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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

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

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

• Asymmetric

verifier知 a public key

### 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

• Static :

• Dynamic :

### 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

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

### 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

### 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