Cryptographic processing device and cryptographic processing method

A cryptographic processing method comprising:

• generating, by a cryptographic processing device, a first encrypted polynomial by encrypting a first polynomial that corresponds to a first vector obtained by adding a first random number generated by the cryptographic processing device to a zero vector as a component;
• transmitting, by the cryptographic processing device, to a terminal, first cryptographic information that represents the first encrypted polynomial;
• receiving, by the cryptographic processing device, from a calculation device, second cryptographic information that represents a fourth encrypted polynomial, and receiving, by the cryptographic processing device, from the calculation device, third cryptographic information that represents a second random number generated by the terminal, the fourth encrypted polynomial including a first operation result that is a result of an operation of a fifth vector and a sixth vector that is obtained by adding, to a second vector, a result of a multiplication of the first random number by the second random number as a component, the first operation result being obtained by calculating from a second encrypted polynomial and a third encrypted polynomial, wherein the second encrypted polynomial is obtained by adding a result of a multiplication of the first encrypted polynomial by the second random number to a second polynomial that corresponds to a third vector obtained by adding zero to the second vector as a component, and the third encrypted polynomial is obtained by encrypting a third polynomial that corresponds to the fifth vector obtained by adding zero to a fourth vector as a component;
• decrypting, by the cryptographic processing device, the second cryptographic information and the third cryptographic information;
• and generating, by the cryptographic processing device, a second operation result that is a result of an operation of the second vector and the fourth vector, on the basis of a result of decrypting the second cryptographic information and a result of decrypting the third cryptographic information, wherein the processor uses the result of the decrypting the second cryptographic information and a result of decrypting the third cryptographic information to prevent replay attacks.

A non-transitory computer-readable recording medium having stored therein a cryptographic processing program for causing a computer to execute a process, the process comprising:

• generating a first encrypted polynomial by encrypting a first polynomial that corresponds to a first vector obtained by adding a first random number generated by the computer to a zero vector as a component;
• transmitting, to a terminal, first cryptographic information that represents the first encrypted polynomial;
• receiving, from a calculation device, second cryptographic information that represents a fourth encrypted polynomial, and receiving, from the calculation device, third cryptographic information that represents a second random number generated by the terminal, the fourth encrypted polynomial including a first operation result that is a result of an operation of a fifth vector and a sixth vector that is obtained by adding, to a second vector, a result of a multiplication of the first random number by the second random number as a component, the first operation result being obtained by calculating from a second encrypted polynomial and a third encrypted polynomial, wherein the second encrypted polynomial is obtained by adding a result of a multiplication of the first encrypted polynomial by the second random number to a second polynomial that corresponds to a third vector obtained by adding zero to the second vector as a component, and the third encrypted polynomial is obtained by encrypting a third polynomial that corresponds to the fifth vector obtained by adding zero to a fourth vector as a component;
• decrypting the second cryptographic information and the third cryptographic information;
• and generating a second operation result that is a result of an operation of the second vector and the fourth vector, on the basis of a result of decrypting the second cryptographic information and a result of decrypting the third cryptographic information, wherein the processor uses the result of the decrypting the second cryptographic information and a result of decrypting the third cryptographic information to prevent replay attacks.