Method and system for homomorphic encryption
View Patent ↗A system for matrix-based homomorphic encryption including a processor of a computing node configured to host a homomorphic encryption module and connected to at least one cloud server and a memory on which are stored machine-readable instructions that when executed by the processor, cause the processor to: acquire plaintext M required to be encrypted; select a size of a matrix and modulus n; select invertible × matrix S 1 over n , wherein n is a residue ring modulo n; compute an invertible × matrix S 2 over n ; set a secret key (S 1 , S 2 ); and encode the plaintext M by an integer m over n , wherein m is encoded by an envelope matrix comprising a form V ( m ) = ( α 0 β m ) , wherein α and β are numbers chosen at random α, β∈ n .
1. A system for matrix-based homomorphic encryption, comprising:
a processor of a computing node configured to host a homomorphic encryption module and connected to at least one cloud server; and
a memory on which are stored machine-readable instructions that when executed by the processor, cause the processor to:
acquire plaintext M required to be encrypted;
select a size of a matrix and modulus n;
select invertible × matrix S 1 over n , wherein n is a residue ring modulo n;
compute an invertible × matrix S 2 over n ;
set a secret key (S 1 ,S 2 ); and
encode the plaintext M by an integer m over n ,
wherein m is encoded by an envelope matrix comprising a form
V
(
m
)
=
(
α
0
β
m
)
,
wherein α and β are numbers chosen at random α, β∈ n .
2. The system of claim 1 , wherein the machine-readable instructions that when executed by the processor, cause the processor to:
select the invertible × matrix S 1 over wherein is a field of real numbers; and
compute the invertible × matrix S 2 over .
3. The system of claim 2 , wherein the machine-readable instructions that when executed by the processor, cause the processor to encode the M by a floating-point number m, over wherein m is encoded by an envelope matrix comprising a form
V
(
m
)
=
(
α
0
β
m
)
,
wherein α and β are floating point numbers chosen over at random.
4. The system of claim 1 , wherein the machine-readable instructions that when executed by the processor, cause the processor to access the envelop matrix V(m) over n .
5. The system of claim 4 , wherein the machine-readable instructions that when executed by the processor, cause the processor to compute a ciphertext C(m) of the plaintext M by C(m)=S 2 V(m)S 1 , where (S 1 , S 2 ) is the secret key.
6. The system of claim 1 , wherein the machine-readable instructions that when executed by the processor, cause the processor to access the envelop matrix V(m) over .
7. The system of claim 5 , wherein the machine-readable instructions that when executed by the processor, cause the processor to decrypt encrypted plaintext M by:
accessing the ciphertext C(m) over n ;
computing S 2 −1 (C(m))S 1 −1 =V(m) over n , using (S 1 ,S 2 ), wherein S 1 ,S 2 are two matrices used as the secret key and S 1 −1 and S 2 −1 are inverse matrices, and
extracting the plaintext m from the envelop matrix V(m).
8. The system of claim 5 , wherein the machine-readable instructions that when executed by the processor, cause the processor to decrypt encrypted plaintext M by:
accessing the ciphertext C(m) over ;
computing S 2 −1 (C(m))S 1 −1 =V(m) over using the secret key(S 1 ,S 2 ), wherein S 1 ,S 2 are two matrices used as the secret key and S 1 −1 and S 2 −1 are inverse matrices; and
extracting the plaintext m from the envelop matrix V(m).
9. The system of claim 5 , wherein the machine-readable instructions that when executed by the processor, cause the processor to execute homomorphic operations over cyphertexts computed as C(m)=S 2 V(m)S 1 , wherein the homomorphic operations comprising any of: addition, subtraction, multiplication, and division of encrypted data.
10. The system of claim 9 , wherein the machine-readable instructions that when executed by the processor, cause the processor to execute homomorphic operations over ciphertexts computed as C(m)=S 2 V(m)S 1 , comprising any of: encrypted search based on homomorphic index, generation of homomorphic hash and homomorphic comparison.
11. A method for matrix-based homomorphic encryption, comprising:
acquiring, by a computing node, plaintext M required to be encrypted;
selecting, by the computing node, a size of a matrix and modulus n;
selecting, by the computing node, invertible × matrix S 1 over n , wherein n is a residue ring modulo n;
computing, by the computing node, an invertible × matrix S 2 over n ;
setting, by the computing node, a secret key (S 1 ,S 2 ); and
encoding the plaintext M by an integer m over n ,
wherein m is encoded by an envelope matrix comprising a form
V
(
m
)
=
(
α
0
β
m
)
,
wherein α and β are numbers chosen at random α, β∈ n .
12. The method of claim 11 , further comprising:
selecting the invertible × matrix S 1 over , wherein is a field of real numbers; and
computing the invertible × matrix S 2 over .
13. The method of claim 11 , further comprising encoding the M by a floating-point number m, over , wherein m is encoded by an envelope matrix comprising a form
V
(
m
)
=
(
α
0
β
m
)
,
wherein α and β are floating point numbers chosen at random over .
14. The method of claim 11 , further comprising accessing the envelop matrix V(m) over n .
15. The method of claim 14 , further comprising computing a ciphertext C(m) of the plaintext M by C(m)=S 2 V(m)S 1 , where (S 1 ,S 2 ) is the secret key.
16. The method of claim 11 , further comprising accessing the envelop matrix V(m) over .
17. The method of claim 11 , further comprising decrypting encrypted plaintext M by:
accessing the ciphertext C(m) over n ;
computing S 2 −1 (C(m))S 1 −1 =V(m) over n , using (S 1 ,S 2 ), wherein S 1 ,S 2 are two matrices used as the secret key and S 1 −1 and S 2 −1 are inverse matrices, and
extracting the plaintext m from the envelop matrix V(m).
18. The method of claim 11 , further comprising decrypting encrypted plaintext M by:
accessing the ciphertext C(m) over ;
computing S 2 −1 (C(m))S 1 −1 =V(m) over using the secret key(S 1 ,S 2 ), wherein S 1 ,S 2 are two matrices used as the secret key and S 1 −1 and S 2 −1 are inverse matrices; and
extracting the plaintext m from the envelop matrix V(m).
19. A non-transitory computer-readable medium comprising instructions, that when read by a processor, cause the processor to perform:
acquiring plaintext M required to be encrypted;
selecting a size of a matrix and modulus n;
selecting invertible × matrix S 1 over n , wherein n is a residue ring modulo n;
computing an invertible matrix S 2 over n ;
setting a secret key (S 1 ,S 2 ); and
encoding the plaintext M by an integer m over n ,
wherein m is encoded by an envelope matrix comprising a form
V
(
m
)
=
(
α
0
β
m
)
,
wherein α and β are numbers chosen at random α, β∈ n .
20. The non-transitory computer-readable medium comprising instructions, that when read by a processor, cause the processor to compute a ciphertext C(m) of the plaintext m by C(m)=S 2 V(m)S 1 , where (S 1 ,S 2 ) is the secret key.