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AKE via 2-key KEM Haiyang Xue, Xianhui Lu, Bao Li, Bei Liang Jingnan - PowerPoint PPT Presentation

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Understanding and Constructing AKE via 2-key KEM Haiyang Xue, Xianhui Lu, Bao Li, Bei Liang Jingnan He Outline Authenticated key exchange Motivations & our contributions AKE 2-key KEM AKE in a post quantum world

  1. Understanding and Constructing AKE via 2-key KEM Haiyang Xue, Xianhui Lu, Bao Li, Bei Liang Jingnan He

  2. Outline  Authenticated key exchange  Motivations & our contributions  AKE ← 2-key KEM ←  AKE in a post quantum world

  3. Diffie-Hellman Key Exchange [DH76] 𝑽 𝑩 𝑽 B 𝑦 → 𝑕 𝑦 = 𝑌 𝑧 → 𝑕 𝑧 = 𝑍 X Y 𝐿 = 𝑍 𝑦 𝐿 = 𝑌 𝑧 • Passive secure under DDH assumption • Adaptive attacks: Man-in-the-middle attack etc. • Basic and general idea: Authenticated Key Exchange (AKE)

  4. Authenticated Key Exchange • Authenticated Key Exchange (AKE). Binding id with static public key using PKI etc. 1. Security models BR model, CK model, HMQV-CK, eCK model, CK+ model 2. Constructions • Explicit : BR, CK01,IKE, Krawczyk03(SIGMA), …, Peikert14 etc. • Implicit: MTI, MQV, HMQV, OAKE, Okamoto07,NAXOS, BCNP+09, FSXY12-13 etc

  5. General Structure of AKE Static Pub/Sec Static Pub/Sec Key 𝑞𝑙 𝐵 /𝑡𝑙 𝐵 Key 𝑞𝑙 𝐶 /𝑡𝑙 𝐶 Ephemeral Ephemeral Pub/Sec Key Pub/Sec Key 𝑞𝑙 𝐵0 /𝑡𝑙 𝐵0 𝑞𝑙 𝐶0 /𝑡𝑙 𝐶0 Session Key

  6. Challenges of AKE • The models are tedious to describe and difficult to get right; • just describing a concrete protocol itself can be hard enough; • the security proofs and checking even more so.

  7. Security of AKE • Test (Target) Session Adversary Capability 𝐿 ∗ ≈ 𝑑 𝐿 𝑉 • Send 𝒕𝒍 𝑩 /𝒃 𝒕𝒍 𝑩𝟏 /𝒚 𝒕𝒍 𝑪𝟏 /𝒛 𝒕𝒍 𝑪 /𝒄 • Session state Reveal 1 0 0 1 • Session Key Reveal • (1, 1) wPFS • (1, -) KCI • Corrupt • … • 8 cases

  8. Security of AKE • Bellare-Rogaway 93 (BR93) indistinguishable type definition • Canetti-Krawczyk 01(CK01) stronger security (session key, session state) • LaMacchia-Lauter-Mityagin 07 (eCK) stronger (session key, ephemeral randomness,wPFS+KCI+MEX) • Fujioka-Suzuki-Xagawa-Yoneyama 12 (CK+) reform the security of HMQV: CK01+wPFS+KCI+MEX

  9. Outline  Authenticated key exchange  Motivations & our contributions  AKE ← 2-key KEM ←  AKE in a post quantum world

  10. Constructions of AKE • Explicit AKE: using additional primitives i.e., signature or MAC 1. IKE, Canetti-Krawczyk 02 2. SIGMA, Krawczyk 03, Peikert 14 3. TLS, Krawczyk 02 • Implicit AKE: unique ability so as to compute the resulted session key 1. MTI 86 : the first one 2. MQV 95 : various attacks 3. HMQV 05 : the first provable secure implicit-AKE via gap-DH and KEA 4. Okamoto 07 : in standard model from DDH (Hashing Proof Sys.) 5. LLM 07 : NAXOS scheme from gap-DBDH 6. Boyd et al. 08 : Diffie-Hellman+KEM 7. FSXY 12 (std.), FSXY 13 (RO) 8. ZZD+15 HMQV-type based on RLWE with weaker aim

  11. Motivation • Explicit AKE • Implicit AKE SIGMA ??? Krawczyk 03

  12. Motivations • What is the (non-interactive) core building block of implicit AKE? • How to grasp and simplify the construction and analysis of implicit AKE?

  13. Our Works • What is the (non-interactive) core building block of implicit AKE? • propose a new primitive 2-key KEM • How to grasp and simplify the construction and analysis of AKE? • give frames of AKE to understand several well-know AKEs • construct new AKEs from 2-key KEM

  14. Outline  Authenticated key exchange  Motivations & our contributions  AKE ← 2-key KEM ←  AKE in a post quantum world

  15. Key Encapsulation Mechanism(KEM) 𝐹𝑜𝑑 𝑠 𝑞𝑙 (𝐷, 𝐿) 𝐸𝑓𝑑 𝐿 ′ = 𝐿 𝑡𝑙 𝐿𝐻𝑓𝑜

  16. Key Exchange (transport) and KEM 𝑽 A 𝑽 B 𝑞𝑙 (𝐷, 𝐿) = 𝐹𝑜𝑑(𝑞𝑙, 𝑠) 𝐷 𝐸𝑓𝑑(𝑡𝑙, 𝐷) = 𝐿 = 𝐹𝑜𝑑(𝑞𝑙, 𝑠)

  17. Our 2-key KEM 𝐿𝐻𝑓𝑜1 𝐿𝐻𝑓𝑜0 𝐹𝑜𝑑 𝑠 𝑞𝑙 1 𝑞𝑙 0 (𝐷, 𝐿) 𝐸𝑓𝑑 𝐿 ′ = 𝐿 𝑡𝑙 1 𝑡𝑙 0 It is simple, not a big deal

  18. One-side AKE from 2-key KEM? 𝑽 A 𝑽 B 𝑞𝑙 1 𝑞𝑙 0 (𝐷, 𝐿) = 𝐹𝑜𝑑(𝑞𝑙 1 , 𝑞𝑙 0 , 𝑆 𝐶 ) 𝐷 𝐸𝑓𝑑(𝑡𝑙 1 , 𝑡𝑙 0 , 𝐷) = 𝐿 The key point is how to define its security to fit the requirement of AKE

  19. 𝐷𝐷𝐵,⋅ Security of 2-key KEM Challenger 𝑩 𝑗 /𝑡𝑙 0 𝑗 } ← 𝐿𝐻𝑓𝑜0 𝑞𝑙 1 , 𝑀 𝑀 = {𝑞𝑙 0 𝑞𝑙 1 ← 𝐿𝐻𝑓𝑜1, Session State Reveal DecO ′ , 𝐷′ ′ ∈ 𝑀 If 𝑞𝑙 0 𝑞𝑙 0 Session Key Reveal ′ , 𝐷′) 𝐿 ′ = 𝐸𝑓𝑑(𝑡𝑙 1 , 𝑡𝑙 0 ∗ 𝑞𝑙 0 (𝐷 ∗ , 𝐿 ∗ ) = 𝐹𝑜𝑑 𝑞𝑙 1 , 𝑞𝑙 0 ∗ , 𝑠 𝐷 ∗ Send ′ , 𝐷 ′ ≠ (𝑞𝑙 0 ∗ , 𝐷 ∗ ) DecO 𝑞𝑙 0 𝐿′ 𝐿 ∗ ? = 𝐿′

  20. 𝐷𝐷𝐵,⋅ Security of 2-key KEM Challenger 𝑩 𝑗 /𝑡𝑙 0 𝑗 } ← 𝐿𝐻𝑓𝑜0 𝑞𝑙 1 , 𝑀 𝑞𝑙 1 ← 𝐿𝐻𝑓𝑜1, 𝑀 = {𝑞𝑙 0 Session State Reveal DecO ′ , 𝐷′ ′ ∈ 𝑀 If 𝑞𝑙 0 𝑞𝑙 0 𝐷𝑄𝐵,⋅ security Session Key Reveal ′ , 𝐷′) 𝐿 ′ = 𝐸𝑓𝑑(𝑡𝑙 1 , 𝑡𝑙 0 ⋅, 𝐷𝐷𝐵 security ∗ 𝑞𝑙 0 (𝐷 ∗ , 𝐿 ∗ ) = 𝐹𝑜𝑑 𝑞𝑙 1 , 𝑞𝑙 0 ∗ , 𝑠 𝐷 ∗ Send ′ , 𝐷 ′ ≠ (𝑞𝑙 0 ∗ , 𝐷 ∗ ) DecO 𝑞𝑙 0 𝐿′ 𝐿 ∗ ? = 𝐿′

  21. One-side AKE from [CCA, CPA] 2-key KEM 𝑽 A 𝑞𝑙 𝐵1 𝑽 B 𝑞𝑙 𝐵0 (𝐷, 𝐿) = 𝐹𝑜𝑑(𝑞𝑙 𝐵1 , 𝑞𝑙 𝐵0 , 𝑠 𝐶 ) 𝐷 𝐿 = 𝐸𝑓𝑑(𝑡𝑙 𝐵1 , 𝑡𝑙 𝐵0 , 𝐷)

  22. The other side AKE from [CCA, CPA] 2-key KEM 𝑽 A 𝑽 B 𝑞𝑙 𝐶1 𝑞𝑙 𝐶0 𝐷 𝐶 (𝐷 𝐶 , 𝐿 𝐶 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐶1 , 𝑞𝑙 𝐶0 ) 𝐿 𝐶 = 𝐸𝑓𝑑(𝑡𝑙 𝐶1 , 𝑡𝑙 𝐶0 , 𝐷 𝐵 )

  23. Main AKE frame? ← [𝐷𝐷𝐵, 𝐷𝑄𝐵] 2-key KEM 𝑽 A 𝑞𝑙 𝐵1 𝑽 B 𝑞𝑙 𝐶1 𝑞𝑙 𝐵0 𝐷 𝐶 (𝐷 𝐶 , 𝐿 𝐶 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐶1 , 𝑞𝑙 𝐶0 ) 𝐿 𝐶 = 𝐸𝑓𝑑(𝑡𝑙 𝐶1 , 𝑡𝑙 𝐶0 , 𝐷 𝐵 ) 𝑞𝑙 𝐶0 𝐷 𝐵 (𝐷 𝐵 , 𝐿 𝐵 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐵1 , 𝑞𝑙 𝐵0 ) 𝐿 𝐵 = 𝐸𝑓𝑑(𝑡𝑙 𝐵1 , 𝑡𝑙 𝐵0 , 𝐷 𝐵 ) 𝐿 = 𝐼𝑏𝑡ℎ 𝑡𝑗𝑒, 𝐿 𝐵 , 𝐿 𝐶 𝑝𝑠 𝑄𝑆𝐺 𝐿 𝐶 ⊕ 𝑄𝑆𝐺(𝐿 𝐵 )

  24. Several AKE frames with Tricks 𝑽 A 𝑞𝑙 𝐵1 𝑽 B 𝑞𝑙 𝐶1 𝑞𝑙 𝐵0 𝐷 𝐶 (𝐷 𝐶 , 𝐿 𝐶 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐶1 , 𝑞𝑙 𝐶0 ) 𝐿 𝐶 = 𝐸𝑓𝑑(𝑡𝑙 𝐶1 , 𝑡𝑙 𝐶0 , 𝐷 𝐵 ) 𝑞𝑙 𝐶0 𝐷 𝐵 All the randomness for 𝐹𝑜𝑑 and 𝐿𝐻𝑓𝑜0 (𝐷 𝐵 , 𝐿 𝐵 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐵1 , 𝑞𝑙 𝐵0 ) 𝐿 𝐵 = 𝐸𝑓𝑑(𝑡𝑙 𝐵1 , 𝑡𝑙 𝐵2 , 𝐷 𝐵 ) is generated from both ephemeral secret 𝑠 𝐵0 Trick 1 and static secret key 𝑡𝑙 𝐵 𝐿 = 𝐼𝑏𝑡ℎ 𝑡𝑗𝑒, 𝐿 𝐵 , 𝐿 𝐶 𝑝𝑠 𝑄𝑆𝐺 𝐿 𝐶 ⊕ 𝑄𝑆𝐺(𝐿 𝐵 )

  25. Several AKE frames with Tricks 2-key KEM is public key 𝑞𝑙 𝐶0 independent 𝑽 A 𝑞𝑙 𝐵1 𝑽 B 𝑞𝑙 𝐶1 𝑞𝑙 𝐵0 𝐷 𝐶 (𝐷 𝐶 , −) = 𝐹𝑜𝑑1(𝑞𝑙 𝐶1 , −) Trick 2 𝐿 𝐶 = 𝐸𝑓𝑑(𝑡𝑙 𝐶1 , 𝑡𝑙 𝐶0 , 𝐷 𝐵 ) 𝑞𝑙 𝐶0 𝐷 𝐵 (𝐷 𝐵 , 𝐿 𝐵 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐵1 , 𝑞𝑙 𝐵0 ) 𝐿 𝐵 = 𝐸𝑓𝑑(𝑡𝑙 𝐵1 , 𝑡𝑙 𝐵0 , 𝐷 𝐵 ) 𝐿 = 𝐼𝑏𝑡ℎ 𝑡𝑗𝑒, 𝐿 𝐵 , 𝐿 𝐶 𝑝𝑠 𝑄𝑆𝐺 𝐿 𝐶 ⊕ 𝑄𝑆𝐺(𝐿 𝐵 )

  26. Several AKE frames with Tricks 𝑽 A 𝑞𝑙 𝐵1 𝑽 B 𝑞𝑙 𝐶1 𝑞𝑙 𝐵0 𝐷 𝐶 (𝐷 𝐶 , 𝐿 𝐶 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐶1 , 𝑞𝑙 𝐶0 ) 𝐿 𝐶 = 𝐸𝑓𝑑(𝑡𝑙 𝐶1 , 𝑡𝑙 𝐶0 , 𝐷 𝐵 ) 𝑞𝑙 𝐶0 𝐷 𝐵 (𝐷 𝐵 , 𝐿 𝐵 ) = 𝐹𝑜𝑑(𝑞𝑙 𝐵1 , 𝑞𝑙 𝐵0 ) 𝐿 𝐵 = 𝐸𝑓𝑑(𝑡𝑙 𝐵1 , 𝑡𝑙 𝐵0 , 𝐷 𝐵 ) Trick 3 𝐷 𝐶 can be publicly computed from 𝑞𝑙 𝐵0 𝐷 𝐵 can be publicly computed from 𝑞𝑙 𝐶0 𝐿 = 𝐼𝑏𝑡ℎ 𝑡𝑗𝑒, 𝐿 𝐵 , 𝐿 𝐶 𝑝𝑠 𝑄𝑆𝐺 𝐿 𝐶 ⊕ 𝑄𝑆𝐺(𝐿 𝐵 )

  27. Understanding HMQV-A based on 2-key KEM 𝑽 A 𝐵 = 𝑕 𝑏 𝑽 B 𝑌 𝑌 = 𝑕 𝑦 𝑍 = 𝑕 𝑧 , 𝐷 𝐵 = 𝑍𝐶 𝑓 𝑒 = ℎ(𝑌, 𝐶) 𝑓 = ℎ(𝑍, 𝐵) 𝑍𝐶 𝑓 𝐿 𝐶 = 𝑌𝐵 𝑒 𝑧+𝑐𝑓 𝐵 = 𝑍𝐶 𝑓 𝑦+𝑏𝑒 𝐿

  28. Understanding HMQV-B based on 2-key KEM 𝑽 A 𝐶 = 𝑕 𝑐 𝑽 B 𝑌𝐵 𝑒 𝑌 = 𝑕 𝑦 , 𝐷 𝐶 = 𝑌𝐵 𝑒 𝑍 = 𝑕 𝑧 𝑒 = ℎ(𝑌, 𝐶) 𝑓 = ℎ(𝑍, 𝐵) 𝑍 𝐿 𝐶 = 𝑌𝐵 𝑒 𝑧+𝑐𝑓 𝐵 = 𝑍𝐶 𝑓 𝑦+𝑏𝑒 𝐿

  29. Understanding HMQV based on 2-key KEM 𝑽 A 𝐵 = 𝑕 𝑏 𝐶 = 𝑕 𝑐 𝑽 B 𝑌𝐵 𝑒 𝑌 𝑌 = 𝑕 𝑦 , 𝐷 𝐶 = 𝑌𝐵 𝑒 𝑍 = 𝑕 𝑧 , 𝐷 𝐵 = 𝑍𝐶 𝑓 𝑒 = ℎ(𝑌, 𝐶) 𝑓 = ℎ(𝑍, 𝐵) 𝑍𝐶 𝑓 𝑍 𝐿 𝐶 = 𝑌𝐵 𝑒 𝑧+𝑐𝑓 𝐵 = 𝑍𝐶 𝑓 𝑦+𝑏𝑒 𝐿 𝐿 = 𝐼𝑏𝑡ℎ(A, B, 𝑌, 𝑍, 𝐿 𝐵 , 𝐿 𝐶 )

  30. Understanding AKE • Every well-known implicit AKE implies a 2-key KEM • HMQV(&OAKE): 2-key KEM from gap-DH and KEA • LLM07: (aka. NAXOS) 2-key KEM from gap-DH • Okamoto 07: 2-key KEM from DDH (modified Cramer-Shoup) • FSXY12, improved KEM combiner in std. model • FSXY13, improved KEM combiner in RO model

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