JP2002247027A - Method and device for preparing latin square - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide Latin square preparing method and device capable of extending the application range of a Latin square and remarkably improving the application value and application effect of the Latin square. SOLUTION: An operation part 1 successively reads out symbols stored in an existing n-order Latin square set up in a Latin square storing array 10 in the set selection order and the selecting direction, reads out conversion values in the order of inputted symbol values from a conversion value storage part 11, obtains a remainder result by allowing a remainder operation part 17 to execute the modulo n operation of an added/subtracted result obtained by an addition/subtraction part 16 by using the conversion values, and repeats conversion operation for storing a symbol corresponding to the remainder result as the symbol m of the position of the inputted symbol up to the final position of the Latin square. Although the storage pattern of the Latin square is stored as it is, an effect for changing the selection order of stored element arrays can be fulfilled.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for creating a Latin square, and more particularly to a conversion table used for encryption communication or identification password creation, or a combination having no identity in the design of experiments and statistics. TECHNICAL FIELD The present invention relates to a method and an apparatus for creating a Latin square used for setting of a square.

[0002]

2. Description of the Related Art The basic properties of Latin squares are disclosed in detail in the literature (Iwanami Mathematics Dictionary, 3rd edition, Iwanami Shoten). The Latin squares will be briefly described. A set of n symbols A = {a1,. . . . . Using each element of an｝ n times, a total of n ² elements are arranged in a square of n rows and n columns, and in each row and column, the element that appears once in set A is represented by the Latin square on A , Or the nth Latin square.

[0003] In addition, a case where both the first row and the first column are natural permutations is called a regular or standard Latin square. If the number of irreducible or standard Latin squares is represented by L (n), the total number of Latin squares of order n is n!・ (N
-1)! -L (n) is obtained. The value of L (n) is as follows when n is 9 or less, that is, when n = 1 to 9.

L (1) = 1 L (2) = 1 L (3) = 1 L (4) = 4 L (5) = 56 L (6) = 9,408 L (7) = 16,942 080 L (8) = 535, 281, 401, 856 L (9) = 377, 597, 570, 964, 258,
816

FIG. 8A shows a fourth-order element A = {0, 1,
Shows the basic form of a Latin square of 2,3｝. The basic form of this Latin square is that both the first row and the first column array elements are 0
As shown in FIG. 8 (b), the order is ascending order (natural permutation).
It belongs to the standard type Latin square shown in. In FIG. 8B, it is assumed that an arbitrary value from 0 to 3 forming the Latin square is set as the value of the array element of (•). The inventor of the present invention has previously disclosed a method of regularly forming such a Latin square in Japanese Patent Application Laid-Open No. 10-105544.

In the Latin square creating method proposed by the inventor, the degree and symbol of the Latin square to be created are set,
When selecting and determining symbols in order as an array element at each position in the Latin square, select and determine in order along the row or column, and use a symbol so that each position does not have the same symbol as the position before the same row and column Select to create Latin squares.

[0007]

However, in the above-described Latin square creation method proposed by the present inventor, the order of the created Latin squares is the order according to the permutation of symbols and the selection order. Since the Latin square to be created next is uniquely determined, there is a problem that the Latin square to be used is not necessarily guessed when used for encryption or the like.

[0008] The present invention has been made in view of the above points,
By creating a new Latin square of the same degree desired from the existing Latin square according to a certain procedure and using specific conversion information, a third party must know the existing Latin square and the conversion information if they do not know the existing Latin square and conversion information. Although it is difficult to create a Latin square, it is an object of the present invention to provide a Latin square creating method and a creating apparatus that can accurately create a Latin square when the creation information is known.

Another object of the present invention is to provide a method and an apparatus for creating a Latin square which can expand the range of use of the Latin square and greatly enhance the use value and the utilization effect of the Latin square. is there.

[0010]

In order to achieve the above object, the present invention provides a method for forming a Latin square according to the first invention, wherein n symbols m different from each other are placed at the same position in the same row and the same column. Differently, in a creation method for creating a Latin square of degree n set as an array element at the position of n rows and n columns, the order n, the selection order of the symbols m, and the symbol m of the n rows and n columns And the symbol m
Are arranged along the row direction or the column direction of n rows and n columns, a desired existing nth-order Latin square is set in the storage array, and n symbols m of the nth-order Latin square are further set. A first step of preparing an integer conversion value to be added or subtracted from the selection order or the symbol itself, and capturing a symbol m at a set position of an existing nth-order Latin square set in the storage array, A value obtained by adding or subtracting an integer conversion value to or from the selection order of the symbol m or the symbol m itself, and taking the remainder of the addition or subtraction result with n as a symbol in the selection order, and a symbol at the set position m, and converting the symbol m
A third step of determining whether or not the converted position is the final position of n rows and n columns. If the third step determines that the position is not the final position, the position for converting the symbol The next position according to the symbol arrangement direction set in the first step is designated as the set position, and the symbol conversion in the second step is performed again. When it is determined that the symbol is the final position, the process ends. And a fourth step of performing the following.

According to the present invention, symbols at respective positions of a desired existing n-th Latin square preset in the storage array are sequentially fetched in the set order, and the symbols m fetched from the storage array are added to the symbols m. On the other hand, an integer conversion value is added or subtracted to the selection order of the symbol m or the symbol m itself, and a value obtained by taking the remainder of the addition or subtraction by n is set in the symbol of the selection order in the position set. Symbol m
Since the conversion and storing are performed for all the symbols m of the existing n-th Latin square, it is possible to newly create an n-th Latin square converted based on the conversion values in the storage array. it can.

In order to achieve the above object, a second aspect of the present invention provides a fourth step of the first aspect, wherein the conversion of all symbols of the n-th Latin square in the second step is set in advance. It is characterized in that the final position when repeated one or more times is determined to be the final position and the process is terminated. According to the present invention, the existing n-th Latin square can be further deformed, particularly when it is repeated a plurality of times. From n types of conversion values and 2n types of conversion information from two types of operations of addition and subtraction, at most n-1 except for one type whose value does not change when the conversion value is 0 and addition / subtraction is performed. A variety of variations are possible.

[0013] In order to achieve the above object, a Latin square creating method according to a third aspect of the present invention is directed to a Latin square creating method according to the fourth aspect of the first aspect of the present invention. For the Latin squares, and in order to further select and determine the symbols as array elements at each position of the nth Latin square, the selection decision is made in the row or column along the row or column, starting at the last row and column position. The symbols are selected in the order of selection so that the symbols do not have the same symbol as the previously determined array element at the same row and the same position before the same column at each position. When there is no symbol that can be determined, the symbol of the array element that has already been determined at a position before that position is replaced with a selectable symbol having a lower order than the symbol, and the selection determination is continued. One And further comprising a fifth step of creating a.

In the third aspect, another new Latin square can be created by combining another Latin square creation method based on the Latin square converted into the storage array by the conversion information. According to the third invention, another Latin square creating method described above is disclosed in Japanese Patent Laid-Open No. 10-105544.
This is a method for creating a Latin square described in Japanese Patent Publication No.

In order to achieve the above object, a Latin square forming apparatus according to a fourth aspect of the present invention has a total of n ² storage elements in n rows and n columns, and each of the storage elements is different from each other. Among the n symbols, a Latin square storage array in which one arbitrarily selected symbol m is stored, and a storage element at a set position among n ² storage elements constituting the Latin square storage array , A conversion value storage unit storing a conversion value for changing the value of the selection order of the element symbol or the value of the element symbol itself, and addition / subtraction specification for specifying addition or subtraction of the conversion value Part, the symbol selection order or the symbol m itself, adding or subtracting the converted value, performing a calculation of taking the remainder of the addition or subtraction by n, and the degree n of the Latin square to be created, , Symbol m
And the order in which the symbols m of the Latin square memory array are first arranged and the order in which the symbols m are arranged along the row direction or the column direction of the Latin square memory array are preset and designated. Controlling the means to fetch the symbols stored in the existing nth-order Latin square set in the Latin square storage array in the selected selection order and sequentially in the selection direction, and to convert the order of the values of the fetched symbols; The conversion operation of reading the value from the conversion value storage unit, causing the remainder calculation unit to calculate the value, and converting the obtained value of the remainder result into a symbol in the order of selection as the symbol m at the set position is referred to as a symbol installation position. Is repeated until the final position of n rows and n columns is reached, and all the symbols of the existing Latin squares set in the Latin square storage array are replaced by the value of the remainder result obtained by the remainder calculating means. Change using It is obtained by a structure for creating a new Latin square by.

According to the fourth aspect of the present invention, all the symbols of the existing Latin square set in the Latin square storage array are converted by using the conversion values stored in the conversion value storage unit, thereby obtaining a new symbol. Creates a Latin square.

In order to achieve the above object, a fifth aspect of the present invention provides a computing unit according to the fourth aspect of the present invention, wherein the conversion of all the symbols of the nth-order Latin square is performed one or two or more times in advance.
It is characterized in that the final position when repeated is determined as the final position and the process is terminated.

Further, in order to achieve the above object, a sixth aspect of the present invention provides an arithmetic unit, wherein an arithmetic unit is further provided with an nth order Latin square in the Latin square storage array when the final position is determined. When sequentially selecting and determining symbols as array elements at each position of the Latin square, the selection is determined by controlling the designating means, starting from the last position of the row or column, and ending at the last position of the row or column along the row or column. Up to the same order, and select symbols in the order of selection so that they do not have the same symbol as the previously determined array element at the same row and column before each position, and select and determine at that position When there is no symbol that can be made, a Latin square is created by continuing the selection decision by replacing the symbol of the array element already determined at the position before that position with a selectable symbol that is lower in order than the symbol Do The features. According to the sixth aspect, since a Latin square is newly created by performing conversion using the conversion value and then a Latin square is created by another Latin square creation method, the change of the Latin square element is irregular. it can.

[0019]

Next, an embodiment of the present invention will be described with reference to the drawings. In the following description, the degree n is set to 4 and the symbol m is a natural element A =
{0, 1, 2, 3}, and the permutation and selection order thereof are the same as the natural permutation (0, 1, 2, 3).

FIG. 1 is a block diagram showing an embodiment of a Latin square forming apparatus according to the present invention. In FIG. 1, a calculation unit 1 executes calculation processing by software,
The order n, the selection order of the symbol m, the position where the symbol m is first arranged in the n rows and n columns of the nth Latin square, and the symbol m
Are arranged along the row direction or the column direction of n rows and n columns, and the existing Latin squares are set in the Latin square storage array 10. Various calculations are executed in accordance with the determined control program, and the connected Latin square creating unit 2 designates the matrix position of the data of the Latin square R created, compares, judges, sets and reads.

The Latin square creating unit 2 is connected to the arithmetic unit 1, and stores a row position setting storage unit 3, a column position setting storage unit 4, a row position comparison storage unit 5, and a column position comparison storage unit 6. Setting symbol storage unit 7, comparison symbol storage unit 8, symbol comparison unit 9, Latin square storage array 10, conversion value storage unit 11, addition / subtraction designation storage unit 12, degree storage unit 13, element symbol storage unit 14, It comprises a selection order storage unit 15, an addition / subtraction unit 16, and a remainder operation unit 17.

The row position setting storage unit 3 specifies the row position of the symbol m which is selected and determined based on the output signal of the arithmetic unit 1 in the Latin square storage array 10. The column position setting storage unit 4 specifies the column position of the symbol m that is selected and determined based on the output signal of the arithmetic unit 1 in the Latin square storage array 10.

The row position comparison storage unit 5 stores the row position of the symbol m ′ to be compared with the symbol m selected and determined based on the output signal of the arithmetic unit 1, and the column position comparison storage unit 6 stores The column position of the symbol m ′ to be compared with the symbol m that is selected and determined based on the output signal of the arithmetic unit 1 is specified for the Latin square storage array 10. The setting symbol storage unit 7
Stores the symbol m selected and determined based on the output signal of the arithmetic unit 1 or the symbol m from the Latin square storage array 10.

The comparison symbol storage unit 8 stores the comparison symbol m 'read from the Latin square storage array 10. The symbol comparing unit 9 compares the data m set by the arithmetic unit 1 stored in the setting symbol storage unit 7 with the compared symbol m ′ stored in the comparison symbol storage unit 8, The result of the comparison is output to the arithmetic unit 1. An existing nth-order Latin square is created in the Latin square storage array 10 in advance.

The conversion value storage unit 11 stores the absolute value of the conversion value, and the addition / subtraction designation storage unit 12 adds or subtracts the value of the Latin square element or the value of the element selection order according to the sign of the conversion value. Is specified. Order storage unit 13
Stores the value of the degree n of the Latin square to be created and uses it for various calculations such as remainder calculation. Element symbol storage unit 14
Stores the value of the element symbol set in the Latin square to be created, and stores the value of the order of the selection order corresponding to the element symbol in the selection order storage unit 15.

The addition / subtraction unit 16 performs addition or subtraction on the values of the elements in the Latin square or the values in the order of selection and the converted values according to the designation of the addition / subtraction designation storage unit 12. The remainder operation unit 17 performs a remainder, that is, mod n (modulo n) operation on the converted value or the value of the operation result of the addition / subtraction unit 16 with the value of the degree n of the Latin square stored in the order storage unit 13.

When the degree is n, the Latin square R created by the Latin square creating unit 2 is composed of n rows and n columns, and the position of the I row and J column is represented by _KIJ , as shown in FIG. , array element (symbol m) which is arranged in the position _{K IJ} is represented by _{E IJ.} When creating an n-th order Latin square, the Latin square storage array 10 in FIG. 1 has a total of n ² array elements (storage elements) in n rows and n columns, similarly to the Latin square R shown in FIG. ), Of which the array element at the position K _IJ at the I row and the J column is represented by 10 _IJ . Here, each array element 10
Each _IJ stores one symbol (data) m.

The arithmetic unit 1 stores the order n of the Latin square to be created, the selection order of the symbol m, the position where the symbol m of the Latin square storage array 10 is first arranged, and the symbol m in the Latin square storage. The order in which the array 10 is arranged in the row direction or the column direction is set in advance, and the row position is set in the row position setting storage unit 3 and the column position is set in the column position setting storage unit 4, respectively. The symbols stored in the existing n-th Latin square set in the square storage array 10 are sequentially fetched in the set selection order and in the selection direction, and the converted value F of the order of the fetched symbol values is The conversion operation of reading from the conversion value storage unit 11 and the addition / subtraction designation storage unit 12 and storing the result of conversion with the conversion value F at the position of the fetched symbol is repeated until the final position of the Latin square is reached. To create a new Latin square to 10.

For example, the conversion value F is set to “−3”, and the existing nth-order Latin square set in the Latin square storage array 10 is replaced with the fourth-order Latin square shown in FIGS. 4 (a) and 7 (a). Assuming that the value of the element symbol is directly converted, the sign of the conversion value F is negative, so that the subtraction is specified, and the symbol A = ｛0, set in the Latin square by the absolute value “3” of the conversion value 1,
2, 3}.

Therefore, when the conversion value F is "-3",
For the Latin square setting element “0”, “3” is subtracted from the value to obtain a subtraction result of −3 (= 0−3), and the subtraction result is an order of 4 (= n). By taking the remainder (by performing modulo 4 calculation), the value of the element symbol is converted to “1”. When the set element is “1”, the result of subtraction from the conversion value is −2 (= 1−3), and the remainder of the subtraction result is converted to “2” by taking the remainder by 4. Is done. Similarly, when the setting element is "2", the subtraction result is -1 (= 2-3), and the remainder of the subtraction result is converted to "3" by taking the remainder of 4. When the element symbol is “3”, the subtraction result is 0 (= 3−3).
Since 3), the value of the element symbol becomes “0” by taking the remainder of 4 in the subtraction result. As a result, all elements are converted to new elements. The selection order of the resulting elements is (1, 2, 3, 0).

Although the absolute value of the converted value is usually smaller than the order n, the absolute value of the converted value to be added or subtracted is n.
In the above case, mod n operation is performed on the absolute value to obtain n.
Addition / subtraction is performed with a smaller value, and mod n is further obtained as a conversion result, or mod n is performed after addition / subtraction is performed on the value of the conversion value element to obtain the result.

Next, a method for creating a Latin square according to the present invention, which is created using the above-described Latin square creating apparatus, will be described. FIG. 3 is a flowchart illustrating an embodiment of a method for creating a Latin square according to the present invention. Here, the arithmetic unit 1 sets the symbol m which is disposed at each position K _IJ row I and column J of the existing Latin square R 'in Latin square for storing sequence 10 shown in FIG. 1 as an array element E _IJ At the same time, the arithmetic unit 1 arranges the order n as creation information, the position where the symbol m of the n rows and n columns is first arranged, and the symbols m along the row direction or the column direction of the n rows and n columns. The order and the selection order of the symbol m are set respectively. Further, the absolute value of the conversion value F is set in the conversion value storage unit 11, and addition or subtraction according to the sign of the conversion value F is set in the addition / subtraction designation storage unit 12.

Here, as an example, a fourth-order Latin square shown in FIGS. 4A and 7A is stored in advance as an existing Latin square R ′ in the Latin square storage array 10. , As described above, the degree n is 4, and the symbol m
Is a natural number (0, 1, 2, 3), and the permutation and selection order are the same as the natural permutation. The direction of travel of the position is shown in FIG.
There is a column direction that progresses in the direction indicated by the arrow in FIG. 3, and a row direction that advances in the direction indicated by the arrow in FIG. Here, it is assumed that the column direction is set as the traveling direction of the position. Further, the first position is in the general form Latin square is K ₁₁ in the first row and the first column. Further, it is assumed that “3” is stored in the conversion value storage unit 11 and subtraction is specified in the addition / subtraction designation storage unit 12 (that is, the conversion value F is “−3”).

In this state, the arithmetic unit 1 first sets "1" as the row position I in the row position setting storage unit 3 (step S1), and then stores the column position in the column position setting storage unit 4. "1" is set as J (step S2). This allows
The first position of the Latin square for storing sequence 10 which is set by the row position setting storage unit 3 and the column position setting storage unit 4 K _{1 1}
The element E (1,1) (= 0) is output to the setting symbol storage unit 7 and stored.

[0035] Then, the calculating portion 1 takes in the element E of the first position _{K 11} of Latin square for storing sequence 10 from the setting symbol storage unit 7 (1,1) (= 0), the conversion value storing unit it 11 and the conversion value “−3” from the addition / subtraction designation storage unit 12, and the addition / subtraction unit 16 performs a subtraction operation between the element “0” and the absolute value “3” of the conversion value.
3 (= 0-3) is further modulo 4 operated by the remainder operation unit 17 to obtain a remainder result of 1 (= -3 mod 4).

The operation unit 1 converts the remainder result "1" obtained by the remainder operation unit 17 as an element symbol, and converts the converted symbol "1" from the setting symbol storage unit 7 again into the row position setting storage unit. set to part 3 and elements of first position _{K 11} of Latin squares storing array 10 as an element E (1, 1) position _{K 11} set in the column position setting storage unit 4 E (1,1) (Step S3). As a result, in the Latin square storage array 10, the symbol of the element E (1,1) is converted to "1" as shown by underlining in FIG. 4B.

Next, the arithmetic unit 1 determines whether the value of the column position J set in the column position setting storage unit 4 is smaller than the degree n (step S4). At this point, J = 1, n
= 4 and J <n, so the value of column position J is
After adding “1” and setting “2” in the column position setting storage unit 4 (step S5), the process proceeds to step S3. At this time, the value of the row position setting storage unit 3 remains “1”, which is the same as the previous time.

[0038] Therefore, in step S3, the calculating portion 1 element E (1, 2) at the next position _{K 12} of Latin square for storing sequences 10 through setting symbol storage unit 7 (= 1) the incorporation, addition, transformation Value storage unit 11 and addition / subtraction designation storage unit 12
The subtraction operation of the element “1” and the absolute value of the converted value “3” is performed by the adding / subtracting unit 16 based on the value “−3” of the conversion information F read from, and the obtained subtraction result −2 (= 1 -3)
And further modulo 4 operation is performed by the remainder operation unit 17,
2 (= −2 mod 4) is obtained.

The operation unit 1 converts the remainder result “2” obtained by the remainder operation unit 17 as an element symbol, and converts the converted symbol “2” from the setting symbol storage unit 7 again to the row position setting storage unit. set to part 3 and elements of positions _{K 12} elements E (1, 2) as a Latin square for storing sequence 10 position _{K 12} set in the column position setting storage unit 4 E (1,2). As a result, in the Latin square storage array 10, the symbol of the element E (1,2) is converted to "2" as shown by underlining in FIG.

[0040] Then, the calculating portion 1 turn elements next position _{K 13} of Latin square for storing sequence 10 E (1,3) (=
2), and based on the value “−3” of the conversion information F read from the conversion value storage unit 11 and the addition / subtraction designation storage unit 12, the addition / subtraction unit 16 converts the element “2” and the absolute value of the conversion value “3”. A subtraction operation is performed, and the obtained subtraction result -1
(= 2-3), and to further perform the operation of modulo 4 remainder operation unit 17, 3 - to give (= 1 mod 4) remainder result of it position _{K 13} element E (1, 3) Is set in the Latin square storage array 10 (steps S4, S5,
S3). As a result, the element E (1,3) of the Latin square storage array 10 is converted into the symbol "3" as shown by underlining in FIG. 4D.

[0041] Then, the calculating portion 1 turn elements next position _{K 14} of Latin square for storing sequence 10 E (1,4) (=
3), and based on the value “−3” of the conversion information F read from the conversion value storage unit 11 and the addition / subtraction designation storage unit 12,
The addition and subtraction unit 16 calculates the element “3” and the absolute value “3” of the converted value.
Is performed, and the obtained subtraction result 0 (= 3-
3), and further perform the calculation of modulo 4 remainder operation unit 17, 0 (= 0 mod 4 ) to obtain the remainder result of, for Latin squares stores it as the position _{K 14} element E (l, 4) It is set in array 10 (steps S4, S5, S3). As a result, the element E (1,
4) is converted to the symbol “0” as shown by underlining in FIG.

At this stage, J = 4, which is equal to the value of n. Thus, the arithmetic unit 1 determines at step S4 that the value of the row position I set in the row position setting storage unit 3 is the order n
It is determined whether it is smaller than (Step S6). At this point, since I = 1 and n = 4, since I <n,
After adding “1” to the value of the row position I and setting “2” in the row position setting storage unit 3 (step S7), the process proceeds to step S2, where the column set in the column position setting storage unit 4 is set. Position J
Is set to “1”.

Subsequently, the arithmetic unit 1 fetches the element E (2,1) (= 1) at the next position K ₂₁ of the Latin square storage array 10 and reads it from the conversion value storage unit 11 and the addition / subtraction designation storage unit 12. Based on the value “−3” of the conversion information F, the addition / subtraction unit 16 performs a subtraction operation between the element “1” and the absolute value “3” of the conversion value, and the obtained subtraction result−2 (= 1−3) ),
Further, the modulo 4 operation is performed by the remainder operation unit 17, and 2
To give (= -2 mod 4) remainder result of setting it to Latin square for storing sequence 10 as element E (2,1) position _{K 21} (step S3). As a result, the element E (2,1) of the Latin square storage array 10 is changed as shown in FIG.
Is converted to the symbol "2" as shown by underlining the "."

[0044] Hereinafter, the same operation as described above is repeated, the calculating portion 1 as elements E position _{K 43} of Latin square for storing sequence 10 (4,3), underlined in FIG. 4 (g) into a symbol "2" as shown, as an element E of the last position K ₄₄ of Latin square for storing sequence 10 (4,4), the symbol as shown underlined in Figure 4 (h) " 1 ". At this point, the symbols of all the elements are converted, and J = 4 and I = 4.
Then, the process of creating the Latin square is completed via step S6 and step S6, respectively (step S8).

Next, FIGS. 1, 3 and 5 show another example.
It is explained together with. In this other example, a fourth-order Latin square shown in FIG. 5A and FIG. 7C is stored in advance as an existing Latin square R ′ in the Latin square storage array 10, and as described above. Thus, the degree n is 4, and the symbol m is (a, b, c, d). Fig. 6
It is assumed that the column direction shown in FIG. Also,
The first position is K in the 1st row and 1st column in the general Latin square
It is ₁₁ . Further, it is assumed that “2” is stored in the conversion value storage unit 11 and addition is specified in the addition / subtraction specification storage unit 12 (that is, the conversion value F is “+2”).

In this state, the arithmetic unit 1 first sets "1" as the row position I in the row position setting storage unit 3 (step S1), and then sets the column position in the column position setting storage unit 4. "1" is set as J (step S2). This allows
The first position of the Latin square for storing sequence 10 which is set by the row position setting storage unit 3 and the column position setting storage unit 4 K _{1 1}
Is output to the setting symbol storage unit 7 and stored.

[0047] Then, the calculating portion 1 takes in the element E of the first position _{K 11} of Latin square for storing sequence 10 from the setting symbol storage unit 7 (1,1) (= a) , conversion value storing unit it The conversion value “+2” is read from the addition and subtraction designation storage unit 12 and supplied to the addition and subtraction unit 16. Here, assuming that the selection order of the symbol A = {a, b, c, d} of the element set in the Latin square is (0, 1, 2, 3), the selection order of the symbol a is 0, and addition / subtraction is performed. The section 16 selects the symbol “a” in the selection order “0”.
And the conversion value “2”.

The remainder operation unit 17 obtains the remainder result “2” by taking the remainder of 4 (by performing modulo 4 operation) on the addition result 2 (= 0 + 2) obtained by the addition / subtraction unit 16.
The operation unit 1 converts the symbol c in the selection order 2 as a symbol of an element based on the remainder result “2”, and converts the converted symbol “c”.
From the setting symbol storage unit 7 again to the row position setting storage unit 3.
And the position K ₁₁ set in the column position setting storage unit 4
It is set as the element E (1, 1) to the element E of the first position _{K 11} of Latin square for storing sequence 10 (1,1) (step S3). As a result, the Latin square memory array 10
The symbol of the element E (1,1) is converted to "c" as shown in FIG. 5B with an underline.

[0049] Then, the calculating portion 1 turn elements next position _{K 12} of Latin square for storing sequence 10 E (1,2) (=
b), and based on the value “+2” of the conversion information F read from the conversion value storage unit 11 and the addition / subtraction designation storage unit 12, the addition / subtraction unit 16 selects “1”, which is the selection order of the element “b”, and The addition operation with the absolute value “2” is performed,
The obtained addition result 3 (= 1 + 2) is further divided into the remainder operation unit 1
7, the modulo 4 operation is performed, and 3 (= 3 mod
To give a residue result of 4), converts a symbol d selection order "3", it sets it to Latin square for storing sequence 10 as the element at position _{K 12} E (1,2) (step S4, S5,
S3). As a result, the element E (1,2) of the Latin square storage array 10 is converted into the symbol "d" as shown by underlining in FIG. 5 (c).

[0050] Then, the calculating portion 1 turn elements next position _{K 13} of Latin square for storing sequence 10 E (1,3) (=
c), and based on the value “+2” of the conversion information F read from the conversion value storage unit 11 and the addition / subtraction designation storage unit 12, the addition / subtraction unit 16 selects “2”, which is the selection order of the element “c,” and the conversion value of the conversion value. The addition operation with the absolute value “2” is performed,
The obtained addition result 4 (= 2 + 2) is further divided into the remainder operation unit 1
7, the modulo 4 operation is performed, and 0 (= 4 mod
To give a residue results in 4), is converted into symbols a selection order "0", it sets the Latin square for storing sequence 10 as element E (1, 3) position _{K 13} (step S4, S5,
S3). As a result, the element E (1, 3) of the Latin square storage array 10 is converted to the symbol “a” as shown by underlining in FIG. 5D.

[0051] Then, the calculating portion 1 turn elements next position _{K 14} of Latin square for storing sequence 10 E (1,4) (=
d), and based on the value “+2” of the conversion information F read from the conversion value storage unit 11 and the addition / subtraction designation storage unit 12,
The addition / subtraction unit 16 performs an addition operation on the selection order “3” of the element “d” and the absolute value of the converted value “2”. The obtained addition result 5 (= 3 + 2) is further modulo-modulated by the remainder operation unit 17. to perform the fourth computing, 1 (= 5 mod 4) to obtain the remainder result of the element E of the position _{K 14} symbols b selection order "1"
(1, 4) is set in the Latin square storage array 10 (steps S4, S5, S3). As a result, the element E (1, 4) of the Latin square storage array 10 is converted into the symbol “b” as shown by underlining in FIG.

At this stage, J = 4, and becomes equal to the value of n. Therefore, the arithmetic unit 1 determines at step S4 that the value of the row position I set in the row position setting storage unit 3 is n
It is determined whether it is smaller than (Step S6). At this point, since I = 1 and n = 4, since I <n,
After adding “1” to the value of the row position I and setting “2” in the row position setting storage unit 3 (step S7), the process proceeds to step S2, where the column set in the column position setting storage unit 4 is set. Position J
Is set to “1”.

Thereafter, the same operation as above is repeated, and the element E (2,1) of the Latin square storage array 10 is
As shown in (f) with an underline, the symbol "d"
In addition, the element E (4,4) is added to the symbol “d” as shown by underlining in FIG.
Is converted to the symbol "c" as shown by underlining in FIG. 5 (h). At this point, the symbols of all the elements are converted to J = 4 and I = 4, so that the Latin square creation processing ends via steps S4 and S6 (step S8). In this embodiment, the order of selecting the resulting elements is (c, d, a,
b).

As described above, according to the present embodiment, each element of the existing Latin square is converted into an element by the conversion value F stored in the conversion value storage unit 11, thereby storing the Latin square. The pattern is intact, but the effect is the same as changing the selection order of the memorized element array, making it possible to convert existing Latin squares and Latin squares of the same order reliably and easily Can be. By the element conversion, the original Latin square can be transformed into n-1 types, and the utility value is also increased by n-1 times. This makes it difficult for a third party to guess the newly created Latin square.

The present invention is not limited to the above-described embodiment. For example, the above-described conversion may be repeated a predetermined number of times to create a new Latin square R. In addition, the present inventor has disclosed in
A new Latin square can be created by combining with the Latin square creating method proposed in Japanese Patent No. 5544.
In the Latin square creation method proposed by the inventor,
When the degree n and the symbol m of the Latin square to be created are set, and the symbols are sequentially selected and determined as array elements at each position of the Latin square R, the selection is determined starting from the last position of the row and column, and starting with the row or column. Along with the last position of the row or column, and select symbols in the order of selection so that each position does not have the same symbol as the already determined array element at the same position of the previous row and column. If there is no symbol that can be selected and determined at that position, the symbol of the array element that has already been determined at the position before that position is replaced with a selectable symbol that is lower in order than the symbol. This is a way to create a Latin square by continuing the selection decision.

Alternatively, the present inventor has previously filed Japanese Patent Application
A new Latin square can be obtained by combining with a Latin square created by the Latin square creating method proposed in No. 3105. The proposed Latin square creation method uses a Latin square of degree n set as an array element at the position of n rows and n columns so that n different symbols are different at each position of the same row and the same column. In the creating method, the order n, the selection order of the symbol m, the position where the symbol m is first arranged in the n rows and n columns, and the symbol m are assigned to the n rows and n columns of the row. A first step of setting the order of arrangement along the direction or the column direction, a second step of setting a desired existing n-th Latin square in the storage array, and a step of setting the existing n-th Latin square. Setting a symbol in the next selection order of the symbol at the first position set in the first step, and if there is no symbol in the next selection order to be set, returns the position to the previous position, Set next selection symbol for position symbol And a third step that,
The symbol set in the previous step is compared with the symbol in the same row and the previous position in the same column as the set position of the symbol, and if there is the same symbol, the process of the third step is executed again. If the same symbol does not exist, the fourth step of storing the symbol set in the previous step in the storage array, and the position of the symbol stored in the fourth step is determined by the Latin square to be created. If the position is the last position, all the processes are terminated. If not the last position, the designated position is advanced to the next position, and the first symbol in the selection order is set at that position. And a fifth step for executing the processing of the step.

The Latin square created by the Latin square creation method proposed by the inventor of the present invention is used as the existing Latin square R 'in the above embodiment, and a new square created by the above embodiment is used. The Latin square is defined as an intermediate Latin square R ", and the intermediate Latin square R" is defined as an existing Latin square, and a new Latin square is created according to the above-described embodiment, or a Latin square which is proposed earlier by the present inventor. The Latin square created by the creation method may be created. That is, the Latin square creating method proposed by the present inventor and the Latin square creating method of the above-described embodiment are combined and repeated one or more times to create a new Latin square R. Is also good.

[0058] Also, of course be able to create each array element E _IJ of Latin square in the row direction as shown in FIG. 6 (b), also in the same manner the following number of Latin square other than fourth order Can be created. Also,
The symbol m to be set is not particularly limited.
As shown in FIG. 7 (a) and FIG. 7 (a), in addition to the numerical values starting from 0 as (0, 1, 2, 3), for example, as shown in FIG. ), Or alphabets in the order of (a, b, c, d) as shown in FIG. 7C. Further, the present invention can be applied to words in a specific order and other character strings in addition to numerical values and alphabets.

Similarly, the conversion value storage unit 11 is not limited to the addition / subtraction designation storage unit 12 and the conversion value storage unit 11 for integer values, and may be configured to add a positive integer or a negative integer. The value is not limited to a number smaller than n and may be a number equal to or greater than n, and it is possible to take the remainder of n before conversion.

When the symbol of the element of the Latin square of the n-th order to be converted is 0 to n-1, the conversion value can be directly applied to the element. 5, the selection order of the element symbols is set from 0 to n−1, and a conversion value is applied to the selection order to set the converted selection order symbol, as described with reference to FIG. By doing so, a new Latin square can be created.

[0061]

As described above, according to the first and fourth aspects of the present invention, an integer conversion value is added or subtracted to or from the symbol m selection order or the symbol m itself, and the addition or subtraction result is represented by n. Is converted into a symbol of the order of selection as a symbol m at a set position and stored as a symbol m at the set position for all the symbols m of the existing nth-order Latin square. Because an nth-order Latin square converted based on the converted values is newly created in the array, a Latin square of the same order as the existing Latin square is assured, and
It can be easily created.

According to the second and fifth aspects of the present invention, the generation of the nth-order Latin square converted based on the conversion values is repeated a plurality of times, so that at most n-1 types of deformations can be performed. The value is also n-1 times, which makes it more difficult for a newly created Latin square to guess by a third party.

Further, according to the third and sixth aspects of the present invention, after a Latin square is newly created by converting based on the conversion value, a Latin square is created by another Latin square creating method. , The changes in the Latin square elements are irregular, the effects of the element changes are also magnified, and it is difficult for a third party who does not know these creation information to infer a new Latin square from the existing Latin square, A person who knows the creation information can easily and accurately create a new Latin square.

[Brief description of the drawings]

FIG. 1 is a block diagram of an embodiment of a creation device of the present invention.

FIG. 2 is a diagram showing a configuration of a Latin square created according to the present invention.

FIG. 3 is a flowchart illustrating an embodiment of the method of the present invention.

FIG. 4 is a specific explanatory view of an example of a procedure for creating a Latin square by the creation method of the present invention.

FIG. 5 is a specific explanatory diagram of another example of a procedure for creating a Latin square according to the creation method of the present invention.

FIG. 6 is an explanatory diagram of a creation direction of a Latin square created according to the present invention.

FIG. 7 is an explanatory diagram of each example of a Latin square.

FIG. 8 is an explanatory diagram of a basic configuration of a Latin square.

[Explanation of symbols]

Reference Signs List 1 arithmetic unit 2 Latin square creating unit 3 row position setting storage unit 4 column position setting storage unit 5 row position comparison storage unit 6 column position comparison storage unit 7 setting symbol storage unit 8 comparison symbol storage unit 9 symbol Comparison unit 10 Latin square storage array 10 _IJ array element (storage element) 11 Conversion value storage unit 12 Addition / subtraction designation storage unit 13 Order storage unit 14 Element symbol storage unit 15 Selection order storage unit 16 Addition / subtraction unit 17 Remainder operation unit R Latin square

Claims (6)

[Claims] 1. A method for creating a Latin square of degree n set as an array element at an n-row and n-column position so that n different symbols m are different at the same row and the same column position. In the method, the order n, the selection order of the symbols m, the position where the symbols m of the n rows and n columns are arranged first, and the symbol m is arranged in the row direction or column of the n rows and n columns The order of arrangement along the direction is set, and the desired existing nth-order Latin square is set in the storage array, and further added to the selection order of the n symbols m of the nth-order Latin square or the symbol itself. Or a first step of preparing an integer conversion value to be subtracted, and taking in the symbol m at the set position of the existing n-th Latin square set in the storage array, and reading the symbol m
Is added or subtracted to the selection order or the symbol m itself, and the result of the addition or subtraction is referred to as n.
A second step of converting the value obtained by taking the remainder into a symbol in the order of selection as the symbol m at the set position, and the position where the symbol m is converted in the second step is the n Third to determine whether or not it is the last position in row n column
And when the third step determines that the position is not the final position, the position for converting the symbol is set to the next position according to the symbol arrangement direction set in the first step. And the fourth step of terminating the process when it is determined that the symbol is the final position. How to make. 2. The method according to claim 1, wherein the fourth step is a step in which the conversion of all the symbols of the n-th Latin square in the second step is repeated one or two or more times in advance, and the final position is determined as the final position. 2. The method according to claim 1, wherein the processing is terminated after determining the position. 3. A symbol as an array element at each position of the n-th Latin square in the n-th Latin square in the storage array at the time of determining the last position in the fourth step. When making a selection decision in order, the selection decision is performed in order from the last position of the row and column to the last position of the row or column along the row or column, and the same row and the front of the same column for each position. The symbols are selected in the order of selection so that they do not have the same symbol as the already determined array element at the position, and if there is no symbol that can be selected and determined at that position, the symbol is already determined at a position before that position. 5. The method according to claim 1, further comprising a fifth step of generating a Latin square by continuing the selection decision by replacing the symbol of the array element with a selectable symbol having a lower order than the symbol. or Is the Latin square creation method described in 2. 4. A storage device comprising n ² storage elements in a total of n rows and n columns, and each storage element stores one symbol m arbitrarily selected from n different symbols. An array for storing Latin squares, a designating means for designating a storage element at a set position among the n ² storage elements constituting the array for Latin square storage, A conversion value storage unit that stores a conversion value for changing the value itself of the symbol of the element, an addition / subtraction designation unit that specifies addition or subtraction of the conversion value, and a selection order of the symbols or the symbol m itself, A remainder calculating means for adding or subtracting the converted value and taking the remainder of the addition or subtraction result with the n, an order n of a Latin square to be created, a selection order of the symbol m, and the Latin Before the square memory array The position where the symbols m are arranged first and the order in which the symbols m are arranged along the row direction or the column direction of the Latin square storage array are set in advance, and the Latin square is controlled by controlling the designating means. The symbols stored in the existing n-th Latin square set in the storage array are sequentially taken in the set selection order and in the selection direction, and the converted values in the order of the values of the taken symbols are stored in the converted value storage. A conversion operation of reading from the unit and calculating the value of the obtained remainder result to the symbol of the order of selection as the symbol m at the set position, the symbol installation position is calculated by the remainder calculation means. an arithmetic unit that repeats until a final position of n rows and n columns is reached, and all symbols of the existing Latin squares set in the Latin square storage array are replaced with the remainder result obtained by the remainder calculating means. The value A Latin square creating device, wherein a new Latin square is created by performing conversion. 5. The processing unit according to claim 1, wherein the final position when the conversion of all the symbols of the n-th Latin square is repeated one or more predetermined times is determined as the final position. 5. The apparatus according to claim 4, wherein the processing is terminated. 6. The n-th latin square in the latin-square storage array when the arithmetic unit is determined to be the final position, further includes a symbol as an array element at each position of the n-th latin square. When selecting and determining in order, the selection is determined starting from the last position of a row and a column by controlling the specifying means, and sequentially performed up to the last position of a row or a column along a row or a column. The symbols are selected in the order of selection so that they do not have the same symbol as the already determined array element at the same position before the same row and column, and if there is no symbol that can be selected and determined at that position, that position The Latin square is created by replacing the symbol of an array element already determined at an earlier position with a selectable symbol whose order is lower than the symbol and continuing the selection decision. 4 or 5. A Latin square creation device according to 5.