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-dr) 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 =

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter18: Deterministic Dynamic Programming

Section18.4: Resource-allocation Problems

Problem 3P

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Alice	Bob
Chooses p=23
Chooses a primitive element α=5
Choose a random integer d=4
Compute β = α^d mod p =
Public key is k_pub = (p, α, β) = Private key is k_pr = d =
Send Public key k_pub = (p, α, β) to Bob:	Receives Alice’s public key k_pub = (p, α, β)=
Choose an ephemeral key K_E = 7
Message to send is m=8
Computes signatures (s,r) for m r= α^KE mod p = Compute K_E^-1 mod (p-1) s= (m-dr) K_E^-1 mod (p-1) =
Send (m, (r,s)) to Bob:	Receives (m, (r,s)) =
	Compute t = β^r * r^s mod p =
	Verifies if t = α^m mod p =