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Fujitsu Corporation

Hitachi, Ltd.

Wired Connections LLC

Wired Communications LLC

Tsuyoshi Takagi

Tetsuya Izu

Bodo Möller

Katsuyuki Okeya

An elliptic curve multiplication method comprises three stages. In the first stage, randomly selected point representations are stored in variables. In the second stage, a right-to-left loop is executed that modifies the variable values in dependency of a multiplier. In the last stage, the result is calculated from the modified variable values.

Method for elliptic curve point multiplication

A scalar multiplication can be performed on an elliptic curve cryptosystem at a high speed. P is set as an initial value of Q[0], and 2&#xd7;P is set as an initial value of Q[1]. An elliptic curve doubling ECDBL of Q[d[i]] is performed, and an arithmetic result is stored in Q[2]. An elliptic curve addition ECADD of Q[0] and Q[1] is performed, and an arithmetic result is stored in Q[1]. Q[2&#x2212;d[i]] is stored in Q[0]. Q[1+d[i]] is stored in Q[1]. The elliptic curve addition ECADD and the elliptic curve doubling ECDBL are concurrently performed in the respective processors.

Elliptic curve cryptosystem apparatus, storage medium storing elliptic curve cryptosystem program, and elliptic curve cryptosystem arithmetic method

The method comprises three stages. In the first stage, randomly selected point representations are stored in variables. In the second stage, a right-to-left loop is executed that modifies the variable values in dependency of a multiplier. In the last stage, the result is calculated from the modified variable values.

A decryption method of decrypting a plaintext m from a secret exponent d, a public key n, and a ciphertext c includes steps of converting the ciphertext c into a randomized ciphertext t, a step of converting the randomized ciphertext t into a randomized plaintext u, and steps of converting the randomized plaintext u into the plaintext m.

Computation method for modular exponentiation operation in decryption or signature generation

A scalar multiplication can be performed on an elliptic curve cryptosystem at a high speed. P is set as an initial value of Q[], and 2&#xd7;P is set as an initial value of Q[. An elliptic curve doubling ECDBL of Q[d[i]] is performed, and an arithmetic result is stored in Q[. An elliptic curve addition ECADD of Q[and Q[is performed, and an arithmetic result is stored in Q[. Q[d[i]] is stored in Q[. Q[+d[i]] is stored in Q[. The elliptic curve addition ECADD and the elliptic curve doubling ECDBL are concurrently performed in the respective processors.

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Hofheim-Wallau, Germany

Tsuyoshi Takagi