1. A pseudorandom number generating system, which outputs a cryptographically secure pseudorandom number sequence generated based on a sequence of numbers prepared ahead of time, said pseudorandom number generating system, comprising: a storage means, which is stored with predetermined number of bits (words) to which an initial value is preset; a pseudorandom number generating means, which generates a pseudorandom number sequence based on the sequence of numbers; and a secure pseudorandom number generating means, which generates a secure pseudorandom number sequence based on the pseudorandom number sequence, wherein the secure pseudorandom number generating means cuts out a word from the pseudorandom number sequence and sets the least significant bit of the word to 1, stores in the storage means the value resulting from multiplying value stored in the storage means by the cut out word in conformity with modulo 2 to the power of a word length, and outputs a part or all of a bit sequence resulting from repeated multiplication as the secure pseudorandom number sequence.