In a blockchain, Alice wants to send a transaction to Bob. S…
In a blockchain, Alice wants to send a transaction to Bob. She signs the transaction with her private key, and Bob wants to verify the authenticity of the transaction. Alice’s transaction has the following form: Transaction Data: TT Alice’s private key: kAk_A Alice’s public key: pAp_A The transaction signature is given as σA=Signk(T) where Signk(T)\text{Sign}_k(T) is the digital signature of the transaction data TT, signed using Alice’s private key kAk_A. To verify the authenticity, Bob computes the following equation: Verifyp(T,σA)=TrueifVerifyp(T,σA)=Decryptp(σA)==H(T) \text{Verify}_p(T, \sigma_A) = \text{True} \quad \text{if} \quad \text{Verify}_p(T, \sigma_A) = \text{Decrypt}_p(\sigma_A) == H(T)Where: Verifyp(T,σA)\text{Verify}_p(T, \sigma_A) is the verification function using Alice’s public key pAp_A. H(T)H(T)is the hash of the transaction TT. What conditions must hold for Bob to accept the transaction as valid?