Multi–stage fully homomorphic encryption and compression system for secure data processing and analysis

A system for decoding, enhancing, and securely processing lossy compressed data streams using fully homomorphic encryption, comprising:

• a computing device comprising at least a memory and a processor;
• a plurality of programming instructions that, when operating on the processor, cause the computing device to:
• perform a first compression stage on data, wherein the first compression stage comprises the steps of:
• analyzing an input data stream to determine its statistical properties;
• applying one or more transformations to the input data stream to increase compressibility and security;
• producing a conditioned data stream and an error stream;
• transforming the conditioned data stream into a dyadic distribution;
• creating and manage a transformation matrix for reshaping the data distribution;
• performing Huffman coding on the transformed data stream;
• and
• combining the Huffman-encoded data stream with a secondary transformation data stream to produce a compressed and encrypted output stream;
• wherein upon completion of the first compression stage, a second compression stage is operated on the compressed and encrypted data;
• and
• wherein all operations are performed on encrypted data without decryption.