Complexity and fast algorithms for multiexponentiations
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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. Authentication. Symmetric

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Complexity and Fast Algorithms for Multiexponentiations

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Complexity and fast algorithms for multiexponentiations

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


Authentication

Authentication

  • Symmetric

    verifier知 the secret (secret key) or an image of the secret (password)

  • Asymmetric

    verifier知 a public key


Symmetric authentication

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


Asymmetric authentication

Asymmetric Authentication

  • Static :

  • Dynamic :


Dynamic asymmetric authentication

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


Dynamic asymmetric gq1

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


Dynamic asymmetric gq2

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


Conclusion

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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