چكيده به لاتين
Abstract
Secret sharing schemes are attractive section of advanced Cryptography and has an efficient role for saving important documents and information against loose, termination and fraud.
Secret sharing is to share one or more secrets between individuals called participants by dealer called share. When predistined subset of participants set aggregated and share their private shares with public values published by participant, enable to restore secret or secrets. One of the biggest chalenges in this section of cryptography is participants fraud. Because one of the participants for reason to co-working with enemy, change its private share and share a different share that is not original. It is obvious that the system will restore incorrect secrets. So investigating about add abilty to system to find out safety of participants shares before restoring them, is considerable for scientists.
In this thesis we decide to study types of sharing schemes according to the security and existency of fraud. Also I decided to increase security for some pre-introduced schemes. Also we try to introduce mathematical tools for increasing security for secret sharing schemes. In another topic we discuss about dynamicity of secret sharing schemes which causes decreasing cost of deploying scheme and complexity of arithmetic operations.
Key Words: Secret Sharing, Access Structure, fraud, Security Channel, Verifiable, complexity of arithmetic, Dynamic, Polynomial Interpolation
