Electronic device for estimating approximate rank of homomorphic ciphertext and control method thereof

1 . An electronic device for estimating an approximate rank of a homomorphic ciphertext, the electronic device comprising:

a communication device;

a memory storing at least one instruction; and

a processor connected to the memory and configured to control the electronic device,

wherein the processor:

obtains N homomorphic ciphertexts;

generates K knots for calculating approximate ranks, K being a number smaller than N;

calculates approximate ranks of the N homomorphic ciphertexts based on probabilities that the N homomorphic ciphertexts exist between the K knots, wherein the processor calculates the approximate ranks of the N homomorphic ciphertexts according to the following formula:

r

i

′

=

r

′

(

x

i

;

ξ

)

=

N

⁢

∑

j

=

1

k

Pr

⁡

(

ξ

j

-

1

≤

x

i

<

ξ

j

)

·

I

⁡

(

ξ

j

≤

x

i

)

where x i denotes a homomorphic ciphertext, r i ′ denotes an approximate rank of the homomorphic ciphertext, Pr(ξ j−1 ≤x i ξ j ) denotes a probability that x i exists between ξ j−1 and ξ j , and I(ξ j ≤x i ) denotes a function that is 1 when ξ j ≤x i , and 0 otherwise; and

identifies a specific decile group or a top-ranked group within a recommendation model or exploratory data analysis using the calculated approximate ranks.

2 . The electronic device as claimed in claim 1 , wherein the K knots have values between maximum and minimum values of the N homomorphic ciphertexts.

3 . The electronic device as claimed in claim 1 , wherein intervals between the K knots are equal.

4 . The electronic device as claimed in claim 1 , wherein the processor:

obtains N first homomorphic ciphertexts and N second homomorphic ciphertexts; and

obtains a Spearman rank correlation coefficient of the first homomorphic ciphertexts and the second homomorphic ciphertexts based on approximate ranks of the first homomorphic ciphertexts and the second homomorphic ciphertexts.

5 . A control method of an electronic device for estimating an approximate rank of a homomorphic ciphertext, the control method comprising:

obtaining N homomorphic ciphertexts;

generating K knots for calculating approximate ranks, K being a number smaller than N;

calculating approximate ranks of the N homomorphic ciphertexts based on probabilities that the N homomorphic ciphertexts exist between the K knots, wherein the calculating of the approximate ranks of the N homomorphic ciphertexts are calculated according to the following formula:

r

i

′

=

r

′

(

x

i

;

ξ

)

=

N

⁢

∑

j

=

1

k

Pr

⁡

(

ξ

j

-

1

≤

x

i

<

ξ

j

)

·

I

⁡

(

ξ

j

≤

x

i

)

where x i denotes a homomorphic ciphertext, r i ′ denotes an approximate rank of the homomorphic ciphertext, Pr(ξ j−1 ≤x i ξ j ) denotes a probability that x i exists between ξ j−1 and ξ j , and I(ξ j ≤x i ) denotes a function that is 1 when ξ j ≤x i , and 0 otherwise; and

identifying a specific decile group or a top-ranked group within a recommendation model or exploratory data analysis using the calculated approximate ranks.

6 . The control method as claimed in claim 5 , wherein the K knots have values between maximum and minimum values of the N homomorphic ciphertexts.

7 . The control method as claimed in claim 5 , wherein intervals between the K knots are equal.

8 . The control method as claimed in claim 5 , wherein in the obtaining of the N homomorphic ciphertexts, N first homomorphic ciphertexts and N second homomorphic ciphertexts are obtained, and

the control method further comprises: obtaining a Spearman rank correlation coefficient of the first homomorphic ciphertexts and the second homomorphic ciphertexts based on approximate ranks of the first homomorphic ciphertexts and the second homomorphic ciphertexts.

9 . An electronic device for estimating an approximate rank of a homomorphic ciphertext, the electronic device comprising:

a communication device;

a memory storing at least one instruction; and

a processor connected to the memory and configured to control the electronic device, wherein the processor:

obtains N homomorphic ciphertexts;

generates K knots for calculating approximate ranks, K being a number smaller than N;

calculates approximate ranks of the N homomorphic ciphertexts based on probabilities that the N homomorphic ciphertexts exist between the K knots, wherein the processor calculates the approximate ranks of the N homomorphic ciphertexts according to the following formula:

r

i

′

=

r

′

(

x

i

;

ξ

)

=

N

⁢

∑

j

=

1

k

Pr

⁡

(

ξ

j

-

1

≤

x

i

<

ξ

j

)

·

I

⁡

(

ξ

j

≤

x

i

)

where x i denotes a homomorphic ciphertext, r i ′ denotes an approximate rank of the homomorphic ciphertext, Pr(ξ j−1 ≤x i <ξ j ) denotes a probability that x i exists between ξ j−1 and ξ j , and I(ξ j ≤x 1 ) denotes a function that is 1 when ξ j ≤x i , and 0 otherwise; and

performs a nonparametric statistical operation to obtain a robust statistic from the encrypted data based on the calculated approximate ranks.

10 . An electronic device for estimating an approximate rank of a homomorphic ciphertext, the electronic device comprising:

a communication device;

a memory storing at least one instruction; and

a processor connected to the memory and configured to control the electronic device, wherein the processor:

obtains N homomorphic ciphertexts;

generates K knots for calculating approximate ranks, K being a number smaller than N;

calculates approximate ranks of the N homomorphic ciphertexts based on probabilities that the N homomorphic ciphertexts exist between the K knots, wherein the processor calculates the approximate ranks of the N homomorphic ciphertexts according to the following formula:

r

i

′

=

r

′

(

x

i

;

ξ

)

=

N

⁢

∑

j

=

1

k

Pr

⁡

(

ξ

j

-

1

≤

x

i

<

ξ

j

)

·

I

⁡

(

ξ

j

≤

x

i

)

where x i denotes a homomorphic ciphertext, r i ′ denotes an approximate rank of the homomorphic ciphertext, Pr(ξ j−1 ≤x i <ξ j ) denotes a probability that x i exists between ξ j−1 and ξ j , and I(ξ j ≤x i ) denotes a function that is 1 when ξ j ≤x i , and 0 otherwise; and

identifies a key value for a query from a homogeneous knowledge database by identifying a top-ranking ciphertext among the calculated approximate ranks.