1. A cryptographic processing device comprising: a memory that stores therein a first vector; a processor that generates a first encrypted polynomial by encrypting a first polynomial that corresponds to a first binary vector obtained by performing a binary transformation on elements of the first vector; and a transmitter that transmits cryptographic information that represents the first encrypted polynomial to a cryptographic operation device that multiplies the first encrypted polynomial by a second encrypted polynomial that is generated by encrypting a second polynomial that corresponds to a second binary vector obtained by performing a binary transformation on elements of a second vector, so as to generate a third encrypted polynomial, wherein a result of an operation of the first vector and the second vector is obtained when assigning 2 to a variable in a prescribed portion of a third polynomial obtained by decrypting the third encrypted polynomial.