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Complexity and Fast Algorithms for Multiexponentiations in Authentication Systems

This IEEE study explores symmetric and asymmetric verification methods. It covers rounds, dynamic authentication, and GQ equations. The research details efficient protocols for GQ1 and GQ2 verification keys, showcasing practical applications in NetWare and smart card systems.

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Complexity and Fast Algorithms for Multiexponentiations in Authentication Systems

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  1. Complexity and Fast Algorithms for Multiexponentiations Source: IEEE Transactions on Computers Vol. 49 pp.141-147 2000 Author: Vassil S. Dimitrov, Graham A. Jullien, and William C. Miller Speaker: Lai, Yi-Peng Date: 04/25/2002

  2. Authentication • Symmetric verifier知 the secret (secret key) or an image of the secret (password) • Asymmetric verifier知 a public key

  3. Symmetric Authentication • One-way function without challenge 1981 1st round: Image = fk (r), input i = fk-1 (r), compute f(i), verify f(i) ?= image, replace image with i. …… n-th round: Image = fk-n+1 (r) input i = fk-n (r), compute f(i), verify f(i) ?= image, replace image with i. • Dynamic authentication

  4. Asymmetric Authentication • Static : • Dynamic :

  5. Dynamic Asymmetric Authentication • generic equation: GQv=1 mod n • public number deduced from id: G • public verification key: (v,n) • private number: Q • non-zero random number: r

  6. Dynamic Asymmetric GQ1 Verification key: (v, n) verifier claimant id Format Mechanism r{1,2,…,n-1} R=rv mod n G d{0,1,…,v-1} d Secret Q D=rQd mod n 注:因為於id訂定時已藏入相關於該id對應的public number G 並算出符合generic equation(GQv=1 mod n)的secret Q

  7. Dynamic Asymmetric GQ2 Verification key: (v, n), where v=2k verifier claimant id Format Mechanism r{1,2,…,n-1} R=rv mod n G1, G2,…, Gm d1 ~ dm{0,1,…,2k-1–1} d1 ~ dm Secret g1, g2,…, gm 注: Gi = gi2 mod n, where i= 1~m

  8. Conclusion • Computation引入中國餘數定理 • NetWare 4.11 and 5.0 based on GQ1 challenge 32bits v=216+1 • Smart card (ST 16601 3.57MHz): (1)14sec for RSA – 512bits, CRT, n=p1p2p3 (2)14sec for GQ1 – 768bits, v=216+1 (3)1 sec for GQ2 – 512bits,k=5,m=3,n=p1p2p3

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