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Fine-Grained MSR Specifications for Quantitative Security Analysis

This paper presents a quantitative security analysis technique for fine-grained MSR specifications, going beyond the Dolev-Yao model. The technique includes assigning costs to operations, estimating actual resources needed for attacks, and assessing DoS resistance. The analysis is applied to protocol specifications using multiset rewriting and includes the use of traces and scripts. The paper also introduces the concept of cost-aware security analysis and provides examples of its application.

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Fine-Grained MSR Specifications for Quantitative Security Analysis

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  1. Fine-Grained MSR SpecificationsforQuantitative Security Analysis Iliano Cervesatoiliano@itd.nrl.navy.mil ITT Industries, inc @ NRL Washington, DC http://theory.stanford.edu/~iliano/ Security Analysis of Protocols @ DIMACS July 9, 2004

  2. Qualitative (Dolev-Yao) Analysis • Classifies protocol operations in • Possible (Dolev-Yao) • Reception/transmission • Crypto with key, … • Impossible • Guessing keys • Breaking crypto, … • Security assessed only on possible ops • “Easily” achieved by most current tools • What next? “Easy”(polynomial) “Hard”(exponential) Quantitative Security Analysis

  3. Analysis beyond Dolev-Yao D a t a Symbolic Bit-oriented Perfect More ops- xor- DH, … Crypto Type confusion Guessing Probabilistic Crypto hybrid- probability- complexity Cost-aware Real Quantitative Security Analysis

  4. Cost-Aware Security Analysis • Assign cost to operations [Meadows,01] • Including non Dolev-Yao • Discrete logarithm, factoring, … • (Verifiable) guessing [Lowe,02] • Principal subversion, … • Applications • Estimate actual resources needed for attacks • Resources limitation (smart cards, PDAs, …) • DoS resistance assessment • Comparing attacks or protocols Quantitative Security Analysis

  5. Outline • Protocol specification • MSR  Fine-Grained MSR • Technique applies to other languages • Traces and Scripts • Cost Model • Operations  Scripts • Cost-aware Security • Threshold analysis • Comparative analysis Quantitative Security Analysis

  6. MSR Advertisement • Executable protocol specification language • Theoretical results • Decidability • Most powerful intruder, … • 3 generations already • MSR 1: (here) • MSR 2: 1 + strong typing • MSR 3: 2 + w-multisets • Based on MultiSet Rewriting • Foundations in (linear) logic • Ties to Petri nets and process algebra • Practice • Kerberos V • Implementation underway Quantitative Security Analysis

  7. Multiset Rewriting … • Multiset: set with repetitions allowed • a,b,c  a,a,b,c,c,c • Rewrite rule: r: N1 N2 • Application: M1  M2 state M’, N1 M’, N2 Quantitative Security Analysis

  8. … with Existentials • msets of 1st-order atomic formulas • Rules: r: F(x) n. G(x,n) • Application M1  M2 M’, F(t) M’, G(t,c) c not in M1 Quantitative Security Analysis

  9. Traces and Scripts • Traces • Rewrite sequence (r1,q1),…,(rn,qn) from M0 to Mn • Rules ri • Substitutions qi • Scripts • Parametric traces • S, (r,x) • S1 + S2 • !n S • Normal run: SNR • Attack scripts: SA Vitaly’s symbolic traces Quantitative Security Analysis

  10. MSR for Security Protocols • Messages • A, k, n,… Princ., keys, nonces, … • {m}k, (m,m’), … Encryption, concat., … • Predicates • N(m) Network messages • M*(t1,…,tn) Public data • MA(t1,…,tn) Private data • I(m) Intruder info. • Lv(t1,…,tn) Local states Quantitative Security Analysis

  11. A B: {nA, A}kB B A: {nA, nB}kA A B: {nB}kB Example • Needham-Schroeder protocol • Initiator role PrvKA(kA,k’A),PubK*(B,kB),L(kA,k’A,kB,nA),N({nA,A}kB) PrvKA(kA,k’A),PubK*(B,kB)     nA. L(kA,k’A,kB,nA),N({nA,nB}kA)  N({nB}kB) Quantitative Security Analysis

  12. Preparing for Cost Assignment • Isolate operations • Verification • Success • Failure • Construction • Apply rule in stages • Pre-screening • Detailed verification • Split LHS into atomicsteps • Allow failure Quantitative Security Analysis

  13. Fine-Grained MSR (1) • Rules • Clean-up lhs  rhs else cr • Predicates • Registers Rv(m) • Headers Nh(m) • Phased execution • Select rule based only on predicates • Verify if arguments match • Allow failure Quantitative Security Analysis

  14. Fine-Grained MSR (2) • Verification rules • Nh(x)  R(x) • Lv(x) R(x) • R(y), R’(opy(x)) R’’(x) else cr • R(x), R’(x)  . else cr • R(x) R’(m) • … • Construction rules • Remain the same Quantitative Security Analysis

  15. Fine-Grained Intruder I(g), I(gx)  I(x) Dolev-Yao style SubversionGuessing • Nh(x)  I(x) • M*(x)  I(x) • I(y), I(opy(x)) I(x) • I(x)  Nh(x) • . x. I(x) • I(x) I(op(x)) • .  X(A) • X(A)  . • X(A), MA(x)  X(A), I(x) …  G(x) …  V1(m1) …  V2(m2) G(x), V1(y), V2(y)  I(x) Quantitative Security Analysis

  16. Cost SvtA • t: cost type • Time, space, energy, … • A: principal incurring cost • v: amount of cost • Physical measurements • 0 /  (Dolev-Yao model) • Complexity classes Quantitative Security Analysis

  17. Assigning Cost – Basic Operations • Network • Storage • Operations • Construction • Successful verification • Failed verification • Subversion • Guessing • Various ways • Supportsvery highprecision • Difficultydepends onprecision • Possiblysubjective Quantitative Security Analysis

  18. Assigning Costs – Traces & Scripts • Traces: k(T) • Add up basic costs • Monotonic costs: time, energy, … • Non-monotonic: space, … • Scripts: k(S) • Interval arithmetic • Script alternative Quantitative Security Analysis

  19. C  0 (Dolev-Yao) C k1 C k2 Quantitative Security Analysis A model checking view • Explicit state MC • Direct • Symbolic MC • Via encoding Quantitative Security Analysis

  20. Threshold Analysis • k(SNR) kHW/HCI? • Cost of normal run acceptable? • PDAs, cell phones, … • k(SA) kI? • Cost of attack/defense acceptable? • Cost of candidate attack vs. resources • Non Dolev-Yao operations • min x. k(SA(x)) kI++? • Design protocol • Fine-tuning parameters Quantitative Security Analysis

  21. Comparative Analysis • k(SA1) k(SA2) ? • Comparing attacks • Protocol can always be attacked • k(SP1) k(SP2) ? • Comparing protocols • kB(SA) kI(SA) ? • Comparing attack and defense costs • Denial of Service • “Tit for tat” – Carl Gunter Quantitative Security Analysis

  22. Typical Client/Server Exchange Server Client request scq tcq ssq tsq challenge scc tcc ssc tsc  T response scr tcr -(ssq+ssc) tsr ok sco tco 0 tso  B Quantitative Security Analysis

  23. Time DoS  • Service rate: 1/tsq • Usually dominated by networking costs  tsq • Service rate • 1/(tsq + tsc + tsr) • Attack rate • 1/tcq q • Service rate • 1/(tsq + tsc) • Attack rate • 1/tcq tcq tsq c 0 tsc q tcq tsq Betterattack c 0 tsc   tsr Quantitative Security Analysis

  24. q tcq 0 ssq tsq Space DDoS c 0 tsc 0 ssc  T  tsr  0 -(ssq+ssc)  B • Max concurrent requests • n(B) = B / (ssq + ssc) • Optimal time-out • tminT • T  (tsq + tsc)* (n(B) – 1) • Example • ssq + ssc = 128 b • tsq + tsc = 100 ms • tmin = 90 s • n(B) = 10,000 Space B n(B) - 1 ssc 1 ssq B = 1.28 MbT  ~16 min Time tsq tsc  T tsr Quantitative Security Analysis

  25. Conclusions • Quantitative protocol analysis • Cost conscious attacks (non Dolev-Yao) • Fine-Grained specification languages (MSR) • Related work • C. Meadows: Cost framework for DoS • G. Lowe: guessing attacks • D. Tomioka, et al: cost for spi-calculus • Future work • Attack costs: WEP • DoS aware protocols: JFK, client puzzles, bins • Protocol analysis as optimization problem • Economics of network security • Complexity-based costs and mixing probability Quantitative Security Analysis

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