Logical Analysis and Verification of Cryptographic Protocols - Loria

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64 CHAPTER 3. PROTOCOLS WITH VULNERABLE HASH FUNCTIONS x1, . . . , xn → f(x1, . . . , xn) with f a public function symbol in F. Unfortunately, such intruder deduction rules are not sufficient to represent an intruder taking advantage of the collision vulnerability property for hash functions. To this end, we introduce next another definition of intruder deduction rules. This representation of intruder deduction rules have been given initially in [72]. Definition 35 (Intruder deduction rules) An intruder deduction rule is a rule of the form with • l1, . . . , ln, l ∈ T (F, X ), l1, . . . , ln → l • all.Cons((lσ)↓) ⊆ � n i=1 all.Cons((liσ)↓) ∪ Cspec, for any ground substitution σ. This second condition in the definition above is very similar to the origination condition for well-definedness in [157]. It is easy to see that if the equation theory H verifies the property: V ar(u) = V ar(v) for each u · = v ∈ H, then the second condition in the definition above is verified if and only if V ar(l) ⊆ V ar({l1, . . . , ln}). Example 16 Let F = {., ɛ} with . denotes the concatenation, and ɛ denotes the empty word, and let ⎧ ⎨ (x.y).z = x.(y.z) H = x.ɛ = x ⎩ ɛ.x = x be the associated equational theory. The following rule x.y → x is an intruder deduction rule as per definition 35. Definition 36 (Intruder deduction system) An intruder deduction system I, also called an intruder system, is a triple I = 〈F, LI, H〉 where F is a signature, LI is a set of intruder deduction rules (as per Definition 35), and H is an equational theory over T (F, X ). Given two set of terms E, F ⊆ T (F, X ), E →I F and I-derivations are defined as in Chapter 2.
3.3. THE MODEL 65 Definition 37 (well-formed derivation) Let I = 〈F, LI, H〉 be an intruder deduction system, and let E (respectively t) be a set of ground terms (respectively a ground term) in normal form. A derivation D : E →I E, t1, →I . . . →I E, t1, . . . , tn−1, t is wellformed if for every 1 ∈ {1, . . . , n − 1}, ti ∈ Sub(E ∪ t). Definition 38 (locality) Let I = 〈F, LI, H〉 be an intruder deduction system. I is local if for every E, t with E a set of ground terms in normal form and t a ground term in normal form, if there is a derivation starting from E of goal t then there is a well-formed derivation starting from E of goal t. Example 17 We present here an intruder operating on words who is able to concatenate messages and extract prefixes and suffixes. The intruder system is given by 〈F, LI, H〉 with: • F = {., ɛ}; . denotes the concatenation, and ɛ denotes the empty word ⎧ ⎪⎨ x, y → x.y x.y → x • LI = ⎪⎩ x.y → y ∅ → ɛ ⎧ ⎨ (x.y).z = x.(y.z) • H = x.ɛ = x ⎩ ɛ.x = x Combination of intruder deduction systems We recall in Definition 39 the notion of disjoint combination (also called disjoint union) of intruder deduction systems. This notion has been initially introduced by Y. Chevalier and M. Rusinowitch [73] who used this notion to show that the analysis of cryptographic protocols in presence of an intruder deduction system I may be reduced to the analysis of cryptographic protocols in presence of simpler intruder deduction systems I1, . . . , In provided that I is the disjoint union of I1, . . . , In. Definition 39 Let I1 = 〈F1, LI 1, H1〉 and I2 = 〈F2, LI 2, H2〉 be two intruder deduction systems such that F1 and F2 are disjoints, H1 an equational theory on F1 and H2 an equational theory on F2. The following intruder deduction system I = 〈F1 ∪ F2, LI 1 ∪ LI 2, H1 ∪ H2〉 denotes the disjoint union of the two intruder deduction systems I1 and I2.
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Logical Analysis and Verification o
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Abstract This thesis is developed i
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x CONTENTS 2.1.7 Unification . . .
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2 CHAPTER 1. INTRODUCTION Figure 1.
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4 CHAPTER 1. INTRODUCTION Secrecy T
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114 CHAPTER 5. SATURATED DEDUCTION
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178 CHAPTER 7. VOTER VERIFIABILITY
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198 CHAPTER 8. CONCLUSION AND PERSP
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202 BIBLIOGRAPHY [12] M. Abadi and
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204 BIBLIOGRAPHY [36] M. Bellare, A
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206 BIBLIOGRAPHY [60] U. Hustadt Ch
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208 BIBLIOGRAPHY [83] H. Comon-Lund
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210 BIBLIOGRAPHY [108] B. Donovan,
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212 BIBLIOGRAPHY [132] T. Kohno, A.
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214 BIBLIOGRAPHY [160] J. C. Mitche
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216 BIBLIOGRAPHY [187] H. Seidl and
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Logical Analysis and Verification of Cryptographic Protocols - Loria

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