Checking Unwinding Conditions for Finite State Systems Deepak D’Souza, Raghavendra K.R. Indian Institute of Science, Bangalore, India Checking Unwinding Conditions for Finite State Systems – p.1/14
MAKS Framework of Heiko Events. V isible, C onfidential, N either Checking Unwinding Conditions for Finite State Systems – p.2/14
MAKS Framework of Heiko Events. V isible, C onfidential, N either Trace: finite sequence of events Checking Unwinding Conditions for Finite State Systems – p.2/14
MAKS Framework of Heiko Events. V isible, C onfidential, N either Trace: finite sequence of events System: A set of traces Checking Unwinding Conditions for Finite State Systems – p.2/14
MAKS Framework of Heiko Events. V isible, C onfidential, N either Trace: finite sequence of events System: A set of traces Information flow properties for all x in L with some conditions ⇒ there exists y in L with some conditions Checking Unwinding Conditions for Finite State Systems – p.2/14
MAKS Framework of Heiko Events. V isible, C onfidential, N either Trace: finite sequence of events System: A set of traces Information flow properties for all x in L with some conditions ⇒ there exists y in L with some conditions Non-Inference( NF ) ∀ τ ∈ L ⇒ ∃ τ ′ ∈ L τ ′ = τ ↾ V Checking Unwinding Conditions for Finite State Systems – p.2/14
An Example (1) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old e Checking Unwinding Conditions for Finite State Systems – p.3/14
An Example (1) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old e V = { e, f } C = { gen - new - pin } N = φ Checking Unwinding Conditions for Finite State Systems – p.3/14
An Example (1) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old e V = { e, f } C = { gen - new - pin } N = φ Tr = { gen - new - pin e f , e } + prefixes Checking Unwinding Conditions for Finite State Systems – p.3/14
An Example (1) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old e V = { e, f } C = { gen - new - pin } N = φ Tr = { gen - new - pin e f , e } + prefixes Confidentiality compromised. Noninference fails Checking Unwinding Conditions for Finite State Systems – p.3/14
An Example (2) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old rcv - enc - rej e f Checking Unwinding Conditions for Finite State Systems – p.4/14
An Example (2) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old rcv - enc - rej e f V = { e, f } C = { gen - new - pin } N = φ Checking Unwinding Conditions for Finite State Systems – p.4/14
An Example (2) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old rcv - enc - rej e f V = { e, f } C = { gen - new - pin } N = φ Tr = { gen - new - pin e f , e f } + prefixes Checking Unwinding Conditions for Finite State Systems – p.4/14
An Example (2) snd - enc - new rcv - enc - acc e f gen - new - pin gen - new - pin snd - enc - old rcv - enc - rej e f V = { e, f } C = { gen - new - pin } N = φ Tr = { gen - new - pin e f , e f } + prefixes Confidentiality maintained. Noninference holds Checking Unwinding Conditions for Finite State Systems – p.4/14
Information Flow Properties Non−Interference Goguen, Meseguer − 82 Noninference Separability Generalized Non−Interference Non−Deducibility Checking Unwinding Conditions for Finite State Systems – p.5/14
Information Flow Properties Mantel − BSPs FCIA Non−Interference R Goguen, Meseguer − 82 FCD Noninference D Separability I BSI BSIA Generalized IA Non−Interference FCI BSD Non−Deducibility Checking Unwinding Conditions for Finite State Systems – p.5/14
Basic Security Predicates (BSPs) Trace based information flow properties in BSPs Checking Unwinding Conditions for Finite State Systems – p.6/14
Basic Security Predicates (BSPs) Trace based information flow properties in BSPs BSP Removal ( R ) new N events Checking Unwinding Conditions for Finite State Systems – p.6/14
Basic Security Predicates (BSPs) Trace based information flow properties in BSPs BSP Deletion ( D ) α c β new N events β ′ α ′ Checking Unwinding Conditions for Finite State Systems – p.6/14
Basic Security Predicates (BSPs) Trace based information flow properties in BSPs BSP Insertion ( I ) α β β ′ α ′ new C Checking Unwinding Conditions for Finite State Systems – p.6/14
Basic Security Predicates (BSPs) Trace based information flow properties in BSPs BSP Insertion ( I ) α β β ′ α ′ new C Generalized Non-Interference - I and D Noninference - R Checking Unwinding Conditions for Finite State Systems – p.6/14
Verification using Model Checking Properties of sets of traces, Classical Model Checking techniques (Temporal Logic etc) cannot be used Checking Unwinding Conditions for Finite State Systems – p.7/14
Verification using Model Checking Properties of sets of traces, Classical Model Checking techniques (Temporal Logic etc) cannot be used {DRS05} Sound and Complete Model Checking method for Finite State Systems Checking Unwinding Conditions for Finite State Systems – p.7/14
Verification using Model Checking Properties of sets of traces, Classical Model Checking techniques (Temporal Logic etc) cannot be used {DRS05} Sound and Complete Model Checking method for Finite State Systems L satisfies a BSP P is reduced to op 1 ( L ) ⊆ op 2 ( L ) Checking Unwinding Conditions for Finite State Systems – p.7/14
Verification using Model Checking Properties of sets of traces, Classical Model Checking techniques (Temporal Logic etc) cannot be used {DRS05} Sound and Complete Model Checking method for Finite State Systems L satisfies a BSP P is reduced to op 1 ( L ) ⊆ op 2 ( L ) Examples • L satisfies Removal R iff L ↾ V ⊆ N L . • L satisfies Deletion D iff l-del ( L ) ⊆ N L . Checking Unwinding Conditions for Finite State Systems – p.7/14
Verification using Model Checking Properties of sets of traces, Classical Model Checking techniques (Temporal Logic etc) cannot be used {DRS05} Sound and Complete Model Checking method for Finite State Systems L satisfies a BSP P is reduced to op 1 ( L ) ⊆ op 2 ( L ) Examples • L satisfies Removal R iff L ↾ V ⊆ N L . • L satisfies Deletion D iff l-del ( L ) ⊆ N L . Regularity Preserving: Algorithm to construct automata for op ( L ) , given an automata for L Checking Unwinding Conditions for Finite State Systems – p.7/14
Verification using Model Checking Properties of sets of traces, Classical Model Checking techniques (Temporal Logic etc) cannot be used {DRS05} Sound and Complete Model Checking method for Finite State Systems L satisfies a BSP P is reduced to op 1 ( L ) ⊆ op 2 ( L ) Examples • L satisfies Removal R iff L ↾ V ⊆ N L . • L satisfies Deletion D iff l-del ( L ) ⊆ N L . Regularity Preserving: Algorithm to construct automata for op ( L ) , given an automata for L Running time: Exponential in the size of the system Checking Unwinding Conditions for Finite State Systems – p.7/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Checking Unwinding Conditions for Finite State Systems – p.8/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Unwinding relation ⋉ : a binary relation on Q satisfying osc Checking Unwinding Conditions for Finite State Systems – p.8/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Unwinding relation ⋉ : a binary relation on Q satisfying osc osc e p q ⋉ r Checking Unwinding Conditions for Finite State Systems – p.8/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Unwinding relation ⋉ : a binary relation on Q satisfying osc osc e p q ⋉ ⋉ δ r t Checking Unwinding Conditions for Finite State Systems – p.8/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Unwinding relation ⋉ : a binary relation on Q satisfying osc T satisfies unwinding condition lrf w.r.t. ⋉ Checking Unwinding Conditions for Finite State Systems – p.8/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Unwinding relation ⋉ : a binary relation on Q satisfying osc T satisfies unwinding condition lrf w.r.t. ⋉ c p q Checking Unwinding Conditions for Finite State Systems – p.8/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Unwinding relation ⋉ : a binary relation on Q satisfying osc T satisfies unwinding condition lrf w.r.t. ⋉ c p q ⋉ Checking Unwinding Conditions for Finite State Systems – p.8/14
Unwinding - Definitions Σ -labelled transition system T = ( Q, s, − → ) Unwinding relation ⋉ : a binary relation on Q satisfying osc T satisfies unwinding condition lrf w.r.t. ⋉ c p q ⋉ T satisfies unwinding condition lrb w.r.t. ⋉ Checking Unwinding Conditions for Finite State Systems – p.8/14
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