Tamper-proof elliptic encryption with private key

An encryption device for performing modular exponentiation encryption processing with a private key, comprising:

• a randomizing unit for setting, into an initial value V0, an integer r generated in accordance with a random value;
• an operation unit for performing a first operation of modular exponentiation V1=V0ad (mod n)=r×ad (mod n) for the initial value V0 and a particular input value a in accordance with a bit sequence of a particular value d for said modular exponentiation encryption processing;
• a de-randomizing unit for performing a second operation of modular multiplication V=V1×r−1 (mod n) on the value V1 determined by said first operation and an inverse element r−1 (mod n) of r (mod n);
• and
• a unit for providing, as an output, the value V determined by said de-randomizing unit.

A program recorded on a recording medium for use in an information processing device and for performing elliptic encryption processing with a private key, said program being operable to effect the steps of:

• generating an elliptic point R on an elliptic curve at random that is generated in accordance with a random value;
• setting the elliptic point R into an initial elliptic point V0;
• performing a first operation of summing the initial elliptic point V0 and a scalar multiple of a particular input elliptic point A on the elliptic curve, V1=V0+dA, in accordance with a bit sequence of a particular scalar value d for said elliptic encryption processing;
• performing a second operation of subtracting the initial elliptic point V0 from the sum V1 determined by said first operation, V=V1−V0;
• and
• providing, as an output, the elliptic point V determined by said de-randomization unit.

A program recorded on a recording medium for use in an information processing device and for performing modular exponentiation encryption processing with a private key,

• setting, into an initial value V0, an integer r generated in accordance with a random value;
• performing a first operation of modular exponentiation V1=V0ad (mod n)=r×ad (mod n) for the initial value V0 and a particular input value a in accordance with a bit sequence of a particular value d for said modular exponentiation encryption processing;
• performing a second operation of modular multiplication V=V1×r−1 (mod n) on the value V1 determined by said first operation and an inverse element r−1 (mod n) of r (mod n);
• and
• providing, as an output, the value V determined by said de-randomizing unit.

A method for use in an information processing device and for performing elliptic encryption processing with a private key, said method comprising the steps of:

• generating an elliptic point R on an elliptic curve at random that is generated in accordance with a random value;
• setting the elliptic point R into an initial elliptic point V0;
• performing a first operation of summing the initial elliptic point V0 and a scalar multiple of a particular input elliptic point A on the elliptic curve, V1=V0+dA, in accordance with a bit sequence of a particular scalar value d for said elliptic encryption processing;
• performing a second operation of subtracting the initial elliptic point V0 from the sum V1 determined by said first operation, V=V1−V0;
• and
• providing, as an output, the elliptic point V determined by said de-randomization unit.

A method for use in an information processing device and for performing modular exponentiation encryption processing with a private key, said method comprising the steps of:

• setting, into an initial value V0, an integer r generated in accordance with a random value;
• performing a first operation of modular exponentiation V1=V0ad (mod n)=r×ad (mod n) for the initial value V0 and a particular input value a in accordance with a bit sequence of a particular value d for said modular exponentiation encryption processing;
• performing a second operation of modular multiplication V=V1×r−1 (mod n) on the value V1 determined by said first operation and an inverse element r−1 (mod n) of r (mod n);
• and
• providing, as an output, the value V determined by said de-randomizing unit.