Розподіл секретного вмісту даних за (k,n)-схемою з використанням зашифрованих блоків

Abstract

In this paper, we present a threshold secret sharing scheme designed for the large-scale data, which are pre-encrypted prior to distribution. The relevance of this research stems from the continuous growth of data volumes processed in modern information systems, which imposes additional requirements on existing secret sharing schemes. Traditional secret sharing approaches, despite their solid theoretical foundation and proven information-theoretic security, demand significant computational resources due to the use of complex mathematical operations and are primarily tailored for small-sized secrets (e.g., cryptographic keys). Consequently, they are poorly suited for protecting large datasets. Furthermore, in such schemes the volume of distributed shares may substantially exceed the size of the original data. The objective of this work is to reduce the overall volume of distributed data by designing a (k, n) secret sharing scheme that operates on pre-encrypted blocks of the original dataset. The distinguishing feature of the proposed (k, n)-scheme lies in the integration of a preliminary encryption stage, followed by splitting the encrypted data into n blocks and generating shares for coalition participants. All these operations are performed by the dealer, who is also responsible for reconstructing the secret from the shares provided by coalition members. At least k shares are required for secret reconstruction, while any coalition smaller than the threshold is unable to recover the secret. The dealer additionally retains a dedicated share, which ensures the possibility of secret recovery even if the coalition provides only n − 1 blocks. In conventional secret sharing schemes, the cumulative size of the distributed data is typically ���� times greater than the size of the secret. Experimental results confirm that the proposed (k, n)-scheme reduces the cumulative storage requirements for coalition participants. The reduction factor ���� depends on the values of ���� and n, and increases as ���� grows. The proposed scheme exhibits linear time complexity with respect to the input data size, which represents a significant advantage for practical deployment. Compared to well-known threshold secret sharing methods, the scheme achieves higher performance. The performance gain is attained by employing simple byte-wise operations instead of computationally intensive procedures. Moreover, the scheme is resilient to partial compromise, since secret recovery requires the presence of at least the threshold number of shares. The practical value of the developed scheme lies in its applicability to large-scale data distribution. This makes it a promising solution for domains where rapid data processing and storage efficiency are critical, including secure media storage systems and the protection of critical infrastructure.