Homomorphic encryption and decryption methods using ring isomorphism, and apparatuses using the same
AssigneeSnu R&Db Foundation
InventorsJung Hee CHEON, Jinsu KIM, Moon Sung LEE
Life of this patent
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Abstract
A homomorphic encryption method using ring isomorphism is provided. The homomorphic encryption method includes: randomizing a plaintext (m) by adding an error (e) to the plaintext (m); and converting randomized data (r) to r′ using the following equation: Ψ:R→R′, where r∈R, r′∈R′, and the function (Ψ) is ring isomorphism.
Claims19
A homomorphic encryption method using ring isomorphism, the method comprising:
- executing, by one or more computer processors in a computer system, program logic loaded in a memory of the computer system to cause the computer system to perform operations, the operations comprising:
- randomizing a plaintext (m) by adding an error (e) to the plaintext (m);
- and
- converting randomized data (r) to r′ using the following equation:
- Ψ:R→R′
- where r∈R, r′∈R′, and the function (Ψ) is ring isomorphism.
A method for decrypting a ciphertext, the method comprising:
- executing, by one or more computer processors in a computer system, program logic loaded in a memory of the computer system to cause the computer system to perform operations, the operations comprising:
- evaluating a ciphertext (c) by applying a key (s) to the ciphertext (c);
- and
- calculating a modulo by dividing a value calculated in the evaluating operation by q,
- wherein the ciphertext (c) is a ciphertext that is encrypted in a homomorphic encryption method using ring isomorphism,
- wherein the homomorphic encryption method comprises converting a plaintext (m) or a randomized plaintext to r′ using the following equation:
- Ψ:R→R′
- where r is a plaintext (m) or a randomized plaintext, r∈R, r′∈R′, and the function (Ψ) is ring isomorphism,
- where q∈Q, Q={qi|1≦i≦k, i and k are positive integers}, qi is positive integers which are relatively prime to one another, S={ai|ai−ai∈{Z*n}, 1≦i, j≦k, i, j, and k are positive integers}=(a1, a2, . . . , ak).
A homomorphic encryption apparatus using ring isomorphism, the homomorphic encryption apparatus comprising a converter configured to convert a plaintext or data (r) which is a randomized plaintext to r′ using the following equation:
- Ψ:R→R′
- where r∈R, r′∈R′, and the function (Ψ) is ring isomorphism.
An apparatus for decrypting a ciphertext, the apparatus comprising:
- an evaluator configured to evaluate a ciphertext (c) by applying a key (s) to the ciphertext (c);
- and
- a modulo calculator configured to calculate a modulo by dividing a value calculated by the evaluator by q,
- wherein the ciphertext (c) is a ciphertext that is encrypted in a homomorphic encryption method using ring isomorphism,
- wherein the homomorphic encryption method comprises encrypting a plaintext or data (r) which is a randomized plaintext into r′ using the following equation:
- Ψ:R→R′
- where r∈R, r′∈R′, and the function (Ψ) is ring isomorphism.
Dependencies are inferred from the claim text.