A device for multiplying two bit sequences has a controller that selects and activates exactly one multiplier unit from a plurality of parallel multiplier units, according to a random signal. A partial multiplier unit shared by all the multiplier units receives and multiplies operands formed by the respectively activated multiplier unit. Each multiplier unit implements a different multiplication method with a respective selector unit that selects segments of the bit sequences to be multiplied, in accordance with a selection plan adapted to the respective multiplication method, to form operands from one or more segments and outputs the operands. The respective accumulation unit receives step by step partial products from the partial multiplier unit, accumulates the partial products in accordance with an accumulation plan adapted to the implemented multiplication method and matching the selection plan, and outputs the calculated product of after accumulation has been completed.

A system for securely computing an elliptic curve scalar multiplication in an unsecured environment, including: a secure processor including secure memory, the secure processor configured to: split a secure scalar K into m.sub.2 random values k.sub.i, where i is an integer index; randomly select m.sub.1−m.sub.2 values k.sub.i for the indices m.sub.2<i≦m.sub.1; select m.sub.1 mask values δ.sub.i; compute m.sub.1 residues c.sub.i based upon random residues a.sub.i, δ.sub.π(i).sup.−1, and k.sub.π(i), wherein π(i) is a random permutation; compute m.sub.1 elliptic curve points G.sub.i based upon random residues a.sub.i and an elliptic point to be multiplied; receive m.sub.1 elliptic curve points; and compute the elliptic curve scalar multiplication by combining a portion of the received elliptic curve points and removing the mask values δ.sub.i from the portion of the received elliptic curve points; a memory device; and a processor in communication with the memory device, the processor being configured to: receive m.sub.1 residues c.sub.i and elliptic curve points G.sub.i; compute m.sub.1 elliptic curve points P.sub.i based upon the m.sub.1 residues c.sub.i and elliptic curve points G.sub.i; send the m.sub.1 elliptic curve points P.sub.i to the secure processor.

A cryptographic data processing method, implemented in an electronic device including a processor, the method including steps of providing a point of an elliptic curve in a Galois field, and a whole number, and of calculating a scalar product of the point by the number, the coordinates of the point and the number having a size greater than the size of words that may be processed directly by the processor, the scalar multiplication of the point by the number including steps of: storing scalar multiples of the point multiplied-by the number 2 raised to a power belonging to a series of whole numbers, setting a resulting point for each non-zero bit of the first number, adding the resulting point and one of the stored multiple points, and providing at the output of the processor the resulting point as result of the scalar product.

A device for multiplying two bit sequences has a controller that selects and activates exactly one multiplier unit from a plurality of parallel multiplier units, according to a random signal. A partial multiplier unit shared by all the multiplier units receives and multiplies operands formed by the respectively activated multiplier unit. Each multiplier unit implements a different multiplication method with a respective selector unit that selects segments of the bit sequences to be multiplied, in accordance with a selection plan adapted to the respective multiplication method, to form operands from one or more segments and outputs the operands. The respective accumulation unit receives step by step partial products from the partial multiplier unit, accumulates the partial products in accordance with an accumulation plan adapted to the implemented multiplication method and matching the selection plan, and outputs the calculated product of after accumulation has been completed.