Elgamal Signature Scheme: Given the following table describing the procedure for Alice to send a signed message with Elgamal signature to Bob, calculate the unknown entities and verify that Bob has received the correct message sent by Alice. Alice Bob Chooses p=23 Chooses a primitive element α=5 Choose a random integer d=4 Compute β = αd mod p = Public key is kpub = (p, α, β) = Private key is kpr = d = Send Public key kpub = (p, α, β) to Bob: Receives Alice’s public key kpub = (p, α, β)= Choose an ephemeral key KE = 7 Message to send is m=8 Computes signatures (s,r) for m r= αKE mod p = Compute KE-1 mod (p-1) s= (m-d*r)* KE-1 mod (p-1) = Send (m, (r,s)) to Bob: Receives (m, (r,s)) = Compute t = βr * rs mod p = Verifies if t = αm mod p =
Elgamal Signature Scheme: Given the following table describing the procedure for Alice to send a signed message with Elgamal signature to Bob, calculate the unknown entities and verify that Bob has received the correct message sent by Alice.
Alice |
Bob |
Chooses p=23 |
|
Chooses a primitive element α=5 |
|
Choose a random integer d=4 |
|
Compute β = αd mod p = |
|
Public key is kpub = (p, α, β) = Private key is kpr = d = |
|
Send Public key kpub = (p, α, β) to Bob: |
Receives Alice’s public key kpub = (p, α, β)= |
Choose an ephemeral key KE = 7 |
|
Message to send is m=8 |
|
Computes signatures (s,r) for m r= αKE mod p = Compute KE-1 mod (p-1) s= (m-d*r)* KE-1 mod (p-1) = |
|
Send (m, (r,s)) to Bob: |
Receives (m, (r,s)) = |
|
Compute t = βr * rs mod p = |
|
Verifies if t = αm mod p = |
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