Given the following table describing the procedure for Alice to send a signed message with RSA signature to Bob, calculate the unknown entities and verify that Bob has received the correct message sent by Alice. Fill in the values of the "???" below. Alice Bob Public key (n,e) =(55,3); Private key (n,d)=(55,27) Send Public key (n,e ) to Bob: Receives Alice’s public key (n,e): Message to be sent is m=3 Computes signatures s for m = mdmod n = ??? Send (m,s) to Bob Receives (m,s) = ??? Compute m’ : se mod n = ??? b.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. Fill in the values of the "???" below. Alice Bob Chooses p=23 Chooses a primitive element α=7 Choose a random integer d=6 Compute β = αd mod p = ??? Public key is kpub = (p, α, β) = ??? Private key is kpr, where d = 6 Send Public key kpub = (p, α, β) to Bob: ??? Receives Alice’s public key kpub = (p, α, β) = ??? Choose an ephemeral key KE = 5 Message to send is m=10 Computes signatures (s,r) for m r= αKE mod p = ??? Compute KE-1mod (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 = ???
Given the following table describing the procedure for Alice to send a signed message with RSA signature to Bob, calculate the unknown entities and verify that Bob has received the correct message sent by Alice. Fill in the values of the "???" below.
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Alice |
Bob |
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Public key (n,e) =(55,3); Private key (n,d)=(55,27) |
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Send Public key (n,e ) to Bob: |
Receives Alice’s public key (n,e): |
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Message to be sent is m=3 |
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Computes signatures s for m = mdmod n = ??? |
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Send (m,s) to Bob |
Receives (m,s) = ??? |
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Compute m’ : se mod n = ??? |
b.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. Fill in the values of the "???" below.
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Alice |
Bob |
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Chooses p=23 |
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Chooses a primitive element α=7 |
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Choose a random integer d=6 |
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Compute β = αd mod p = ??? |
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Public key is kpub = (p, α, β) = ??? Private key is kpr, where d = 6 |
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Send Public key kpub = (p, α, β) to Bob: ??? |
Receives Alice’s public key kpub = (p, α, β) = ??? |
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Choose an ephemeral key KE = 5 |
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Message to send is m=10 |
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Computes signatures (s,r) for m r= αKE mod p = ??? Compute KE-1mod (p-1) = ??? s= (m-d*r)* KE-1 mod (p-1) = ??? |
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Send (m, (r,s)) to Bob: ??? |
Receives (m, (r,s)) = ??? |
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Compute t = βr * rs mod p = ??? |
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Verifies if t = αm mod p = ??? |
c.Given the following table describing the procedure for Alice to send a signed message with DSA signature to Bob, calculate the unknown entities and verify that Bob has received the correct message sent by Alice. Here, for simplicity we assume that the hash of a message m, h(m) is already computed and given to you. Fill in the values of the "???" below.
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Alice |
Bob |
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Choose p=19, q=7, α=2, d=6 |
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Compute β= αd mod p = ??? |
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Public key: kpub = (p,q,α,β) = ??? Private key: kprivwhere d = 6 |
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Send public key to Bob: (p,q,α,β) = ??? |
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Hash of message m , h(m) = 7 (given) |
Receive Alice’ public key (p,q,α,β) = ??? |
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Ephemeral key, kE = 5 |
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Compute kE-1 mod q = ??? |
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Compute r= (αkE mod p) mod q = ??? |
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Compute s= (h(m) + d*r)* kE-1mod q = ??? |
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DSA Signature (r,s) = ??? |
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Send message (m, (r,s)) to Bob |
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Receive message (m, (r,s)) from Alice; here we assume h(m)=7 as known |
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Compute w = s-1mod q = ??? |
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Compute u1 = w*h(m) mod q = ??? |
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Compute u2 = w*r mod q = ??? |
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Compute ν= (αu1* βu2 mod p) mod q = ??? |
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Verification: compute µ = r mod q = ??? |
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