Construction of digital fingerprint system based on discrete logarithm

2.2 Security Analysis

(1) Security of Issuer M

The encrypted data group with copy is encrypted by M using B's public key, and is sent to B after being signed. The third-party fingerprint distribution center cannot obtain the copy with fingerprint, thus avoiding the illegal use of the copy by the third party and reducing the risk of the publisher.

(2) Security of User B

B's decryption key is invisible to M and other users (i.e., the user's decryption key is unknown). The system keeps the linear equations confidential, and M and other users cannot obtain the solution vector from other means. The digital fingerprint contains (gi mod p), where i is a positive integer randomly selected and saved by the user, and p is only disclosed to the fingerprint distribution center. Therefore, M and other users cannot forge digital fingerprints to frame innocent users.

(3) Security of third-party fingerprint distribution center

This solution is based on the complete trust of the third-party fingerprint distribution center. The fingerprint generation required p and decryption key are open to the fingerprint distribution center, and only the copy with fingerprint is kept confidential to the fingerprint distribution center. If the third-party fingerprint distribution center obtains the copy with fingerprint and uses it illegally, the issuer and the user will be at great risk. Therefore, the third-party fingerprint distribution center must be completely trustworthy.

This paper constructs a digital fingerprint system based on the difficulty of discrete logarithm problem. Since the system mainly adopts the encryption and decryption algorithm in the symmetric cryptographic system, and the symmetric key is randomly selected by the publisher; the key used by the user to decrypt the data group, that is, the solution vector of the linear equation system randomly generated by the system, is easy to calculate and has good implementation efficiency. The digital fingerprint in the copy is determined by the user and the trusted third-party fingerprint distribution center, so that the publisher and other users cannot frame innocent users, which increases the security of users. It is worth noting that this scheme requires that the third-party fingerprint distribution center must be completely trusted, otherwise both the publisher and the user will be at risk.