Converter, encryption/decryption system, multi-stage converter, converting method, multi-stage converting method, program, and information recording medium

A converting method performed by a computer executing a program stored in a non-transitory information recording medium, said converting method using:

• conversion functions for a domain A, F1:A×A→A, F2:A×A→A, . . . , Fn:A×A→A;
• a binary exclusive OR operator, XOR:A×A→A;
• and
• a predetermined parameter, aεA, and
• said converting method comprising:
• a generating step which accepts generative inputs, x1εA, x2εA, . . . , xnεA, and generates generative outputs, y1εA, y2εA, . . . , ynεA, using recurrence formulas,
• y1=F1(x1,a), and
• yi+1=Fi+1(xi+1,yi) (for 1≦i≦n−1);
• a key accepting step which accepts key inputs, k1εA, k2εA, . . . , knεA, and gives the accepted key inputs as generative inputs to said generating step;
• a repetition controlling step which gives the generative outputs from said generating step as generative inputs to said generating step, for an “m” (m≧0) number of times, and sets the last of the generative outputs as a random number sequence, r1εA, r2εA, . . . , rnεA;
• a data accepting step for accepting data inputs, d1εA, d2εA, . . . , dnεA;
• and
• a converting step for converting the data inputs into data outputs, e1εA, e2εA, . . . , enεA, using a formula,
• ei=diXORri, and
• outputs the data outputs,
• wherein each of the conversion functions, F1, F2, . . . , Fn, is a function, ma(.,.) and
• the function, ma(.,.), is defined by a positive integer M, a positive integer s, a rounding up function ceil(.), and a rounding down function floor(.), as:
• ma(x,b)=ceil(xMs/b) (for 1≦x≦b), and
• ma(x,b)=floor(Ms(x−b)/(Ms−b))+1 (for b≦x≦Ms).

A converter realized by a computer executing a program stored in a non-transitory information recording medium, said converter using:

• conversion functions for a domain A, F1:A×A→A, F2:A×A→A, . . . , Fn:A×A→A;
• a binary exclusive OR operator, XOR:A×A→A;
• and
• a predetermined parameter, aεA, and
• said converter comprising:
• a generating unit accepting generative inputs, x1εA, x2εA, . . . , xnεA, and generating generative outputs, y1εA, y2εA, . . . , ynεA, using recurrence formulas
• y1=F1(x1,a), and
• yi+1=Fi+1(xi+1,xi) (for 1≦i≦n−1);
• a key accepting unit accepting key inputs, k1εA, k2εA, . . . , knεA, and giving the accepted key inputs as generative inputs to said generating unit;
• a repetition controller giving the generative outputs from said generating unit as generative inputs to said generating unit, for an “m” (m≧0) number of times, and setting the last generative outputs as a random number sequence, r1εA, r2εA, . . . , rnεA;
• a data accepting unit accepting data inputs, d1εA, d2εA, . . . , dnεA;
• and
• a converting unit converting the data inputs into data outputs, e1εA, e2εA, . . . , enεA, using a formula
• ei=diXORri, and
• outputting data outputs,
• wherein each of the conversion functions, F1, F2, . . . , Fn, is a function, ma(.,.), and
• the function, ma(.,.), is defined by a positive integer M, a positive integer s, a rounding up function ceil(.), and a rounding down function floor(.), as:
• ma(x,b)=ceil(xMs/b) (for 1≦x≦b), and
• ma(x,b)=floor(Ms(x−b)/(Ms−b))+1 (for b≦x≦Ms).

A converting method performed by a computer executing a program stored in a non-transitory information recording medium, said converting method using:

• conversion functions for a domain A, F1:A×A→A, F2:A×A→A, . . . , Fn:A×A→A;
• a binary exclusive OR operator, XOR:A×A→A;
• and
• a predetermined parameter, aεA, and
• said converting method comprising:
• a generating step which accepts generative inputs, x1εA, x2εA, . . . , xnεA, and generates generative outputs, y1εA, y2εA, . . . , ynεA, using recurrence formulas,
• y1=F1(x1,a), and
• yi+1=Fi+1(xi+1,xi) (for 1≦i≦n−1);
• a key accepting step which accepts key inputs, k1εA, k2εA, . . . , knεA, and gives the accepted key inputs as generative inputs to said generating step;
• a repetition controlling step which gives the generative outputs from said generating step as generative inputs to said generating step, for an “m” (m≧0) number of times, and sets the last of the generative outputs as a random number sequence, r1εA, r2εA, . . . , rnεA;
• a data accepting step for accepting data inputs, d1εA, d2εA, . . . , dnεA;
• and
• a converting step for converting the data inputs into data outputs, e1εA, e2εA, . . . , enεA, using a formula,
• ei=diXORri, and
• outputs the data outputs,
• wherein each of the conversion functions, F1, F2, . . . , Fn, is a function, ma(.,.) and
• the function, ma(.,.), is defined by a positive integer M, a positive integer s, a rounding up function ceil(.), and a rounding down function floor(.), as:
• ma(x,b)=ceil(xMs/b) (for 1≦x≦b), and
• ma(x,b)=floor(Ms(x−b)/(Ms−b))+1 (for b≦x≦Ms).

A converter realized by a computer executing a program stored in a non-transitory information recording medium, said converter using:

• conversion functions for a domain A, F1:A×A→A, F2:A×A→A, . . . , Fn:A×A→A;
• a binary exclusive OR operator, XOR:A×A→A;
• and
• a predetermined parameter, aεA, and
• said converter comprising:
• a generating unit accepting generative inputs, x1εA, x2εA, . . . , xnεA, and generating generative outputs, y1εA, y2εA, . . . , ynεA, using recurrence formulas
• y1=F1(x1,a), and
• yi+1=Fi+1(xi+1,yi) (for 1≦i≦n−1);
• a key accepting unit accepting key inputs, k1εA, k2εA, . . . , knεA, and giving the accepted key inputs as generative inputs to said generating unit;
• a repetition controller giving the generative outputs from said generating unit as generative inputs to said generating unit, for an “m” (m≧0) number of times, and setting the last generative outputs as a random number sequence, r1εA, r2εA, . . . , rnεA;
• a data accepting unit accepting data inputs, d1εA, d2εA, . . . , dnεA;
• and
• a converting unit converting the data inputs into data outputs, e1εA, e2εA, . . . , enεA, using a formula
• ei=diXORri, and
• outputting data outputs,
• wherein each of the conversion functions, F1, F2, . . . , Fn, is a function, ma−1(.,.), and
• the function, ma−1(.,.), is defined by a positive integer M, a positive integer s, a rounding up function ceil(.), and a rounding down function floor(.), as:
• ma−1(y,b)=x1 (for q<x1);
• and
• ma−1(y,b)=x2 (for x1≦q),
• where
• x1=floor(M−sby);
• x2=ceil((M−sb−1)y+Ms);
• and
• q=b(x2−Ms)/(b−Ms).

A converting method performed by a computer executing a program stored in a non-transitory information recording medium, said converting method using:

• conversion functions for a domain A, F1:A×A→A, F2:A×A→A, . . . , Fn:A×A→A;
• a binary exclusive OR operator, XOR:A×A→A;
• and
• a predetermined parameter, aεA, and
• said converting method comprising:
• a generating step which accepts generative inputs, x1εA, x2εA, . . . , xnεA, and generates generative outputs, y1εA, y2εA, . . . , ynεA, using recurrence formulas,
• y1=F1(x1,a), and
• yi+1=Fi+1(xi+1,yi) (for 1≦i≦n−1);
• a key accepting step which accepts key inputs, k1εA, k2εA, . . . , knεA, and gives the accepted key inputs as generative inputs to said generating step;
• a repetition controlling step which gives the generative outputs from said generating step as generative inputs to said generating step, for an “m” (m≧0) number of times, and sets the last of the generative outputs as a random number sequence, r1εA, r2εA, . . . , rnεA;
• a data accepting step which accepts data inputs, d1εA, d2εA, . . . , dnεA;
• and
• a converting step which converts the data inputs into data outputs, eiεA, e2εA, . . . , enεA, using a formula,
• ei=diXORri, and
• outputs the data outputs,
• wherein each of the conversion functions, F1, F2, . . . , Fn, is a function, ma−1(.,.), and
• the function, ma−1(.,.), is defined by a positive integer M, a positive integer s, a rounding up function ceil(.), and a rounding down function floor(.), as:
• ma−1(y,b)=x1 (for q<x1);
• and
• ma−1(y,b)=x2 (for x1≦q),
• where
• x1=floor(M−sby);
• x2=ceil((M−sb−1)y+Ms);
• and
• q=b(x2−Ms)/(b−Ms).

A converter realized by a computer executing a program stored in a non-transitory information recording medium, said converter using:

• conversion functions for a domain A, F1:A×A→A, F2:A×A→A, . . . , Fn:A×A→A;
• a binary exclusive OR operator, XOR:A×A→A;
• and
• a predetermined parameter, aεA, and
• said converter comprising:
• a generating unit accepting generative inputs, x1εA, x2εA, . . . , xnεA, and generating generative outputs, y1εA, y2εA, . . . , ynεA, using recurrence formulas
• y1=F1(x1,a), and
• yi+1=Fi+1(xi+1,yi) (for 1≦i≦n−1);
• a key accepting unit accepting key inputs, k1εA, k2εA, . . . , knεA, and giving the accepted key inputs as generative inputs to said generating unit;
• a repetition controller giving the generative outputs from said generating unit as generative inputs to said generating unit, for an “m” (m≧0) number of times, and setting the last generative outputs as a random number sequence, r1εA, r2εA, . . . , rnεA;
• a data accepting unit accepting data inputs, d1εA, d2εA, . . . , dnεA;
• and
• a converting unit converting the data inputs into data outputs, eiεA, e2εA, . . . , enεA, using a formula
• ei=diXORri, and
• outputting data outputs,
• wherein each of the conversion functions, F1, F2, . . . , Fn, is a function, ma−1(.,.), and
• the function, ma−1(.,.), is defined by a positive integer M, a positive integer s, a rounding up function ceil(.), and a rounding down function floor(.), as:
• ma−1(y,b)=x1 (for q<x1);
• and
• ma−1(y,b)=x2 (for x1≦q),
• where
• x1=floor(M−sby);
• x2=ceil((M−sb−1)y+Ms);
• and
• q=b(x2−Ms)/(b−Ms).

A converting method performed by a computer executing a program stored in a non-transitory information recording medium, said converting method using:

• conversion functions for a domain A, F1:A×A→A, F2:A×A→A, . . . , Fn:A×A→A,
• a binary exclusive OR operator, XOR:A×A→A;
• and
• a predetermined parameter, aεA, and
• said converting method comprising:
• a generating step which accepts generative inputs, x1εA, x2εA, . . . , xnεA, and generates generative outputs, y1εA, y2εA, . . . , ynεA, using recurrence formulas,
• y1=F1(x1,a), and
• yi+1=Fi+1(xi+1,xi) (for 1≦i≦n−1);
• a key accepting step which accepts key inputs, k1εA, k2εA, . . . , knεA, and gives the accepted key inputs as generative inputs to said generating step;
• a repetition controlling step which gives the generative outputs from said generating step as generative inputs to said generating step, for an “m” (m≧0) number of times, and sets the last of the generative outputs as a random number sequence, r1εA, r2εA, . . . , rnεA;
• a data accepting step which accepts data inputs, d1εA, d2εA, . . . , dnεA;
• and
• a converting step which converts the data inputs into data outputs, eiεA, e2εA, . . . , enεA, using a formula,
• ei=diXORri, and
• outputs the data outputs,
• wherein each of the conversion functions, F1, F2, . . . , Fn, is a function, ma−1(.,.), and
• the function, ma−1(.,.), is defined by a positive integer M, a positive integer s, a rounding up function ceil(.), and a rounding down function floor(.), as:
• ma−1(y,b)=x1 (for q<x1);
• and
• ma−1(y,b)=x2 (for x1≦q),
• where
• x1=floor(M−sby);
• x2=ceil((M−sb−1)y+Ms);
• and
• q=b(x2−Ms)/(b−Ms).