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Information Security and
Management
10. Other Public-key Cryptosystems
Chih-Hung Wang
Fall 2011
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Diffie-Hellman Key Exchange
• Diffie and Hellman 1976
• A number of commercial products employ this
key exchange technique
• This algorithm enables two users to exchange
key securely
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Algorithm of Diffie-Hellman (1/2)
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Algorithm of Diffie-Hellman (2/2)
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Example of D-H Key Exchange
q=97

=5
XA = 36
XB=58
YA=536=50 mod 97
YB=558=44 mod 97
K=(YB)XA mod 97 = 4436 = 75 nod 97
K=(YA)XB mod 97 = 5058 = 75 nod 97
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Diffie-Hellman


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Supplementary (1)
• RSA based hybrid encryption system
A
Randomly selects a DES
Key (or other symmetric
encryption system) KDES
EKDES(M), EKpuB(KDES)
B
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Supplementary (2)
• Diffie-Hellman based hybrid encryption system
A
K=(YB)xA
=(YA)xB
Mod q
SK=h(K)
128 – 256 bits
YA
YB
ESK(M)
B
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ElGamal Cryptographic System
• In 1984, Elgamal announced a public-key
scheme based on discrete logarithms.
• Closely related to the Diffie-Hellman technique.
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Global Public Elements
• q : prime number
• α: α<q and α a primitive root of q
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Key Generation by Alice
•
•
•
•
Select private XA: XA<q-1
Calculate YA: YA= αXA mod q
Public key: PU={q, α, YA}
Private key: XA
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Encryption by Bob with Alice’s Public
Key
•
•
•
•
•
•
Plaintext: M <q
Select random integer k: k<q
Calculate K: K=(YA)k mod q
Calculate C1: C1 = αk mod q
Calculate C2: C2 =KM mod q
Ciphertext: (C1, C2)
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Decryption by Alice with Alice’s Private
Key
• Ciphertext: (C1, C2)
• Calculate K: K=(C1) XA mod q
• Plaintext: M=(C2K-1) mod q