第4章 BAN 类逻辑4.1 BAN 逻辑4.1.1 BAN 逻辑构件的语法和语义 4.1.2 BAN 逻辑的推理规则1.消息含义规则(message-meaning rules )3条:R1. K KX P P Q P }{,| −→←≡┣;|~|X Q P ≡Xsaid Q believes P X sees P P Q believes P KK}{,↔R2. 1}{,|-−→−≡K KX P Q P ┣;|~|X Q P ≡Xs a i d Q b e l i e v e s P X s e e s P Q b e l i e v e s P K K1}{,-R3. P P ≡| Y X P Q }{, ┣X Q P |~|≡ 。
2.临时值验证规则(nonce-verification rule )1条: R4. X Q P X P |~| ),(# |≡≡┣X Q P ≡≡||Xbelieves Q believes P XsaidQ believes P X fresh believes P ),(3.管辖规则(jurisdiction rule )1条:R5. X Q P X Q P ≡≡⇒≡|| ,||┣X P ≡|Xbelieves P Xbelieves Q believes P X controls Q believes P ,4.接收消息规则(seeing rules )5条:R6. ),(Y X P ┣X PXsees P Y X sees P ),(R7. Y X P >< ┣X PXsees P X sees P Y〉〈R8. K KX P Q P P }{,| −→←≡┣X PYXsees P X sees P P Q believes P KK}{,↔R9. K KX P P P }{,| −→−≡┣X PXsees P X sees P P believes P KK}{,R10. 1}{,|-−→−≡K KX P Q P ┣X PXsees P X sees P Q believes P K K1}{,-5.消息新鲜性规则(freshness rule )1条:R11. )(# |X P ≡┣) ,(# |Y X P ≡),()(Y X fresh believes P X fresh believes P6.信念规则(belief rules )4条:R12. Y P X P ≡≡| ,|┣) ,( |Y X P ≡ R13. ) ,( |Y X P ≡┣X P ≡|R14. ) ,(| |Y X Q P ≡≡┣X Q P ≡≡|| R15. ) ,(~| |Y X Q P ≡┣X Q P |~|≡7.密钥与秘密规则(key and secret rules )4条:R16. R R P K'−→←≡|┣R R P K−→←'≡| R17. R R Q P K'−→←≡≡||┣R R Q P K−→←'≡≡|| R18. R P ≡| R '┣R P '≡| RR19. R Q P ≡≡|| R '┣R Q P '≡≡|| R4.1.3 BAN 逻辑的推理步骤 4.2 应用BAN 逻辑分析NSSK 协议 4.2.1 应用BAN 逻辑分析原始NSSK 协议X X X XP1 ;|S A A as K −−→←≡ P2 ;|S B B bsK −−→←≡ P3 ;|S A S as K −−→←≡ P4 ;||B A S A K −→←⇒≡ P5 ;||B A S B K −→←⇒≡ P6 ;|S B S bs K −−→←≡ P7 );(#||B A S A abK −−→←⇒≡ P8 ),(# |b N B ≡P9 ;|B A S abK −−→←≡ P10 ),(# |a N A ≡ P11 );(# |B A B ab K −−→←≡ P12 ).(# |B A S ab K −−→←≡ )(# |B A B abK −−→←≡Afrom B A N B A B from B A N A B B A B A B A B A B A N A S ab ab ab abbs ab as bs ab ab ab K K b K K b K K K K K K K a } ,{ : .5,} ,{: . 4,}{ : .3,}}{ ),(# , ,{ : . 2−−→←→−−→←→−−→←→−−→←−−→←−−→←→Afrom B A N B B from B A N A B A B B A B A B A N A ab ab ab abbs ab as bs ab ab ab K K b K K b K K K K K K K a } ,{ . 5,} ,{ . 4,}{ . 3,}}{ ),(# , ,{ .2−−→←−−→←−−→←−−→←−−→←−−→←a sb s a ba b a b K K K K K a B A B A B A N A }}{ ),(# , ,{ −−→←−−→←−−→← 。