Most of the existing cryptosystems use two keys for encryption, the public key to encrypt messages and the private key t

[answerhappygod]

Most of the existing cryptosystems use two keys for encryption,
the public key to encrypt messages and the private key to decrypt
the resulted cypher. The modular arithmetic is used primarily in
these cryptosystems. Suppose that in some cryptosystem, the private
and public keys are found as follows:




An integer number b is chosen such that 0 , which is
considered the public key of this cryptosystem
The private key p is somehow calculated using some
mathematical equation such that the same message is produced when
we multiply it with the product of the two generated keys, as
follows:





(message*b*p) mod m=message



Example:

Assume that we have the following values:


message=17 b=7 p=3

When we multiply these values with each other under mod 20,
the same message is produced as follows:


(17*7*3) mod 20=17



Q: what is the best way to compose the private key that makes the given formula correct?