/SecurePtrs

Coq formalization for "SecurePtrs" paper

Primary LanguageCoqApache License 2.0Apache-2.0

SecurePtrs

This branch contains the Coq development of the paper:

Installation

Prerequisites

This development has been built with the following combinations of Coq releases and versioned libraries:

Coq 8.12.2

  • Mathematical Components 1.11.0
  • Extensional Structures 0.2.2
  • Equations 1.2.4

Coq 8.13.2

  • Mathematical Components 1.13.0
  • Extensional Structures 0.3.1
  • Equations 1.3

Coq 8.14.1

  • Mathematical Components 1.13.0
  • Extensional Structures 0.3.1
  • Equations 1.3

Dependencies can be installed through the OCaml package manager, OPAM.

  • Coq (package coq) is available through the official Ocaml OPAM repository.
  • Stable releases of Mathematical Components (packages coq-mathcomp-ssreflect, coq-mathcomp-fingroup and coq-mathcomp-algebra), Extensional Structures (package coq-extructures), and Equations (package coq-equations) are available through the Coq OPAM repository.

Build

Run make at the root to build the development.

Definitions and theorems

The following list maps the definitions and statements in the paper to their mechanized counterparts in Coq.

  • Definition 2.1 (RSP~): see statement of Theorem RSC in RSC.v for an instance of this definition

  • Assumption 2.3 (FCC): S2I/Compiler.v, Axiom forward_simulation_star

  • Lemma 2.4 (recomposition): Intermediate/RecompositionRel.v, Theorem recombination_trace_rel

  • Assumption 2.5 (BCC): S2I/Compiler.v, Axiom backward_simulation_star

  • Definition 2.6 (interaction-trace events): CompCert/Events.v, Inductive type event

  • Definition 3.2 (data-flow events) Common/TracesInform.v, Inductive type event_inform

  • Lemma 3.4 (enrichment): Intermediate/CS.v, Lemma star_sem_non_inform_star_sem_inform

  • Lemma 3.5 (data-flow back-translation): Source/Definability.v, Lemma definability

  • Definition 3.9 (turn-taking memory relation): Intermediate/RecompositionRelCommon.v, Inductive proposition mergeable_internal_states

  • Definition 3.10 (relation on interaction traces): Common/RenamingOption.v, Inductive proposition traces_shift_each_other_option

  • Rule Jump (Section 4): Intermediate/CS.v, case Jump of inductive step

  • Rule Store (Section 4): Intermediate/CS.v, case Store of inductive step

  • Theorem 4.1 (RSP~): Theorem RSC in RSC.v

  • Lemma 5.1 (trace prefix mimicking): Source/Definability.v, Lemma definability_gen_rel_right

  • Definition 5.2 (memory relation at interaction events): Intermediate/RecompositionRelCommon.v, Inductive proposition mergeable_border_states

  • Lemma 5.3 (strengthening at interaction events): Intermediate/RecompositionRelStrengthening.v, Theorem threeway_multisem_event_lockstep_program_step

  • Lemma 5.4 (option simulation): Intermediate/RecompositionRelOptionSim.v, Lemma merge_states_silent_star

  • Lemma 5.5 (lockstep simulation): Intermediate/RecompositionRelLockstepSim.v, Theorem threeway_multisem_star_E0

  • Lemma 5.6 (symmetry of the turn-taking state simulation relation): Intermediate/RecompositionRelCommon.v, Lemma mergeable_internal_states_sym

Axioms

How to find axioms/admits

All our results are admit-free and only rely, at most, on some of the axioms specified below. Any other axioms or admitted theorems found in the development are not used in our proofs.

To verify this, use the Coq command Print Assumptions to examine the axioms that apply to the theorems of interest. An index of the above definitions and theorems is given at the end of the top-level file RSC.v.

Axioms about correct compilation of whole programs

We leave some standard statements about the correct compilation of whole programs as axioms because they are not really the focus of our novel secure compilation proof techniques.

Proving these kind of correctness results is typically laborious and we do not expect the proof to be particularly insightful for our chosen pair of languages.

In fact, one of the key goals of the proof technique for the main secure compilation theorem is to demonstrate that standard results about correct compilation can be reused by (rather than implicitly reproved as part of) the secure compilation proof, since proving these theorems is typically a big manual effort that one would wish to avoid duplicating.

Compilation and well-formedness

We assume that every well-formed source program can be successfully compiled (well_formed_compilable), and that compiling preserves certain well-formedness conditions (Compiler.compilation_preserves_well_formedness, compilation_preserves_main, compilation_has_matching_mains).

Compiler.well_formed_compilable
  : forall (p : Source.program) (psz : {fmap Component.id -> nat}),
    Source.well_formed_program p ->
    exists pc : Intermediate.program, compile_program p psz = Some pc

Compiler.compilation_preserves_well_formedness
  : forall (p : Source.program) (psz : {fmap Component.id -> nat})
      (p_compiled : Intermediate.program),
    Source.well_formed_program p ->
    compile_program p psz = Some p_compiled ->
    Intermediate.well_formed_program p_compiled

compilation_preserves_main
  : forall (p : Source.program) (pstksize : {fmap Component.id -> nat})
      (p_compiled : Intermediate.program),
    Source.well_formed_program p ->
    compile_program p pstksize = Some p_compiled ->
    (exists main : expr, Source.prog_main p = Some main) <->
    Intermediate.prog_main p_compiled

compilation_has_matching_mains
  : forall (p : Source.program) (psz : {fmap Component.id -> nat})
      (p_compiled : Intermediate.program),
    Source.well_formed_program p ->
    compile_program p psz = Some p_compiled -> matching_mains p p_compiled

Separate compilation

We assume that the compiler satisfies separate_compilation: compilation and linking commute.

separate_compilation
  : forall (p : Source.program) (psz : {fmap Component.id -> nat})
      (c : Source.program) (csz : {fmap Component.id -> nat})
      (p_comp c_comp : Intermediate.program),
    Source.well_formed_program p ->
    Source.well_formed_program c ->
    linkable (Source.prog_interface p) (Source.prog_interface c) ->
    compile_program p psz = Some p_comp ->
    compile_program c csz = Some c_comp ->
    compile_program (Source.program_link p c) (unionm psz csz) =
    Some (Intermediate.program_link p_comp c_comp)

Compiler correctness

We also assume CompCert-style compiler correctness, in the form of a forward simulation forward_simulation_star and a backward simulation backward_simulation_star:

Compiler.forward_simulation_star
  : forall (p : Source.program) (t : Events.trace Events.event)
      (s : state (S.CS.sem p)) (metasize : Component.id -> nat),
    Source.closed_program p ->
    Source.well_formed_program p ->
    disciplined_program p ->
    NoLeak.good_Elocal_usage_program p ->
    Star (S.CS.sem p) (S.CS.initial_machine_state p) t s ->
    exists
      (s' : I.CS.state) (t' : Events.trace Events.event) 
    (psz : {fmap nat_ordType -> nat}) (p_compiled : Intermediate.program),
      domm (T:=nat_ordType) (S:=nat) psz =
      domm (T:=nat_ordType) (S:=Component.interface)
        (Source.prog_interface p) /\
      compile_program p psz = Some p_compiled /\
      Star (I.CS.sem_non_inform p_compiled)
        (I.CS.initial_machine_state p_compiled) t' s' /\
      traces_shift_each_other_option metasize metasize t t'

Compiler.backward_simulation_star
  : forall (p : Source.program) (psz : {fmap Component.id -> nat})
      (p_compiled : Intermediate.program) (t : Events.trace Events.event)
      (s : state (I.CS.sem_non_inform p_compiled))
      (metasize : Component.id -> nat),
    Source.closed_program p ->
    Source.well_formed_program p ->
    disciplined_program p ->
    NoLeak.good_Elocal_usage_program p ->
    compile_program p psz = Some p_compiled ->
    Star (I.CS.sem_non_inform p_compiled)
      (I.CS.initial_machine_state p_compiled) t s ->
    exists (s' : state (S.CS.sem p)) (t' : Events.trace Events.event),
      Star (S.CS.sem p) (S.CS.initial_machine_state p) t' s' /\
      traces_shift_each_other_option metasize metasize t t'

Compiler preserves the privacy of the local buffer

Finally, we assume Compiler.compiler_preserves_non_leakage_of_private_pointers, which states that our compiler preserves the privacy of the local buffer. Such a result can likely be proved by using the fine-grained simulation invariants in an actual compiler correctness proof.

Compiler.compiler_preserves_non_leakage_of_private_pointers
  : forall (p : Source.program) (psz : {fmap Component.id -> nat})
      (p_compiled : Intermediate.program)
      (metadata_size : Component.id -> nat),
    Source.closed_program p ->
    Source.well_formed_program p ->
    compile_program p psz = Some p_compiled ->
    S.CS.private_pointers_never_leak_S p metadata_size ->
    private_pointers_never_leak_I p_compiled metadata_size

Logical axioms

The following standard axioms are used occasionally in our proofs.

ProofIrrelevance.proof_irrelevance : forall (P : Prop) (p1 p2 : P), p1 = p2

FunctionalExtensionality.functional_extensionality_dep
  : forall (A : Type) (B : A -> Type) (f g : forall x : A, B x),
    (forall x : A, f x = g x) -> f = g

Classical_Prop.classic : forall P : Prop, P \/ ~ P

Index of definitions

The source language SafeP corresponds to Source in the code. The target language Mach corresponds to Intermediate in the code.

  • Backtranslation function ↑: function procedures_of_trace in Source/Definability.v
  • Data-flow events E: inductive event_inform in Common/TracesInform.v
  • Memory projection proj_P(Mem): implicit in definitions mem_of_part_executing_rel_original_and_recombined and mem_of_part_not_executing_rel_original_and_recombined_at_internal in Intermediate/RecompositionRelCommon.v
  • Value renaming valren: function rename_value_template_option in Common/RenamingOption.v
  • The +1 block id renaming: Implemented by instantiating shift_value_option with uniform_shift 0 and uniform_shift 1, in Common/RenamingOption.v
  • Turn-taking simulation invariant state_rel_tt: definition mergeable_internal_states in Intermediate/RecompositionRelCommon.v
  • Turn-taking simulation relation mem_rel_tt: memory part of the mergeable_internal_states definition in Intermediate/RecompositionRelCommon.v
  • Strong memory relation holding at all locations of the executing part mem_rel_exec: definition mem_of_part_executing_rel_original_and_recombined in Intermediate/RecompositionRelCommon.v
  • Memory relation holding only at private locations of the non-executing part mem_rel_not_exec: definition mem_of_part_not_executing_rel_original_and_recombined_at_internal in Intermediate/RecompositionRelCommon.v
  • Function shared: inductive addr_shared_so_far in Common/RenamingOption.v
  • Function private: negation of the inductive addr_shared_so_far in Common/RenamingOption.v
  • Linking C ∪ P: functions program_link in Source/Language.v and Intermediate/Machine.v
  • Trace relation ~: definition traces_shift_each_other_option in Common/RenamingOption.v
  • Compilation function ↓: function compile_program in S2I/Compiler.v
  • Step relation ⇝: definitions kstep in Source/CS.v; step_non_inform for non-data-flow semantics and step for data-flow semantics in Intermediate/CS.v
  • Reflexive transitive closure ^*: inductive star in CompCert/Smallstep.v
  • Interaction (non-data-flow) events e: definition event in CompCert/Events.v
  • Memory Mem or mem: Module Memory in Common/Memory.v
  • Component memory cMem: Module ComponentMemory in Common/Memory.v
  • Source (SafeP) expressions exp: definition expr in Source/Language.v
  • Target (Mach) instructions instr: definition instr in Intermediate/Machine.v
  • Values v: definition value in Common/Values.v
  • Removal of all internal data-flow events remove_df: function project_non_inform in Common/TracesInform.v
  • Back-translation mimicking_state invariant: definition well_formed_state in Source/Definability.v
  • Back-translation of a data-flow event: definition expr_of_event in Source/Definability.v
  • Trace concatenation ++: function Eapp in CompCert/Events.v
  • Border-state relation state_rel_border: definition mergeable_border_states in Intermediate/RecompositionRelCommon.v
  • "Is executing in" relation: is_program_component and is_context_component in Intermediate/CS.v

License

  • This code is licensed under the Apache License, Version 2.0 (see LICENSE)
  • The code in the CompCert dir is adapted based on files in the common and lib dirs of CompCert and is thus dual-licensed under the INRIA Non-Commercial License Agreement and the GNU General Public License version 2 or later (see CompCert/LICENSE)