Question

Digital signature is typically put on the one-way hash of the message, instead of on the message directly. One of the reasons is the cost, because signing a short hash value is more efficient than signing a message that can be very long. Bob says that his message is always short. so he decides to directly sign the message, rather than signing its hash. Without knowing Bobs private key, can you generate a pair (m, s), where s is Bob's signature on m, and m can be anything?

Answer 1

When using a digital signature, it is more efficient to sign a short hash value of a message rather than the message itself. However, it is still possible for someone to generate a signature on a message without knowing the private key.

Step-by-step explanation:

When using a digital signature, it is more efficient to sign a short hash value of a message rather than the message itself. This is because signing a short hash is faster and consumes less computational resources. However, if Bob decides to directly sign his message instead of its hash, it would still be possible for someone to generate a pair (m, s) where s is Bob's signature on m, without knowing Bob's private key.

To understand why, consider that a digital signature is created using Bob's private key and can only be verified using his corresponding public key. If Alice knows Bob's public key, she can forge a signature by randomly generating a message m and then signing it with Bob's public key. This is possible because anyone can generate a valid signature using a public key, but only the corresponding private key can generate a valid signature that can be verified.

Therefore, it is crucial to use best practices when implementing digital signatures and follow industry standards to ensure the security and authenticity of the signed messages.