چكيده به لاتين
Graded encoding schemes are important tools that have found many applications in cryptography, such as one round multi party key exchange, witness encryption, attribute based encryption, functional encryption and indistinguishability obfuscation. In this thesis, two new applications of graded encoding schemes in cryptography are presented. As the first application, we have presented the first secret sharing scheme based on graded encoding schemes. More precisely, for the first time, we have reduced the security of the proposed secret sharing scheme to the hardness of graded decisional Diffie-Hellman problem. As will be mentioned, the proposed secret sharing scheme is the first realization of multilinear map based secret sharing schemes. As the second application, we have presented a new variant of the Winternitz one-time signature scheme based on graded encoding schemes in which the number of operations
required by its algorithms is less than that of other Winternitz scheme variants. Considering that the Winternitz scheme has a lot of applications in many-time digital signature schemes, improving the Winternitz scheme will allow significant progress in many-time digital signature schemes. The important point is that our proposed schemes are generic constructions that can be instantiated using any graded encoding scheme. Thereby, if a used graded encoding scheme becomes insecure (inefficient) for some reason, we can simply replace it by a secure (efficient) one to obtain a new secure (efficient) instantiation.
