KR102491902B1 - Device and method for operation of encrypted data using fully homomorphic encryption - Google Patents

Abstract

The present invention relates to a device for computing data encrypted by a fully homomorphic encryption method, comprising: a communication module for transmitting and receiving encrypted data; a memory in which an arithmetic program is stored; and a processor executing the calculation program. The operation program includes an XOR operation logic, an XNOR operation logic, an AND operation logic, and an OR operation logic for performing bit-by-bit operation on the first homomorphic encryption data and the second homomorphic encryption data, and a complement operation for returning a complement to the homomorphic encryption data. Logic, absolute value calculation logic that returns the absolute value of homomorphic encryption data, right-shift calculation logic that returns the result of shifting homomorphic data to the right, left-shift calculation logic that returns the result of shifting homomorphic data to the left and a MUX operation logic for outputting any one of a plurality of input homomorphic encryption data, and if a value input first between the input first homomorphic encryption data and the input second homomorphic encryption data is a larger value, '1' bit is encrypted. A first case comparison operation logic for outputting a first encryption value and a second case comparison operation logic for outputting the first encryption value when the value input first between the input first homomorphic encryption data and the input second homomorphic encryption data is a smaller value includes

Description

DEVICE AND METHOD FOR OPERATION OF ENCRYPTED DATA USING FULLY HOMOMORPHIC ENCRYPTION}

The present invention relates to an apparatus and method for performing various operations such as comparison operations and four arithmetic operations on data encrypted using fully homomorphic encryption without separate decryption.

In the existing user-cloud model, a key is shared between the user and the server, and the user's data encrypted based on this key is sent to the server, and the server decrypts the user's file through this key to process the service the user wants. do.

However, since the user and the server share a key, there is a problem that the user's personal information may be leaked. For example, in the case of a web server that converts documents into PDFs, there is a possibility of continuously collecting files sent by users and using them for malicious purposes. Likewise, anti-virus programs also gain access to files containing confidential documents or personal information through this path.

Homomorphic encryption is a good means to prevent this and allows the server to process encrypted user data without decryption. In this way, using homomorphic encryption can solve the personal data privacy problem that can occur in a cloud environment.

1 illustrates a mechanism in which homomorphic encryption according to the prior art is used.

As shown, it indicates that the resultant value obtained by calculating the message on the plaintext and the resultant value obtained by decryption after performing the homomorphic encryption operation on the encrypted message are the same.

That is, the present invention intends to develop functions that perform various operations on data in an encrypted state using such a homomorphic encryption mechanism.

Currently, in the case of homomorphic encryption that encrypts based on bit units, basic operations are insufficient. Accordingly, the present invention intends to contribute to constructing basic operations based on homomorphic encryption and creating additional application operations based thereon.

Republic of Korea Patent Publication No. 10-2020-0054119 (Title of Invention: Exponential Function Calculation Server and Method of Data Encrypted with Homomorphic Encryption Technique)

An object of the present invention is to provide an apparatus and method for computing encrypted data that can perform comparison operations and four arithmetic operations on data encrypted using a homomorphic encryption technique.

However, the technical problem to be achieved by the present embodiment is not limited to the technical problems described above, and other technical problems may exist.

An apparatus for computing data encrypted by a fully homomorphic encryption method according to an embodiment of the present invention for solving the above technical problem includes a communication module for transmitting and receiving encrypted data; a memory in which an arithmetic program is stored; and a processor executing the calculation program.

At this time, the operation program includes an XOR operation logic, an XNOR operation logic, an AND operation logic, and an OR operation logic for performing bit-by-bit operation on the first homomorphic encryption data and the second homomorphic encryption data, and returns a complement for the homomorphic encryption data. Complement arithmetic logic, absolute value arithmetic logic that returns the absolute value of homomorphic data, right shift arithmetic logic that returns the result of shifting homomorphic data to the right, left shift that returns the result of shifting homomorphic data to the left It includes an operation logic and a MUX operation logic that outputs any one of a plurality of input homomorphic encryption data, and if a value input first among the input first homomorphic encryption data and the input second homomorphic encryption data is a larger value, '1' bit is output. A first case comparison operation logic for outputting an encrypted first encryption value and a second case comparison for outputting the first encryption value if the value input first between the input first homomorphic encryption data and the input second homomorphic encryption data is a smaller value An operation logic, wherein the first size comparison operation logic calculates a first output value by inputting the input first homomorphic encryption data and second homomorphic encryption data to the XNOR operation logic, and calculates the first output value through MUX operation logic. According to the output value, a second encryption value or first homomorphic encryption data obtained by encrypting '0' bit is output, and the second size comparison operation logic performs the XNOR operation on the inputted first homomorphic encryption data and second homomorphic encryption data. A first output value is obtained by inputting to a logic, and a second encryption value obtained by encrypting a '0' bit or the second homomorphic encryption data is output according to the first output value through the MUX operation logic.

According to another embodiment of the present invention, a method for calculating encrypted data using a device for calculating data encrypted by a fully homomorphic encryption method comprises bit-by-bit first homomorphic encryption data and second homomorphic encryption data. Includes XOR operation logic, XNOR operation logic, AND operation logic, and OR operation logic, respectively, and complement operation logic that returns the complement of homomorphic encryption data, absolute value operation logic that returns the absolute value of homomorphic encryption data, and homomorphic encryption Right-shift operation logic that returns the result value of moving data to the right, left-shift operation logic that returns the result value of moving homomorphic data to the left, and MUX operation logic that outputs any one of a plurality of input homomorphic encryption data An operation program including is installed, and the step of inputting the input first homomorphic encryption data and the second homomorphic encryption data to a first case comparison operation logic to perform case comparison and inputting the input first homomorphic encryption data and the second homomorphic encryption data and performing case comparison by inputting the encryption data to a second case comparison operation logic.

At this time, the first size comparison operation logic outputs a first encryption value obtained by encrypting '1' bit if the first input value is a large value, and converts the inputted first homomorphic encryption data and second homomorphic encryption data into the XNOR A first output value is obtained by inputting it to an operation logic, and a second encryption value or first homomorphic encryption data obtained by encrypting '0' bits according to the first output value is output through the MUX operation logic, and the second size comparison operation The logic outputs the first encryption value if the first input value is a small value, inputs the input first homomorphic encryption data and the second homomorphic encryption data to the XNOR operation logic to obtain a first output value, and performs a MUX operation. A second encryption value obtained by encrypting '0' bit or the second homomorphic encryption data is outputted through logic according to the first output value.

According to the problem solving means of the present invention described above, data encrypted by the fully homomorphic encryption method can be input to comparison calculations or various arithmetic operations in an encrypted state, and the results can be output in an encrypted state.

Through this, data security characteristics can be greatly improved in industries where personal privacy is highly required, such as various cloud services, virus inspection of personal PCs, and human genome data analysis.

In addition, the present invention can be utilized in various fields of mathematics and statistics, and by constructing the most fundamental operations (comparison and arithmetic operations), it can be utilized in various fields in mathematical or statistical fields.

1 illustrates a mechanism in which homomorphic encryption according to the prior art is used.
2 illustrates the configuration of an apparatus for computing encrypted data according to an embodiment of the present invention.
3 is a conceptual diagram illustrating a process of using homomorphically encrypted data according to an embodiment of the present invention.
4 is a diagram for explaining a real number representation technique of encrypted data according to an embodiment of the present invention.
5 is a logic circuit diagram showing the configuration of an addition logic according to an embodiment of the present invention.
6 is a logic circuit diagram showing the configuration of subtraction logic according to an embodiment of the present invention.
7 shows a binary multiplication process used in the present invention.
8 is a block diagram showing the configuration of multiplication logic according to an embodiment of the present invention.
9 illustrates a binary division process used in the present invention.
10 is a block diagram showing the configuration of division logic according to an embodiment of the present invention.

Hereinafter, with reference to the accompanying drawings, embodiments of the present invention will be described in detail so that those skilled in the art can easily practice it. However, the present invention may be embodied in many different forms and is not limited to the embodiments set forth herein. And, in order to clearly explain the present invention in the drawings, parts irrelevant to the description are omitted, and similar reference numerals are attached to similar parts throughout the specification.

Throughout the specification, when a part is said to be "connected" to another part, this includes not only the case of being "directly connected" but also the case of being "electrically connected" with another element in between. . In addition, when a part "includes" a certain component, it means that it may further include other components without excluding other components unless otherwise stated.

Hereinafter, an apparatus and method for calculating data encrypted by a fully homomorphic encryption technique will be described with reference to the accompanying drawings.

2 illustrates the configuration of an apparatus for computing encrypted data according to an embodiment of the present invention.

The arithmetic device 100 includes a memory 110, a processor 120, a communication module 130 and a database 140. The arithmetic device 100 receives various encrypted data received from one or more user terminals 200 and performs various arithmetic processes on the encrypted data.

The memory 110 stores an arithmetic program for performing various arithmetic processes on homomorphic encryption data.

At this time, the calculation program includes an XOR operation logic, an XNOR operation logic, an AND operation logic, and an OR operation logic that respectively operate the first homomorphic encryption data and the second homomorphic encryption data bit by bit. In addition, the operation program includes a complement operation logic that returns the complement of homomorphic encryption data, an absolute value operation logic that returns the absolute value of homomorphic encryption data, a right-shift operation logic that returns the result of shifting homomorphic encryption data to the right, and an isomorphic It includes a left shift operation logic that returns a result value of shifting cryptographic data to the left and a MUX operation logic that outputs any one of a plurality of input homomorphic encryption data.

In addition, the operation program includes first size comparison operation logic, second size comparison operation logic, addition logic, subtraction logic, absolute value logic, multiplication logic, division logic, and exponential function logic. A detailed configuration of each operation logic will be described later.

In addition, the calculation program includes sigmoid function logic for performing sigmoid function calculation, and includes regression analysis logic for performing logistic regression analysis based on the sigmoid function logic.

In addition, the memory 110 performs a function of temporarily or permanently storing data processed by the processor 120 . Here, the memory 110 may include volatile storage media or non-volatile storage media, but the scope of the present invention is not limited thereto. The memory 110 may store a separate program such as an operating system for processing and controlling the processor 120, or may perform a function for temporarily storing input or output data.

The processor 120 executes an arithmetic program stored in the memory 110 to perform various arithmetic processes on data encrypted using a homomorphic encryption technique.

Here, the processor 120 may include all types of devices capable of processing data, such as a processor. Here, a 'processor' may refer to a data processing device embedded in hardware having a physically structured circuit to perform functions expressed by codes or instructions included in a program, for example. As an example of such a data processing device built into hardware, a microprocessor, a central processing unit (CPU), a processor core, a multiprocessor, an application-specific integrated (ASIC) circuit), field programmable gate array (FPGA), etc., but the scope of the present invention is not limited thereto.

The communication module 130 provides a communication interface necessary for processing homomorphic encrypted data transmitted and received to and from the user terminal 200 in conjunction with a communication network. Here, the communication module 130 may be a device including hardware and software necessary for transmitting/receiving a signal such as a control signal or a data signal through a wired/wireless connection with another network device.

The database 140 stores encrypted data and calculation results generated based thereon. These calculation results can be used for various application services provided by the server.

3 is a conceptual diagram illustrating a process of using homomorphically encrypted data according to an embodiment of the present invention.

As shown, the data transmitted from the user terminal is subjected to homomorphic encryption and then received from a cloud server or the like. The calculation device 100 according to the present invention processes various calculations provided by the present invention without decrypting them, and decodes the resulting values based on them and provides them to the user terminal.

Symbols used in the present invention are defined as follows.

,

은 배열의 길이(length)로 나타내며, 각각의 인덱스에 해당하는 요소들은

로

는

부터

사이의 값을 갖는다. 또한, 'Enc'는 암호화를 의미하고 'Dec'는 복호화를 의미한다.Array(Vector) is an alphabetic symbol

,

is represented by the length of the array, and the elements corresponding to each index are

as

Is

from

has a value between Also, 'Enc' means encryption and 'Dec' means decryption.

'bitwise' means to apply a specific operation to each element of each array, and 'sc' means to convert an array (vector) into a scalar value.

boots.XOR

가 의미하는 것은 두 입력 암호비트

에 대해서 XOR 연산을 수행하고, 연산 도중 발생하는 노이즈가 부트스트래핑에 의해 감소되어 반환되는 암호비트 값을

배열의 0번째 요소에 저장하는 것을 의미한다.'boots' is displayed to indicate the difference between homomorphic gates and normal gates. In general, fully homomorphic encryption gates require bootstrapping to remove noise after operation. for example,

boots.XOR

means that the two input cipher bits

The XOR operation is performed on , and the noise generated during the operation is reduced by bootstrapping,

It means to store it in the 0th element of the array.

) 함수는 동형암호 2의 보수 연산으로 입력값

에 대해 2의 보수를 취한 값을 반환하는 알고리즘이다. 다음으로, HE.AbsoluteValue(

) 연산은 암호문

를 받아 이에 대해 절댓값을 결괏값으로 반환하는 함수이다. 다음으로, HE.RightShift(

,

)는 입력 암호문

에 대해서 오른쪽으로

만큼 이동연산을 수행한 결괏값을 반환해주는 함수이다. 또한, HE.LeftShift(

,

)는 왼쪽으로

만큼 이동연산을 수행한 결괏값을 반환해주는 함수이다. The basic ones among the homomorphic encryption functions appearing in the present invention are as follows. First, HE.TwosComplement(

) function is the input value as a homomorphic two's complement operation

It is an algorithm that returns a value obtained by taking the 2's complement of . Next, HE.AbsoluteValue(

) operation is the ciphertext

It is a function that receives and returns the absolute value as the result. Next, HE. RightShift(

,

) is the input ciphertext

to the right about

This function returns the result of performing the shift operation as much as possible. Also, HE. LeftShift(

,

) to the left

This function returns the result of performing the shift operation as much as possible.

4 is a diagram for explaining a real number representation technique of encrypted data according to an embodiment of the present invention.

In the present invention, by using a bit-based homomorphic encryption scheme, a range of real valid digits is determined as shown in FIG. 4, and encrypted real data is expressed through this.

, 암호문의 배열을

,

번째 배열의 성분을

라고 두면, 인덱스

부터

까지의 (

)만큼을 실수 데이터의 소수 부분으로 두고, 인덱스

부터

까지

만큼을 실수 데이터의 정수 부분으로 둔다. 마지막, 최상위 비트,

번째 비트를 부호 비트로 두고 실수를 표현한다.First, the index of the ciphertext array is set opposite to the general expression. That is, the rightmost bit becomes the most significant bit. In general, the length of the input bits

, an array of ciphertext

,

element of array

Let's say, the index

from

until (

) as the fractional part of the real data, and the index

from

Till

Let as much as the integer part of the real data. last, most significant bit,

A real number is expressed with the first bit as the sign bit.

First, a size comparison logic according to an embodiment of the present invention will be described.

The operation program of the present invention is a first method for outputting a first encryption value (Enc(1)) obtained by encrypting '1' bit when the first input value is a larger value among the input first homomorphic encryption data and the second homomorphic encryption data. and a case comparison operation logic and a second case comparison operation logic that outputs the first encryption value when a first input value of the input first homomorphic encryption data and the input second homomorphic encryption data is a smaller value.

)와 제 2 동형암호 데이터(

)를 XNOR 연산 로직에 입력하여 제 1 출력값(t2)을 구하고, MUX 연산 로직을 통해 제 1 출력값(t2)에 따라 ‘0’ 비트를 암호화한 제 2 암호화 값(t1, Enc(0)) 또는 제 1 동형암호 데이터를 출력하는 동작을 수행한다.As shown below, the first size comparison operation logic HE.CompareLarge(ab) is input first homomorphic encryption data (

) and the second homomorphic encryption data (

) is input into the XNOR operation logic to obtain the first output value (t2), and the second encryption value (t1, Enc(0)) obtained by encrypting the '0' bit according to the first output value (t2) through the MUX operation logic, or An operation of outputting first homomorphic encryption data is performed.

At this time, the MUX operation gate performs the same role as the MUX gate in the plain text, and outputs b or c according to the value of a.

)가 제 2 동형암호 데이터(

) 보다 크면 Enc(1)을 출력하고, 반대의 경우에는 Enc(0)을 출력한다.According to this configuration, the first case comparison operation logic is the first homomorphic encryption data (

) is the second homomorphic encryption data (

), Enc(1) is output, and in the opposite case, Enc(0) is output.

)와 제 2 동형암호 데이터(

)를 XNOR 연산 로직에 입력하여 제 1 출력값(t2)을 구하고, MUX 연산 로직을 통해 제 1 출력값(t2)에 따라 ‘0’ 비트를 암호화한 제 2 암호화 값(t1, Enc(0)) 또는 제 2 동형암호 데이터(

)를 출력하는 동작을 수행한다.In addition, the second size comparison operation logic HE.CompareSmall(ab) is input first homomorphic encryption data (

) and the second homomorphic encryption data (

) is input into the XNOR operation logic to obtain the first output value (t2), and the second encryption value (t1, Enc(0)) obtained by encrypting the '0' bit according to the first output value (t2) through the MUX operation logic, or The second homomorphic encryption data (

) is output.

)가 제 2 동형암호 데이터(

) 보다 작으면 Enc(1)을 출력하고, 반대의 경우에는 Enc(0)을 출력한다.According to this configuration, the second case comparison operation logic is the first homomorphic encryption data (

) is the second homomorphic encryption data (

), Enc(1) is output, and in the opposite case, Enc(0) is output.

Next, an addition logic according to an embodiment of the present invention will be reviewed.

5 is a logic circuit diagram showing the configuration of an addition logic according to an embodiment of the present invention.

The operation program may include an addition logic for adding the first homomorphic encryption data and the second homomorphic encryption data in an encrypted state.

)와 제 2 동형암호 데이터(

)가 입력되어 제 1 출력값(t1)을 출력하는 제1 XOR 연산 로직(510, 3번째 줄), 제 1 출력값(t1)과 제 1 캐리 값(

)이 입력되어 결괏값(

)을 출력하는 제 2 XOR 연산 로직(512, 4번째 줄), 제 1 출력값(t1)과 제 1 캐리 값(

)이 입력되어 제 2 출력값(t2)을 출력하는 제1 AND 연산 로직(514, 5번째 줄), 제 1 동형암호 데이터(

)와 제 2 동형암호 데이터(

)가 입력되어 제 3 출력값(t3)을 출력하는 제2 AND 연산 로직(516, 6번째 줄) 및 제 2 출력값(t2)과 제 3 출력값(t3)이 입력되어 제 2 캐리값(

)을 출력하는 OR 연산 로직(518, 7번째 줄)을 포함한다.The addition logic is the first homomorphic encryption data (

) and the second homomorphic encryption data (

) is input and the first XOR operation logic (510, line 3) outputs the first output value t1, the first output value t1 and the first carry value (

) is entered and the resulting value (

), the second XOR operation logic (512, line 4) outputting the first output value (t1) and the first carry value (

) is input and the first AND operation logic (514, line 5) outputs the second output value t2, the first homomorphic encryption data (

) and the second homomorphic encryption data (

) is input and the third output value (t3) is output, and the second AND operation logic (516, line 6) and the second output value (t2) and the third output value (t3) are input and the second carry value (

) and OR operation logic (518, line 7) that outputs.

The algorithm for each operation logic can be expressed as follows.

The addition algorithm is performed sequentially from the least significant bit, and a _i , b _i , and c _i values are input in each loop, and the result value (r _i ) and the carry value (c _i+1 ) used in the next loop are returned. do. Since there is no need to calculate the carry value in the last loop, only the XOR operation logic gate that outputs the result value is used, as described in lines 9 to 10.

On the other hand, boots.AND, boots.OR, and boots.XOR gates include a bootstrapping process that reduces noise generated during operation for two input values.

Next, subtraction logic according to an embodiment of the present invention will be described.

6 is a logic circuit diagram showing the configuration of subtraction logic according to an embodiment of the present invention.

The operation program may include subtraction logic for subtracting the first homomorphic encryption data and the second homomorphic encryption data in an encrypted state.

)와 제 2 동형암호 데이터(

)가 입력되어 제 1 출력값(t1)을 출력하는 제1 XOR 연산 로직(610, 3번째 줄), 제 1 출력값(t1)과 제 1 캐리 값(

)이 입력되어 결괏값(

)을 출력하는 제 2 XOR 연산 로직(614, 4번째 줄), 제 1 동형암호 데이터를 반전시킨 값과 제 2 동형 암호 데이터가 입력되어 제 2 출력값(t2)을 출력하는 제1 AND 연산 로직(612, 6번째 줄), 제 1 출력값(t1)을 반전시킨 값과 제 1 캐리 값이 입력되어 제 3 출력값(t3)을 출력하는 제 2 AND 연산 로직(616, 8번째 줄), 제 2 출력값과 제 3 출력값이 입력되어 제 2 캐리값(

)을 출력하는 OR 연산 로직(618, 9번째 줄)을 포함한다.The subtraction logic is the first homomorphic encryption data (

) and the second homomorphic encryption data (

) is input and the first XOR operation logic (610, line 3) outputs the first output value t1, the first output value t1 and the first carry value (

) is entered and the resulting value (

), a second XOR operation logic (614, line 4) outputting a second output value (t2) by inputting a value obtained by inverting the first homomorphic encryption data and second homomorphic encryption data, and outputting a second output value (t2). 612, line 6), a second AND operation logic (616, line 8) outputting a third output value (t3) by inputting the inverted value of the first output value (t1) and the first carry value, the second output value and the third output value are input to obtain a second carry value (

) and OR operation logic (618, line 9) that outputs.

The subtraction algorithm is performed sequentially from the least significant bit, and a _i , b _i , and c _i values are input in each loop, and the result value (r _i ) and the carry value (c _i+1 ) used in the next loop are returned. do. Since there is no need to calculate the carry value in the last loop, as described in lines 11 and 12, only the XOR operation logic gate that outputs the result value is used.

Next, the absolute value logic according to an embodiment of the present invention will be reviewed.

The calculation program may include an absolute value logic for calculating an absolute value in an encrypted state of the inputted homomorphic encryption data.

The absolute value logic includes a MUX operation logic that outputs either 2's complement (t) of the input homomorphic encryption data or the input homomorphic encryption data according to the ciphertext of the most significant bit of the input homomorphic encryption data, and a detailed algorithm configuration is as follows

Next, multiplication logic according to an embodiment of the present invention will be reviewed.

7 shows a binary multiplication process used in the present invention, and FIG. 8 is a block diagram showing the configuration of a multiplication logic according to an embodiment of the present invention.

As shown in FIG. 7 , it can be confirmed that 35 (= 100011 ₍₂₎ ) is output as a result of multiplying the upper number 7 (=0111 ₍₂₎ ) and the lower number 5 (0101 ₍₂₎ ). The sum of the results (r1, r2, r3) that comes out when the upper binary number is multiplied for each bit of the lower binary number is the final result.

In the present invention, the binary multiplication method, the process of considering the sign of two input values for multiplication, and the process of extracting only a limited number of bits and returning them as a result value are added.

The operation program may include multiplication logic for multiplying the first homomorphic encryption data and the second homomorphic encryption data in an encrypted state.

The multiplication logic is an XOR operation logic for outputting a first sign bit (s ₁ ) by inputting the sign bit (sign(a)) of the first homomorphic encryption data and the sign bit (sign(b)) of the second homomorphic encryption data. (820, 1st line), NOT operation logic (2nd line) for inverting the 1st sign bit to output the 2nd sign bit (s ₂ ), 1st absolute value logic for obtaining the absolute value of the first homomorphic encryption data (810 , line 3), the second absolute value logic (820, line 4) for obtaining the absolute value of the second homomorphic encryption data, the absolute value binary multiplication logic for multiplying the output of the second absolute value logic bit by bit with respect to the output of the first absolute value logic (814, lines 5 to 10), complement output logic (816, line 11) that obtains the 2's complement for the output of the absolute value binary multiplication logic, and multiplying the second sign bit bit by bit for the output of the absolute value binary multiplication logic 1st AND operation logic (12th line) for outputting a 1st result value, 2nd AND operation logic (13th line) for outputting a 2nd resultant value by multiplying the first sign bit by bit with respect to the output of the complement output logic line), and an addition logic (line 14) inputting the first and second result values and outputting the final result value.

,

의 부호 비트

번째 비트들 간에 boots.XOR 연산을 수행한다. 두 입력값이 같은 부호라면, boots.XOR 결과로 Enc(0) 이 출력되고, 반대부호라면 Enc(1)이 출력된다. 이를 활용하여, 두 부호가 만약 같은 부호라면 Enc(0)이 출력되므로, boot.NOT을 취하게 되면 Enc(1)이 되고(2번째 줄), 이에 대해 양의 곱셉 결과 과정(3, 4, 6~10 번째 줄)에 의해

에 대해 비트마다 boot.AND를 적용해주면(12번째 줄), 양의 곱셈 결과가 출력된다. Above, the algorithms in lines 1, 2, 11, 12, 13, and 14 show the process for processing them because the code of the encryption data is not known. For this, the two ciphertext

,

sign bit of

Boots.XOR operation is performed between the th bits. If the two input values have the same sign, Enc(0) is output as the result of boots.XOR, and Enc(1) is output if the two input values have the opposite sign. Using this, if the two codes are the same, Enc(0) is output, so if boot.NOT is taken, Enc(1) becomes (2nd line), and the positive multiplication result process (3, 4, lines 6 to 10)

If boot.AND is applied for each bit (line 12), a positive multiplication result is output.

Similarly, if the signs are reversed, the boots.XOR result of each sign bit becomes Enc(1) (line 1). If boot.AND is applied for each bit to the resultant value (line 11), that is, the negative value obtained by taking the opposite sign to the positive multiplication result value (line 9), a negative result value is obtained (line 13). line). If these two results are added (line 14), the final multiplication between the cipher texts considering the sign is obtained.

Next, a division logic according to an embodiment of the present invention will be described.

9 illustrates a binary division process used in the present invention, and FIG. 10 is a block diagram showing the configuration of a division logic according to an embodiment of the present invention.

First, assume that Q and M are divided by a dividend and a divisor of length l, that is, Q by M, respectively. Also, create a vector called A with length l and all elements are 0. Repeat the following until l becomes 0.

Next, the two arrays, Q and A are combined (Q|A), and the shift operation is performed to the right by 1 bit.

Next, in Q|A of length 2l, the left l bit is called Q, and the right l bit is stored as A.

Next, A is compared with M, and if A is less than M, 0 is stored in Q[0], and in the opposite case, 1 is stored, and the values of A-M are stored in the A array.

Next, the value of l is subtracted by 1.

Finally, the value stored in Q is the quotient of Q divided by M, and returns it.

The operation program may include division logic for dividing second homomorphic encryption data, which is a divisor (M), by first homomorphic encryption data, which is a dividend (Q), in an encrypted state.

The division logic is an XOR operation logic (1020, line 1) in which the sign bit of the first homomorphic encryption data and the sign bit of the second homomorphic encryption data are input and the first sign bit is output, and the absolute value of the first homomorphic encryption data is obtained. The first absolute value logic (1010, line 2), the second absolute value logic (1012, line 3) that obtains the absolute value of the second homomorphic encryption data, and the output of the first absolute value logic is divided bit by bit by the output of the second absolute value logic absolute value binary division logic (1014, lines 4 to 16), complement output logic (1016, line 17) for obtaining 2's complement for the output of absolute value binary division logic (1014), output of absolute value binary division logic (1016 ), the first AND operation logic (line 18) that multiplies the second sign bit obtained by inverting the first sign bit bit by bit and outputs the first resultant value (q _L ), and the output 1016 of the complement output logic 2nd AND operation logic (line 19) that multiplies the 1st sign bit by bit and outputs the 2nd resultant value (q _R ), addition logic that outputs the final resultant value by inputting the 1st resultant value and the 2nd resultant value (line 20).

In homomorphic ciphers, the ciphertext is unknown, so simple comparisons or if assumptions cannot be made as in the plaintext.

First of all, the simple comparison process of comparing A and M in FIG. 9 can be solved through the above-mentioned homomorphic encryption comparison function (9th line of the above algorithm).

)의 값의 반환이 Enc(0) 또는 Enc(1)인 것에 착안하여,

이면 Enc(1)이고, 이 값에 boots.NOT을 취한 값(d)은 Q[0] 값이 된다. 마찬가지로,

이면 HE.CompareSmall(

)의 값은 Enc(0) 이고, Q[0]값이 된다. In addition, the second if assumption in FIG. 9 is HE.CompareSmall(

) is Enc (0) or Enc (1),

If it is Enc(1), the value (d) obtained by taking boots.NOT from this value becomes the Q[0] value. Likewise,

if HE.CompareSmall(

) is Enc(0) and becomes the Q[0] value.

인 상황에서 Enc(0) 에 boots.NOT을 취한 값, 즉 Enc(1)과

을 비트별로 boots.AND 연산을 적용하면,

값이 나오게 되고, 반대의 상황(

)에서는 Enc(1)이므로 boots.NOT을 취한 값, Enc(0)과

을 비트별로 boots.AND 연산을 적용하면 Enc(0)이 나오게 된다.

In the situation of Enc(0), the value of taking boots.NOT, i.e. Enc(1) and

Applying the boots.AND operation bit by bit,

The value comes out, and the opposite situation (

) is Enc(1), so the value taken from boots.NOT, Enc(0) and

By applying the boots.AND operation bit by bit, Enc(0) is obtained.

의 값이 정해지고, 이를

만큼 반복해주면, 몫을 실수 범위까지 확장하여 구할 수 있다.Through this, the ciphertext

is set, and

By repeating as many times as possible, the quotient can be extended to the range of real numbers.

)와 피제수(

)의 부호비트 간에 boots.XOR 연산을 해주어 같은 부호면 Enc(0), 반대 부호면 Enc(1)을

에 저장한다. 2, 3번째 줄에서는 제수와 피제수 모두 양으로 전환하여, 양의 값을 갖는 상황에서 나눗셈을 쭉 진행하여,

값을 얻는다. 이 값에 대해 2의 보수를 취해주어

값을 저장하고, 앞서 말한것처럼 두 입력값의 부호가 같은 경우

= Enc(0) 이기 때문에, 이를 boots.NOT 취한 Enc(1)와

의 비트단위 별로 boots.AND를 취해

을 얻는다. In addition, in the ciphertext, unlike in the plaintext, the sign cannot be known, so an additional operation must be performed. Divisor in line 1 (

) and the dividend (

), boots.XOR operation is performed between the code bits of Enc(0) for the same sign and Enc(1) for the opposite sign.

save to In the 2nd and 3rd lines, both the divisor and the dividend are converted to positive, and the division proceeds continuously in the situation of having a positive value,

get value Take the 2's complement of this value

Save the value and, as mentioned above, if both inputs have the same sign

= Enc(0) , so Enc(1) taking boots.NOT and

Take boots.AND by bitwise of

get

의 비트별로 boots.AND를 취해

을 얻는다. 마지막으로, 이 두 값을 더하게 되면 최종적으로 결괏값

가 된다.Similarly, Enc(1) with the opposite sign

take boots.AND bit by bit of

get Finally, when these two values are added, the final result is

becomes

An embodiment of the present invention may be implemented in the form of a recording medium including instructions executable by a computer, such as program modules executed by a computer. Computer readable media can be any available media that can be accessed by a computer and includes both volatile and nonvolatile media, removable and non-removable media. Also, computer readable media may include computer storage media. Computer storage media includes both volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Although the methods and systems of the present invention have been described with reference to specific embodiments, some or all of their components or operations may be implemented using a computer system having a general-purpose hardware architecture.

The above description of the present invention is for illustrative purposes, and those skilled in the art can understand that it can be easily modified into other specific forms without changing the technical spirit or essential features of the present invention. will be. Therefore, the embodiments described above should be understood as illustrative in all respects and not limiting. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as distributed may be implemented in a combined form.

The scope of the present invention is indicated by the following claims rather than the detailed description above, and all changes or modifications derived from the meaning and scope of the claims and equivalent concepts should be construed as being included in the scope of the present invention. do.

100: arithmetic unit
110: memory
120: processor
130: communication module
140 DB
200: user terminal

Claims (12)

In the calculation device of data encrypted by the fully homomorphic encryption method,
A communication module for transmitting and receiving encrypted data;
a memory in which an arithmetic program is stored; and
Including a processor that executes the calculation program,
The operation program includes an XOR operation logic, an XNOR operation logic, an AND operation logic, and an OR operation logic for bit-by-bit operation of the first homomorphic encryption data and the second homomorphic encryption data, and a complement for returning a complement to the homomorphic encryption data. Operation logic, absolute value operation logic that returns the absolute value of homomorphic encryption data, right shift operation logic that returns the result of shifting homomorphic data to the right, left shift operation that returns the result of shifting homomorphic data to the left Including logic and MUX operation logic for outputting any one of a plurality of input homomorphic encryption data,
If the first input value of the input first homomorphic encryption data and the second homomorphic encryption data is a larger value, a first size comparison operation logic for outputting a first encryption value obtained by encrypting '1' bit and the input first homomorphic encryption data And a second case comparison operation logic for outputting the first encryption value when a first input value of the second homomorphic encryption data is a smaller value,
The first size comparison operation logic obtains a first output value by inputting the inputted first homomorphic encryption data and second homomorphic encryption data to the XNOR operation logic, and obtains '0' according to the first output value through the MUX operation logic. Outputting a second encryption value obtained by encrypting bits or first homomorphic encryption data;
The second size comparison operation logic obtains a first output value by inputting the inputted first homomorphic encryption data and second homomorphic encryption data to the XNOR operation logic, and obtains '0' according to the first output value through MUX operation logic. An apparatus for calculating data encrypted by a fully homomorphic encryption method, outputting a second encryption value obtained by encrypting bits or the second homomorphic encryption data. According to claim 1,
The operation program further includes an addition logic for adding the first homomorphic encryption data and the second homomorphic encryption data in an encrypted state,
The addition logic is
A first XOR operation logic inputting the first homomorphic encryption data and second homomorphic encryption data and outputting a first output value, a second XOR operation logic inputting the first output value and a first carry value and outputting a result value; A first AND operation logic for outputting a second output value by inputting the first output value and the first carry value, and a second AND operation logic inputting the first homomorphic encryption data and second homomorphic encryption data and outputting a third output value. Logic and an OR operation logic for inputting the second output value and the third output value and outputting a second carry value. According to claim 2,
The operation program further includes subtraction logic for subtracting the first homomorphic encryption data and the second homomorphic encryption data in an encrypted state,
The subtraction logic is
A first XOR operation logic inputting the first homomorphic encryption data and second homomorphic encryption data and outputting a first output value, a second XOR operation logic inputting the first output value and a first carry value and outputting a result value; A first AND operation logic for outputting a second output value by inputting a value obtained by inverting the first homomorphic encryption data and second homomorphic encryption data, and a third output value by inputting a value obtained by inverting the first output value and a first carry value. A second AND operation logic for outputting, and an OR operation logic for outputting a second carry value by inputting the second output value and the third output value. According to claim 3,
The calculation program further includes an absolute value logic for calculating an absolute value in a state in which the input homomorphic encryption data is encrypted,
The absolute value logic is a fully homomorphic encryption technique that includes a MUX operation logic that outputs one of 2's complement for the input homomorphic encryption data and input homomorphic encryption data according to the ciphertext of the most significant bit of the input homomorphic encryption data. A computing device for encrypted data. According to claim 4,
The operation program further includes multiplication logic for multiplying the first homomorphic encryption data and the second homomorphic encryption data in an encrypted state,
The multiplication logic is
An XOR operation logic for outputting a first sign bit by inputting the sign bit of the first homomorphic encryption data and the sign bit of the second homomorphic encryption data, and a NOT operation for outputting a second sign bit by inverting the first sign bit. logic, a first absolute value logic for obtaining an absolute value of the first homomorphic encryption data, a second absolute value logic for obtaining an absolute value of the second homomorphic encryption data, and an output of the second absolute value logic for each bit of the output of the first absolute value logic Absolute value binary multiplication logic for multiplication, complement output logic for obtaining 2's complement for the output of the absolute value binary multiplication logic, bit by bit multiplication of the second sign bit with respect to the output of the absolute value binary multiplication logic to output a first resultant value A first AND operation logic, a second AND operation logic for multiplying the output of the complement output logic by bit by bit by the first sign bit and outputting a second resultant value, the first resultant value and the second resultant value are input and finalized An apparatus for calculating data encrypted by a fully homomorphic encryption method, including the addition logic for outputting a resultant value. According to claim 5,
The operation program further includes division logic for dividing second homomorphic encryption data, which is a divisor (M), by first homomorphic encryption data, which is a dividend (Q), in an encrypted state;
The division logic is
XOR operation logic inputting the sign bit of the first homomorphic encryption data and the sign bit of the second homomorphic encryption data and outputting a first sign bit; a first absolute value logic calculating an absolute value of the first homomorphic encryption data; The second absolute value logic for obtaining the absolute value of 2 homomorphic encryption data, the absolute value binary division logic for dividing the output of the first absolute value logic bitwise by the output of the second absolute value logic, and the two's complement for the output of the absolute value binary division logic Complement output logic to obtain, a first AND operation logic for outputting a first resultant value by bitwise multiplying a second code bit obtained by inverting the first code bit with respect to an output of the absolute value binary division logic, and an output of the complement output logic A second AND operation logic for multiplying the first sign bit bit by bit and outputting a second resultant value, and the addition logic for inputting the first resultant value and the second resultant value and outputting a final resultant value, A device for calculating data encrypted by homomorphic encryption. In the method of calculating encrypted data using a calculation device for data encrypted by a fully homomorphic encryption method,
The encrypted data processing unit includes an XOR operation logic, an XNOR operation logic, an AND operation logic, and an OR operation logic for performing bit-by-bit operation on the first homomorphic encryption data and the second homomorphic encryption data, respectively, and repairing the homomorphic encryption data. Complement arithmetic logic that returns , absolute value arithmetic logic that returns the absolute value of homomorphic encryption data, right shift arithmetic logic that returns the result value shifted to the right of homomorphic encryption data, return result value that shifted homomorphic data to the left An operation program including a left shift operation logic to perform and a MUX operation logic to output any one of a plurality of input homomorphic encryption data is installed,
performing case comparison by inputting the input first homomorphic encryption data and the second homomorphic encryption data into a first case comparison operation logic; and
Including inputting the input first homomorphic encryption data and the second homomorphic encryption data to a second case comparison operation logic to perform case comparison;
The first size comparison operation logic outputs a first encryption value obtained by encrypting '1' bit if the first input value is a large value, and performs the XNOR operation on the inputted first homomorphic encryption data and second homomorphic encryption data. Logic input to obtain a first output value, and outputting a second encryption value or first homomorphic encryption data obtained by encrypting '0' bits according to the first output value through MUX operation logic,
The second size comparison operation logic outputs the first encryption value if the first input value is a small value, and inputs the input first homomorphic encryption data and second homomorphic encryption data to the XNOR operation logic to obtain the first Calculating an output value and outputting a second encryption value obtained by encrypting '0' bit or the second homomorphic encryption data according to the first output value through a MUX operation logic. According to claim 7,
The step of adding the first homomorphic encryption data and the second homomorphic encryption data in an encrypted state by inputting them to an addition logic;
The addition logic is
A first XOR operation logic inputting the first homomorphic encryption data and second homomorphic encryption data and outputting a first output value, a second XOR operation logic inputting the first output value and a first carry value and outputting a result value; A first AND operation logic for outputting a second output value by inputting the first output value and the first carry value, and a second AND operation logic inputting the first homomorphic encryption data and second homomorphic encryption data and outputting a third output value. Logic and an OR operation logic for inputting the second output value and the third output value and outputting a second carry value. According to claim 8,
Further comprising inputting the first homomorphic encryption data and the second homomorphic encryption data to a subtraction logic and subtracting them in an encrypted state;
The subtraction logic is
A first XOR operation logic inputting the first homomorphic encryption data and second homomorphic encryption data and outputting a first output value, a second XOR operation logic inputting the first output value and a first carry value and outputting a result value; A first AND operation logic for outputting a second output value by inputting a value obtained by inverting the first homomorphic encryption data and second homomorphic encryption data, and a third output value by inputting a value obtained by inverting the first output value and a first carry value. A method for calculating data encrypted by a fully homomorphic encryption method, comprising: a second AND operation logic for outputting ; and an OR operation logic for outputting a second carry value by inputting the second output value and the third output value. According to claim 9,
Further comprising calculating an absolute value in an encrypted state by inputting the input homomorphic encryption data into an absolute value logic,
The absolute value logic is a fully homomorphic encryption technique that includes a MUX operation logic that outputs one of 2's complement for the input homomorphic encryption data and input homomorphic encryption data according to the ciphertext of the most significant bit of the input homomorphic encryption data. How to calculate encrypted data. According to claim 10,
Further comprising inputting the first homomorphic encryption data and the second homomorphic encryption data into a multiplication logic and multiplying them in an encrypted state;
The multiplication logic is
An XOR operation logic for outputting a first sign bit by inputting the sign bit of the first homomorphic encryption data and the sign bit of the second homomorphic encryption data, and a NOT operation for outputting a second sign bit by inverting the first sign bit. logic, a first absolute value logic for obtaining an absolute value of the first homomorphic encryption data, a second absolute value logic for obtaining an absolute value of the second homomorphic encryption data, and an output of the second absolute value logic for each bit of the output of the first absolute value logic Absolute value binary multiplication logic for multiplication, complement output logic for obtaining 2's complement for the output of the absolute value binary multiplication logic, bit by bit multiplication of the second sign bit with respect to the output of the absolute value binary multiplication logic to output a first resultant value A first AND operation logic, a second AND operation logic for multiplying the output of the complement output logic by bit by bit by the first sign bit and outputting a second resultant value, the first resultant value and the second resultant value being input to obtain a final A method of calculating data encrypted by a fully homomorphic encryption method, comprising the addition logic for outputting a resultant value. According to claim 11,
Further comprising dividing second homomorphic encryption data, which is a divisor (M), by first homomorphic encryption data, which is a dividend (Q), by using division logic in an encrypted state,
The division logic is
XOR operation logic inputting the sign bit of the first homomorphic encryption data and the sign bit of the second homomorphic encryption data and outputting a first sign bit; a first absolute value logic calculating an absolute value of the first homomorphic encryption data; The second absolute value logic for obtaining the absolute value of 2 homomorphic encryption data, the absolute value binary division logic for dividing the output of the first absolute value logic bitwise by the output of the second absolute value logic, and the two's complement for the output of the absolute value binary division logic Complement output logic to obtain, a first AND operation logic for outputting a first resultant value by bitwise multiplying a second code bit obtained by inverting the first code bit with respect to an output of the absolute value binary division logic, and an output of the complement output logic A second AND operation logic for multiplying the first sign bit bit by bit and outputting a second resultant value, and the addition logic for inputting the first resultant value and the second resultant value and outputting a final resultant value, Operation method of data encrypted by homomorphic encryption method.

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