Describe the three operations used by international data encryption algorithm.
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Let's say there is a public key vv. Peggy has to prove to Victor that she has the corresponding private key aa. Of course she doesn't want to disclose aato Victor, but just to prove that she has the key.
Question: What is the benefit of "Solution 2" described below (a.k.a. Fiat-Shamir), which seems more complex and using zero knowledge proofs, when there is an easy solution (see Solution 1)?
Solution 1 (easy):
Victor generates a random number rr, encrypts it with the public key vv, and sends the encrypted message rErE to Peggy
If Peggy has the private key aa, she can decrypt rErE into rr, and send rrback to Victor and claim: "Hey Victor, here is rr, this is the proof I can decrypt your message rErE, so this proves I have aa"
If Peggy doesn't have the private key aa, she cannot decrypt rErE, so she cannot prove anything.
Question: What is the benefit of "Solution 2" described below (a.k.a. Fiat-Shamir), which seems more complex and using zero knowledge proofs, when there is an easy solution (see Solution 1)?
Solution 1 (easy):
Victor generates a random number rr, encrypts it with the public key vv, and sends the encrypted message rErE to Peggy
If Peggy has the private key aa, she can decrypt rErE into rr, and send rrback to Victor and claim: "Hey Victor, here is rr, this is the proof I can decrypt your message rErE, so this proves I have aa"
If Peggy doesn't have the private key aa, she cannot decrypt rErE, so she cannot prove anything.
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