网络安全认证协议形式化分析

1、1/9/2022.1网络安全认证协议形式化分析肖肖 美美 华华南昌大学信息工程学院南昌大学信息工程学院( (南昌南昌,330029),330029)中国科学院软件研究所计算机科学重点实验室中国科学院软件研究所计算机科学重点实验室( (北京北京,100080),100080)1/9/2022.2Organization nIntroductionnRelated WorknFormal System NotationnIntruders Algorithmic Knowledge LogicnVerification Using SPIN/PromelanConclusion 1/9/2022.

2、3 Introduction nCryptographic protocols are protocols that use cryptography to distribute keys and authenticate principals and data over a network.nFormal methods, a combination of a mathematical or logical model of a system and its requirements, together with an effective procedure for determining

3、whether a proof that a system satisfies its requirements is correct. Model; Requirement (Specification);Verification. 1/9/2022.4 Introduction (cont.)In cryptographic protocols, it is very crucial to ensure:Messages meant for a principal cannot be read/accessed by others (secrecy);Guarantee genuinene

4、ss of the sender of the message (authenticity);Integrity;Non-Repudiation (NRO, NRR);Fairness, etc. 1/9/2022.5Related WorkTechniques of verifying security properties of the cryptographic protocols can be broadly categorized:nmethods based on belief logics (BAN Logic)n-calculus based models n state ma

5、chine models (Model Checking) Model checking advantages (compare with theory proving): automatic; counterexample if violation Use LTL (Linear temporal logic ) to specify properties FDR (Lowe); Mur (Mitchell); Interrogator (Millen); Brutus (Marrero) SPIN (Hollzmann)n theorem prover based methods (NRL

6、, Meadows)n methods based on state machine model and theorem prover (Athena, Dawn)nType checkingnISCAS, LOIS, (in China)1/9/2022.6Notation(1) Messages a Atom := C | N | k | m Msg := a | m m | mk(2) Contain Relationship () m a m = a m m1 m2 m = m1 m2 m m1 m m2 m m1k m = m1k m m1 Submessage: sub-msgs(

7、m) m Msg | m m 1/9/2022.7Notation(3) Derivation ( , Dolev-Yao model) m B B m B m B m B m m (pairing) B m m B m B m (projection) B m B k B mk (encryption) B mk B k-1 B m (decryption) 1/9/2022.8Notation(4) Properties Lemma 1. B m B B B m Lemma 2. B m B m m B m Lemma 3. B m X m B X （Y: Y sub-msgs(m) :

8、X Y B Y） （b: b B : Y b） （Z, k: Z Msg k Key : Y = Zk B k-1）Lemma 4. （k, b: k Key b B : k b A k AB k） （z: z sub-msgs(x) : a z A z） (b: b B: a b A a） 1/9/2022.9Logic of Algorithmic KnowledgeDefinition 1. Primitive propositions P0s for security: p, q P0s := sendi (m) Principal i sent message m recvi (m)

9、 Principal i received message m hasi (m) Principal i has message m 1/9/2022.10Logic of Algorithmic KnowledgeDefinition 2. An interpreted security system S = (R, R), where R is a system for security protocols, and R is the following interpretation of the primitive propositions in R. R(r, m) (sendi (m

10、) = true iff j such that send (j, m) ri (m) R(r, m) (recvi (m) = true iff recv(m) ri (m) R(r, m) (hasi (m) = true iff m such that m m and recv(m ) ri (m) 1/9/2022.11Logic of Algorithmic KnowledgeDefinition 3. An interpreted algorithmic security system (R, R, A1, A2, An ), where R is a security syste

11、m, and R is the interpretation in R, Ai is a knowledge algorithm for principal i. 1/9/2022.12Algorithm knowledge logic AiDY(hasi(m),l) K = keyof(l) for each recv(m) in l do if submsg(m, m, K) then return “Yes” return “No”submsg(m, m, K) if m = m then return true if m is m1k and k-1 K then return sub

12、msg(m, m1, K) if m is m1 .m2 then return submsg(m, m1, K) submsg(m, m2, K) return false1/9/2022.13Cont.getkeys(m, K) if m Key then return m if m is m1k and k-1 K then return getkeys(m1, K) if m is m1 .m2 then return getkeys(m1, K) getkeys(m2, K) return keysof(l) K initkeys(l) loop until no change in

13、 K k getkeys(m, K) (when recv(m) l ) return K1/9/2022.14Verification Using SPIN/PromelaSPIN is a highly successful and widely used software model-checking system based on formal methods from Computer Science. It has made advanced theoretical verification methods applicable to large and highly comple

14、x software systems. In April 2002 the tool was awarded the prestigious System Software Award for 2001 by the ACM. SPIN uses a high level language to specify systems descriptions, including protocols, called Promela (PROcess MEta LAnguage). 1/9/2022.15BAN-Yahalom Protocol 1 AB: A, Na 2 BS: B, Nb, A,

15、NaKbs 3 SA: Nb, B, Kab, NaKas , A, Kab, NbKbs 4 AB: A, Kab, NbKbs , NbKab1/9/2022.16Attack 1 (intruder impersonates Bob to Alice).1 AI(B): A, Na .1 I(B)A: B, Na .2 AI(S): A, Na, B, NaKas .2 I(A)S: A, Na, B, NaKas .3 SI(B): Na, A, Kab, NaKas , B, Kab, NaKbs.3 I(S)A: Ne, B, Kab, NaKas , A, Kab, NaKbs.

16、4 AI(B): A, Kab, NbKbs , NeKab 1/9/2022.17Attack 2 (intruder impersonates Alice).1 AB: A, Na.2 BS: B, Nb, A, NaKbs .1 I(A)B: A, (Na, Nb) .2 BI(S): B, Nb, A, Na, NbKas .3 (Omitted).4 I(A)B: A, Na, NbKbs , NbNa 1/9/2022.18Attack 3.1 AB: A, Na.2 BS: B, Nb, A, NaKbs .1 I(B)A: B, Nb .2 AI(S): A, Na, B, N

17、bKas .2 I(A)S: A, Na, B, NbKas .3 SI(B): Na, A, Kab, NbKbs , B, Kab, NaKas .3 I(S)A: Nb, B, Kab, NaKas , A, Kab, NbKbs.4 AB: A, Kab, NbKbs , NbKab1/9/2022.19Optimization strategies nUsing static analysis and syntactical reordering techniquesnThe two techniques are illustrated using BAN-Yahalom verif

18、ication model as the benchmark.ndescribe the model as Original version to which static analysis and the syntactical reordering techniques are not applied, nthe static analysis technique is only used as Fixed version(1),nboth the static analysis and the syntactical reordering techniques are used as F

19、ixed version(2).1/9/2022.20Experimental results show the effectivenessProtocol Model ConfigurationWith type flawsNo type flawsStatesTrans.StatesTrans.Original version15802065549697Fixed version(1)7121690405379Fixed version(2)433512225 2431/9/2022.21Needham-Schroeder Authentication Protocol 1/9/2022.22Attack to N-S Protocol (found by SPIN)1/9/2022.23Conclusionnbased on a logic of knowledge al