چكيده به لاتين
Secret sharing schemes are a way to share secret (confidential information) among a number of shareholders, so that only authorized collections of shares are able to retrieve the secret and unauthorized collections can not be kept secret. In an entire secret facility, unauthorized collections can not obtain any information from the secret. In such schemes, as much as possible, the share of each shareholder should be as close as possible to prevent any leakage of confidential information by any contribution and the establishment of the efficiency of the downstream. Recent developments in the field of quantum computers threaten the security of the existing public key encryption algorithms. In this treatise, for the purpose of designing a cryptography resistant to quantum computers, we first introduce a few mysterious scheme of partitioning, in which, even if some secrets are restored, the computational security of other mysteries, which is based on the difficulty of the problem of lattice, is established. The proposed plan is feasible, in that the participants can review the received shares and the restored secret. Then, to counteract the possible collusion of participants, we add the ability to increase the threshold to the project, thus requiring more participants to retrieve the secrets. Also, using the secret sharing scheme, we propose a public key threshold encryption scheme and a mesh-based threshold signing scheme, so that the message is decoded or signed by a minimal number of companies, and the private key is not disclosed in this process. The security of the designs is based on the stiffness of the lattice issues, which makes them resistant to quantum computers.
