Method and system for a lattice-based homomorphic proxy re-encryption scheme

A system comprising:

• a first client machine, a second client machine, a proxy server machine and a trusted third party server 108, wherein the proxy server machine, the first client machine and the second client machine 102B comprises at least one memory storing programmed instructions;
• one or more Input/Output (I/O) interfaces;
• and one or more hardware processors of the proxy server machine, the first client machine and the second client machine are operatively coupled to a corresponding at least one memory, wherein the system is configured to:
• receive, by a first client machine and a second client machine via corresponding one or more hardware processors, a plurality of public parameters from a trusted third party server, wherein the plurality of public parameters comprises a security parameter, a number of encryption levels and a bit value;
• generate, via the one or more hardware processors of the first client machine, a first public-private key pair of a first user based on the plurality of public parameters and a user index using a probabilistic key generation algorithm;
• simultaneously generate, via the one or more hardware processors of a second client machine, a second public-private key pair of a second user based on the plurality of public parameters and the user index using the probabilistic key generation algorithm;
• generate, via the one or more hardware processors of the first client machine, a ciphertext based on a plaintext associated with the first user, the public key from the first public-private key pair and the plurality of public parameters using a probabilistic encryption algorithm;
• transmit, via the one or more hardware processors of the first client machine, the ciphertext to a proxy server machine, wherein the ciphertext is received by the proxy server machine;
• perform a computation, via one or more hardware processors of the proxy server machine, on the ciphertext using a Fully Homomorphic Encryption (FHE) based technique;
• generate, via the one or more hardware processors of the first client machine, a re-encryption key based on the first public-private key pair of the first user, a public key of the second user and the plurality of public parameter using a probabilistic re-encryption key generation algorithm;
• transmit, via the one or more hardware processors of the first client machine, the generated re-encryption key to the proxy server machine, wherein the re-encryption key is received by the proxy server machine;
• generate, via the one or more hardware processors of the proxy server machine, a re-encrypted ciphertext based on the re-encryption key, the ciphertext and the plurality of public parameters using a probabilistic re-encryption algorithm;
• transmit, via the one or more hardware processors of the proxy server machine, the re-encrypted ciphertext to the second client machine, wherein the re-encrypted ciphertext is received by the second client machine;
• and
• generate, by the one or more hardware processors of the second client machine, a resultant plaintext based on the re-encrypted ciphertext, and a private key of the second public-private key pair of the second user using a probabilistic decryption algorithm.

One or more non-transitory machine-readable information storage mediums comprising one or more instructions to:

• receive, by a first client machine and a second client machine via corresponding one or more hardware processors, a plurality of public parameters from a trusted third party server, wherein the plurality of public parameters comprises a security parameter, a number of encryption levels and a bit value;
• generate, via one or more hardware processors of the first client machine, a first public-private key pair of a first user based on the plurality of public parameters and a user index using a probabilistic key generation algorithm;
• simultaneously generate, via one or more hardware processors of a second client machine, a second public-private key pair of a second user based on the plurality of public parameters and the user index using the probabilistic key generation algorithm;
• generate, via the one or more hardware processors of the first client machine, a ciphertext based on a plaintext associated with the first user, the public key from the first public-private key pair and the plurality of public parameters using a probabilistic encryption algorithm;
• transmit, via the one or more hardware processors of the first client machine, the ciphertext to a proxy server machine, wherein the ciphertext is received by the proxy server machine;
• performing a computation, via one or more hardware processors of the proxy server machine, on the ciphertext using a Fully Homomorphic Encryption (FHE) based technique;
• generate, via the one or more hardware processors of the first client machine, a re-encryption key based on the first public-private key pair of the first user, a public key of the second user and the plurality of public parameter using a probabilistic re-encryption key generation algorithm;
• transmit, via the one or more hardware processors of the first client machine, the generated re-encryption key to the proxy server machine, wherein the re-encryption key is received by the proxy server machine;
• generate, via the one or more hardware processors of the proxy server machine, a re-encrypted ciphertext based on the re-encryption key, the ciphertext and the plurality of public parameters using a probabilistic re-encryption algorithm;
• transmit, via the one or more hardware processors of the proxy server machine, the re-encrypted ciphertext to the second client machine, wherein the re-encrypted ciphertext is received by the second client machine;
• and
• generate, by the one or more hardware processors of the second client machine, a resultant plaintext based on the re-encrypted ciphertext, and a private key of the second public-private key pair of the second user using a probabilistic decryption algorithm.