فاطمه جعفري

In traditional image secret sharing schemes, a secret image is shared among n shareholders who have the same position. In order to retrieve the secret image, shareholders must be present in the threshold number of k. But if the shareholders have different necessary and also unnecessary positions, it is obligatory to use essential image sharing schemes with different ranks. That is, we have to share a picture between n shareholders, where s_1 has the rank of 1 and s_2 has the rank of 2 and ... and s_i has the rank of i ,in such a way that when the secret is retrieved, out of the k shareholders required for the retrieva‎l, at least t_1 people of rank one and t_2 people from rank two and... and t_i people from rank i should be present. In the main article (Chapter 3) and also the proposed scheme (Chapter 4), sharing the essential image secret based on the problem of learning with error (LWE) is presented that maintains the security of the schemes against quantum attacks and places the schemes in the category of post-quantum schemes. In the mentioned two plans, Bloom filters and hash functions are used to verify shares. Also, the shadow images of necessary (of any rank) and unnecessary shareholders have the same size and there is no need to add sub-shadows. In the main article, only one necessary rank and one unnecessary rank have been investigated, but in this thesis, we will improve the scheme for l necessary rank and one unnecessary rank. In addition to that, in the proposed plan, we applied pre-processing to the secret image so that we can improve the randomness of the shares of shareholders and increase the security of the plan.

تسهيم‌راز , يادگيري با خطا , وارسي‌پذير , بلوم فيلتر

secret sharing , Learning with errors , verifiable , bloom filter

Fatemeh Jafari

Dr.Masoud Hadian Dehkordi