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 =

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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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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