Bootstrappable fully homomorphic attribute-based encryption method with unbounded circuit depth

A computer-implemented system for unbounded multi-hop attribute-based fully homomorphic proxy re-encryption (AB-FHPRE), comprising:

• a processor configured to execute instructions;
• and
• a memory coupled to the processor and storing instructions configured to cause the processor to perform operations comprising:
• generating public parameters including matrices A, B1, . . . , Bl, U, and Gadget matrix G, and a master secret key msk;
• generating a secret key skƒ for a first access policy ƒ1 and an associated public key pkƒ, wherein the associated public key pkƒ includes an auxiliary recovery key arkƒ for the first access policy ƒ1;
• encrypting an attribute vector
• x
• ∈
• ℤ
• q
• l
• and a message μ∈(0,1)m associated with the first access policy ƒ1 into a ciphertext ct;
• generating a re-encryption key rekƒ1→ƒ2 for transforming the ciphertext ct from the first access policy ƒ1 to a second access policy ƒ2, wherein the re-encryption key rekƒ1→ƒ2 is a matrix that combines policy-associated matrices and error matrices, enabling a proxy computing device to convert ciphertexts associated with the first access policy ƒ1 to those associated with the second access policy ƒ2 without accessing plaintext;
• and
• re-encrypting, by the proxy computing device, the ciphertext from the first access policy ƒ1 to the second access policy ƒ2 using the re-encryption key rekƒ1→ƒ2 and a public key of the second policy, wherein the re-encryption comprises:
• transforming the ciphertext under the first access policy ƒ1 into an intermediate re-encrypted ciphertext;
• and
• performing a homomorphic AND computation on the intermediate re-encrypted ciphertext, wherein the homomorphic AND computation includes a bootstrapping process to refresh noise and produce a re-encrypted ciphertext for the second access policy ƒ2, and wherein the re-encryption supports an unbounded number of re-encryption hops.

A computer-implemented method for unbounded depth fully homomorphic attribute-based encryption (FHABE), the method comprising:

• generating, by a computing device, public parameters including matrices A, B1, . . . , Bl, U, and Gadget matrix G, and a master secret key msk=TA;
• generating, by the computing device, a secret key skƒ for an access policy ƒ and an associated public key pkƒ, wherein the associated public key pkƒ includes an auxiliary recovery key arkƒ;
• encrypting, by the computing device, an attribute vector
• x
• ∈
• ℤ
• q
• l
• and a message μ∈(0,1)m associated with the access policy ƒ into a ciphertext ct;
• homomorphically evaluating, by the computing device, an operation on one or more of the attribute-based ciphertexts to produce an evaluated ciphertext, wherein the homomorphic evaluation comprises:
• performing a homomorphic arithmetic or logical operation on ciphertext components to achieve a resulting ciphertext component;
• performing a bootstrapping process on the resulting ciphertext component, wherein the bootstrapping process is configured to refresh noise associated with the resulting ciphertext component;
• and
• applying the auxiliary recovery key arkƒ to a noise-refreshed ciphertext component to recover the evaluated ciphertext to a standard form compatible with subsequent homomorphic evaluation or decryption;
• and
• decrypting the ciphertext ct using the secret key skƒ to retrieve the message μ, wherein correctness of the decryption is maintained for ciphertexts evaluated over an unbounded number of operations.