Unit 8 Assignment 2 Mod Mood N

For example consider the RSA scheme, where the signature of a message 0 ≤ M < N is s (M) = Md mod N. thought that the restriction that 0 ≤ M < N is necessary, since s (M) = s (M+N). A collision resistant hash function that hashes arbitrary-length strings into numbers between 0 and N lets the signer sign any message M by exponentiation the hash of the message s(H(M)) = H(M) d mod N. This is a generic mechanism that transforms any signature scheme good for signing messages of a fixed length and a collision-resistant hash function into a signature scheme that can handle arbitrary-length messages. This mechanism is called the hash-and-sign paradigm and is the basis for all modern practical signature schemes. It is additionally very momentous that essentially all practical signature schemes are either outright insecure or lack proof of security in any reasonable model for signing even fixed-length messages if the message is not hashed.
The second role of hash functions is to prevent this attacks or attacks which is similar to this kind of attacks. It is not surely knew which of the properties of the hash function are adequate to satisfy this part. The Cramer-Shoup signature scheme is the unusual example of a signature scheme that uses a hash function only for domain extension that is it does not require a hash function for signing short messages. An attacker prepares two documents M1 and M2, hashes of these documents are identical, and then a hash-and-sign signature on M1 is also a valid signature on