Renesas Electronics Corporation

Hitachi, Ltd.

Camille Vuillaume

Katsuyuki Okeya

Masayuki Yoshino

Erik Dahmen

In power residue calculation in the primality determination, in addition to the conventional randomization of an exponent, a modulus is also randomized. A random number generated by a random number generator is set to a randomizing number, and is input to a modulus generator and an exponent generator. The modulus generator and the exponent generator randomize a prime number candidate P using the randomizing number to generate a randomized modulus Rand exponent R. Using the randomized modulus Rand exponent R, the power residue calculation for primality determination is executed, and based on the result, the primality of the prime number candidate P is determined. The power consumption during the primality determination of a semiconductor device becomes noncorrelated with a value of a prime number candidate to be determined, and the leakage of a prime number due to side channel attacks can be prevented.

Semiconductor device and IC card

A modular multiplication processing apparatus is provided that can process modular multiplication of data exceeding a bit length which a coprocessor can readily process, by using the coprocessor based upon Montgomery multiplication In the modular multiplication processing apparatus, data to be subjected to modular multiplication is decomposed, and the decomposed data elements are transformed into a form suitable for Montgomery multiplication, respectively. Further, after respective data elements are transformed to have sizes that can be inputted into a coprocessor, Montgomery multiplication is repeatedly performed in the coprocessor. A remainder of Montgomery multiplication of an original bit length is restored from the obtained remainder.

Modular multiplication processing apparatus

A technique for efficient encryption for use with devices such as smartcards restricted in memory resource, including a calculation unit for reconstructing a large number of small primes, a sieving unit for checking the divisibility of an integer by small primes, a recoding unit for changing the representation of an integer, and a primality testing unit. The sieving unit eliminates 'bad' candidates by checking their divisibility by small primes reconstructed by the calculation unit. The primality of the remaining candidates is tested using the primality testing unit. The primality testing unit uses the recoding unit to change the representation of prime candidates. The primality testing unit performs a primality test using the representation after change.

Data processing system and data processing method

A system and method for authentication and digital signatures on memory-only supports, comprising a read-once memory unit storing secret arrays, whose contents are destroyed upon reading, a standard memory unit storing encrypted arrays, tree data authenticating the encrypted arrays to one single public key, and a certificate of the public key issued by a certificate authority. The memory support sends its public key and certificate to a verifier, receives a challenge which is signed by elements from secret arrays in the read-once memory. The verifier system checks the authenticity of the data revealed from the read-once memory by encrypting it and comparing the result to one of the encrypted arrays, and verifies that the encrypted array authenticates to the public key using tree data. Finally, the verifier checks the authenticity of the public key using the certificate.

System and method for digital signatures and authentication

A modular multiplication processing apparatus is provided that can process modular multiplication of data exceeding a bit length which a coprocessor can process, by using the coprocessor based upon Montgomery multiplication In the modular multiplication processing apparatus, data to be subjected to modular multiplication is decomposed, and the decomposed data elements are transformed into a form suitable for Montgomery multiplication, respectively. Further, after respective data elements are transformed to have sizes that can be inputted into a coprocessor, Montgomery multiplication is repeatedly performed in the coprocessor. A remainder of Montgomery multiplication of an original bit length is restored from the obtained remainder.

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Kawasaki, Japan

Camille Vuillaume