Constructing Verifiable Random Number in Finite Field

In information security field underlying cryptography, random sequences, which are the base of system security, play a very important role. Random sequences with high security are often needed in cryptography field. From the view of security, real random sequences should be completely unpredictable and reliable. In many circumstances, a random number not only need to be random, but also need to be verifiable. So verifiable random number is much needed in cryptography. Using linear equations in finite field, a method for constructing verifiable random number is proposed. It enjoys advantages of high efficiency and no error. Then the security properties such as unpredictability and unmanipulability are analyzed, and an example is given to show the feasibility of the method. Finally, a way for fast generation and verification of VRN with large amounts of data is given.