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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 - PowerPoint PPT Presentation
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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
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Authentication Symmetric verifier 知 the secret (secret key)
or an image of the secret (password)
Asymmetric verifier 知 a public key
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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
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Asymmetric Authentication Static :
Dynamic :
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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
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Dynamic Asymmetric GQ1
)(mod?
nDGR vd
verifier claimantVerification key: (v, n)
idFormat Mechanism
G
d{0,1,…,v-1}
r{1,2,…,n-1}R=rv mod n
d
Secret QD=rQd 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
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Dynamic Asymmetric GQ2
)(mod...11
?2 nGGRD md
md
verifier claimantVerification key: (v, n), where v=2k
idFormat Mechanism
G1, G2,…, Gm
d1 ~ dm {0,1,…,2k-1 –1}
r{1,2,…,n-1}R=rv mod n
d1 ~ dm
Secret g1, g2,…, gm
注 : Gi = gi2 mod n, where i= 1~m
)(mod...11
12 nggrD mk d
md
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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