Srikar Kale supervised by Dr. Prasad Krishnan received her Master of Science by Research in Computer Science and Engineering (CSE). Here’s a summary of her research work on Improving t-PIR Schemes via star product properties of Berman Family of Codes:

 This thesis explores the development and optimization of Private Information Retrieval (PIR) schemes, a critical component of data security that allows users to access data from public databases without disclosing the details of the retrieved information. Initially, the research focuses on traditional PIR schemes introduced by Chor et al., which are designed to obscure the user’s activity from the databases, thereby safeguarding the content accessed by the users. The study progresses to examine more sophisticated models that incorporate distributed storage systems and advanced coding techniques, such as Berman codes. These codes, which are binary linear codes of length nm for any n ≥ 2 and m ≥ 1, have recently been shown to achieve the capacity of the binary erasure channel. A significant portion of this work delves into the (D,E) retrieval schemes that employ linear codes for storage and retrieval to manage potential collusion among database servers, thus enhancing privacy and data retrieval efficiency. Moreover, this thesis introduces a novel PIR framework capable of handling scenarios involving up to t-colluding servers. This framework utilizes star products of Berman codes and Generalized Reed-Solomon codes to ensure maximum privacy and data integrity. The comprehensive nature of this approach allows for a detailed exploration of the theoretical limits of PIR capacities and the practical implementations that can achieve them. We present a new class of PIR schemes that maintain the privacy of the requested file’s identity even in the presence of up to t colluding servers. These schemes use the class of Berman codes as the storage-retrieval code pairs and offer flexibility in the number of servers, the PIR rate, the storage rate, and the collusion parameter t. The application of Berman codes not only facilitates the development of robust PIR schemes but also simplifies the implementation by requiring only binary fields, unlike the more complex field size requirements of previous systems. The findings highlight the potential of Berman codes to revolutionize PIR schemes, proposing new methodologies that significantly enhance privacy and efficiency in retrieving information from distributed databases. The results are expected to have profound implications for both the theory and application of PIR across various data-sensitive industries.

 May 2025