior or the valid local calculation, independently of the unchecked contract.

    Concept map
    2 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    This concept declares 3 statements. Each proof establishes one of them relative to its assumptions.

    1 complement proven

    2 rekey proven

    3 xor_attack_succeeds proven

    Lean source view on GitHub

    1import Lax755887.ReusedKey
    2
    3/-!
    4---
    5title: Reusing a one-bit encryption pad — independent controls
    6type: theorem
    7---
    8These statements use only the background axioms. They record the actual behavior or the valid local calculation, independently of the unchecked contract.
    9-/
    10
    11namespace Lax755887.ReusedKeyControls
    12
    13open Lax755887.ReusedKey
    14
    15axiom rekey {α : Type} (f : Bool → α) : SameLaw f (fun k => f (!k))
    16
    17axiom complement (event : Bool → Bool) :
    18 probability (fun k => !(event k)) = 1 - probability event
    19
    20axiom xor_attack_succeeds : success (fun c => Bool.xor c.1 c.2) = 1
    21
    22end Lax755887.ReusedKeyControls
    23
    Show ProofShow ProofShow Proof
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    Used by

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    From Mathlib

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