Bounds Of Wide-Sense 2-Frameproof Codes

With the rapid development of the Internet,information is continuously appearing in people's daily life.While people feel the convenience brought by information,they are also deeply worried about information security.More and more incidents show that from personal identity information to cyber attacks,cyber fraud and cyber terrorism,informa-tion disclosure is posing serious threats to personal and national security,and the issue of information security is gradually attracting more and more attention.Electronics scientists and computer scientists define information as signals transmit-ted in electronic circuits,which are processed data to meet the needs of users' decision-making.Digital fingerprint is a technology to protect intellectual property by preventing illegal redistribution of digital data.This technique is implemented by collecting codes called fingerprint codes.There are many kinds of fingerprint codes.This paper stud-ies frameproof codes to prevent innocent users from being framed,and mainly considers frameproof codes with coalition size no more than 2 under the wide-sense model,briefly by 2-wFP codes.The introduction of this paper introduces the research background of fingerprinting codes and the research status of frameproof codes.Corresponding to the dynamic data dis-tribution model in the Internet,the definitions and relationships of four frameproof codes are given.Most of the known works are aimed at the narrow-sense descendant model,which is equivalent to the wide-sense frameproof codes in the binary case.This paper will study 2-wFP codes for general number of symbols.The second chapter studies the lower bounds of 2-wFP codes.Firstly,the probabilistic method-deletion method is used to obtain the first lower bounds of the capacity of wide-sense frameproof codes through a uniform distribution and a nonuniform distribution.Then hypergraph is constructed by using the restriction conditions of wide-sense frameproof codes,and the second lower bounds of code capacity is obtained by using the result of the bounds of independent num-ber in hypergraph theory,which is better than the lower bounds obtained by probabilistic method.The third chapter studies the upper bounds of 2-wFP codes.By combining the coincidence position family of 2-wFP code words with the Sperner family,the upper bounds of the corresponding code capacity is obtained respectively by using the methods of Sperner family,intersecting family,non 2-covering and symmetric chain decomposi-tion in set theory.The new upper bounds obtained for two cases with different parity of code length are improved compared with the existing results.