Pseudo-random number generating method and apparatus therefor

A pseudo-random-number generating method comprising the steps of:

• random-number generating step for generating respectively, using a plurality of pseudo-random-number generating means, a plurality of pseudo-random-numbers A.sub.k, which satisfies 0.ltoreq.A.sub.k <(P.sub.k -1), based an inputted plurality of integer (P.sub.1 -1)(P.sub.2 -1) . . . (P.sub.m -1), where m is a positive integer, k being a positive integer equal to or less than m, and each of P.sub.1, P.sub.2, . . . P.sub.m is a prime number equal to or more than 2;
• first calculating step for calculating an integer X which is represented by a.sub.1 (P.sub.1 P.sub.2. . . P.sub.m /P.sub.1)B.sub.1 +a.sub.2 (P.sub.1 P.sub.2. . . P.sub.m /P.sub.2)B.sub.2 +. . . +a.sub.m (P.sub.1 P.sub.2. . . P.sub.m /P.sub.m)B.sub.m (mod P.sub.1 P.sub.2. . . (P.sub.m), using remainder calculating means, adding means, and multiplying means, where D.sub.k is a plurality of integers expressed by equation D.sub.k =D.sub.k-1 /(P.sub.k -1) wherein D.sub.1 =A (k=1) and 2.ltoreq.k.ltoreq.m, wherein B.sub.k is a plurality of integers represented by D.sub.k ={D.sub.k mod (P.sub.k -1))+1 where k is a positive integer equal to or less than m, and wherein a.sub.K is a plurality of integers each of which satisfies congruence equation a.sub.k (P.sub.1 P.sub.2. . . P.sub.m /P.sub.k)=1(mod P.sub.k);
• and
• second calculating step for generating an integer by adding said integer X to an integer QP.sub.1 P.sub.2. . . P.sub.m using adding means wherein n Is a positive integer, and Q is an integer which satisfies conditions of 2.sup.n-1 .ltoreq.QP.sub.1 P.sub.2. . . P.sub.m and (Q+1) P.sub.1 P.sub.2. . . P.sub.m .ltoreq.2.sup.n.

A pseudo-random-number generating apparatus, comprising:

• random-number generating means for generating a pseudo-random number A, which satisfies 0.ltoreq.A<(P.sub.1 -1)(P.sub.2 -1) . . . (P.sub.m -1), based an inputted integer (P.sub.1 -1)(P.sub.2 -1) . . . (P.sub.m -1), where m is a positive integer and each of P.sub.1, P.sub.2, . . . P.sub.m is a prime number equal to or more than 2;
• first calculating means, which includes dividing means, remainder calculating means, adding means, and multiplying means, for use in calculating an integer X which is represented by a.sub.1 (P.sub.1 P.sub.2. . . P.sub.m /P.sub.1)B.sub.1 +a.sub.2 (P.sub.1 P.sub.2. . . P.sub.m /P.sub.2)B.sub.2 +. . . +a.sub.m (P.sub.1 P.sub.2. . . P.sub.m /P.sub.m)B.sub.m (mod P.sub.1 P.sub.2. . . P.sub.m), where D.sub.k is a plurality of integers expressed by equation D.sub.k =D.sub.k-1 /(P.sub.k -1) wherein D.sub.1 =A (k=1) and 2.ltoreq.k.ltoreq.m, wherein B.sub.k is a plurality of integers represented by D.sub.k ={D.sub.k mod (P.sub.k -1)}+1 where k is a positive integer equal to or less than m, and wherein a.sub.K is a plurality of integers each of which satisfies congruence equation a.sub.k (P.sub.1 P.sub.2. . . P.sub.m /P.sub.k)=1(mod P.sub.k);
• and
• second calculating means for generating an integer by adding said integer X to an integer QP.sub.1 P.sub.2. . . P.sub.m wherein n is a positive integer, and Q is an integer which satisfies conditions of 2.sup.n-1 .ltoreq.QP.sub.1 P.sub.2. . . P.sub.m and (Q+1) P.sub.1 P.sub.2. . . P.sub.m .ltoreq.2.sup.n.

A pseudo-random-number generating apparatus comprising:

• a plurality of random-number generating means for generating respectively a plurality of pseudo-random-numbers A.sub.k, which satisfies 0.ltoreq.A.sub.k <(P.sub.k -1), based an inputted plurality of integer (P.sub.1 -1)(P.sub.2 -1) . . . (P.sub.m -1), where m is a positive integer, k being a positive integer equal to or less than m, and each of P.sub.1, P.sub.2, . . . P.sub.m is a prime number equal to or more than 2;
• first calculating means which includes remainder calculating means, adding means, and multiplying means for use in calculating an integer X which is represented by a.sub.1 (P.sub.1 P.sub.2. . . P.sub.m /P.sub.1)B.sub.1 +a.sub.2 (P.sub.1 P.sub.2. . . P.sub.m /P.sub.2)B.sub.2 +. . . +a.sub.m (P.sub.1 P.sub.2. . . P.sub.m /P.sub.m)B.sub.m (mod P.sub.1 P.sub.2. . . P.sub.m), where D.sub.k is a plurality of integers expressed by equation D.sub.k =D.sub.k-1 /(P.sub.k -1) wherein D.sub.1 =A (k=1) and 2.ltoreq.k.ltoreq.m, wherein B.sub.k is a plurality of integers represented by D.sub.k ={D.sub.k mod (P.sub.k -1)}+1 where k is a positive integer equal to or less than m, and wherein a.sub.K is a plurality of integers each of which satisfies congruence equation a.sub.k (P.sub.1 P.sub.2. . . P.sub.m /P.sub.k)=1 (mod P.sub.k);
• and
• second calculating means for generating an integer by adding said integer X to an integer QP.sub.1 P.sub.2. . . P.sub.m wherein n is a positive integer, and Q is an integer which satisfies conditions of 2.sup.n-1 .ltoreq.QP.sub.1 P.sub.2. . . P.sub.m and (Q+1) P.sub.1 P.sub.2. . . P.sub.m .ltoreq.2.sup.n.