Secure-Ic Sas

Cédric Murdica

Sylvain Guilley

There is provided a device for protecting the execution of a cryptographic operation from attacks, the cryptographic operation being implemented by a cryptographic algorithm, the cryptographic operation comprising at least one modular operation between a main base (m) representing a data block and at least one scalar (d) in at least one finite starting group. The device is configured to determine at least one intermediary group (E') different from the at least one starting group (E), the number of intermediary groups being equal to the number of starting groups E. The device is further configured to determine at least one final group (E&#x2033;) from the at least one starting group E and the at least one intermediary group E&#x2032;. The base m being mapped to an auxiliary element (x) in the at least one intermediary group and to an auxiliary base (m&#x2033;) in the at least one final group E&#x2033;. The device performs a first elementary operation in each final group (E&#x2033;i), the first elementary operation consisting in executing the modular operation between the auxiliary base (m&#x2033;) and an auxiliary scalar (d) in each final group E&#x2033;, which provides at least one result, the auxiliary scalar (d) being determined from the auxiliary element (x) and from the main scalar (d). The device further performs a second elementary operation in each starting group E, the second elementary operation consisting in executing the modular operation between an additional auxiliary base and an additional auxiliary scalar d&#x2032;in each starting group, at least one of the additional auxiliary base and of the additional scalar being derived from the result of the first elementary operation.

Device and method for protecting execution of a cryptographic operation

There is provided a device or a method for executing an operation of a cryptographic scheme, the operation being applied to a given state of a data block of original data, the operation being defined in a basis ring corresponding to the quotient of a starting ring by a basis ideal generated by at least one element of the starting ring. The operation is executed from a state derived from the current state of the data block, in at least one reference ring, which provides a reference value for each reference ring, each reference ring being the quotient of the starting ring by a reference ideal. The operation is executed from the state derived from the current state of the data block in at least one extended ring corresponding to one or more reference rings, which provides at least one extension value for each extended ring, each extended ring corresponding to one or more reference ring being the quotient of the starting ring by the product of the basis ideal and of the reference ideals of the one or more corresponding reference rings.

Method and system for protecting a cryptographic operation

The subject of the invention is a countermeasure method for an electronic component implementing a public-key cryptography algorithm on an elliptic curve E defined over a fieldand comprising an iterative scalar multiplication operation making it possible to obtain a point [k]P on the basis of a point P of the curve E and of an integer k that must remain secret, the electrical consumption of the electronic component being dependent on the value taken by at least one so-called critical point used during said operation to iteratively determine the point [k]P. The method comprises: a step () of providing at least one power of a predefined non-zero constant element c ofdifferent from one; a step () of initializing the coordinates of the at least one critical point to a predefined value; a step () implementing the scalar multiplication operation, the coordinates associated with at least one critical point being modified at each iteration by multiplying at least one of the coordinates of this point by the at least one power of the element c obtained in the providing step ().

Countermeasure method for an electronic component implementing an elliptic curve cryptography algorithm

There is provided a modular multiplication device for performing a multiplication of a first multiplicand and a second multiplicand modulo a given modulus, each of the multiplicand comprising a given number of digits, each digit having a given word size. The modular multiplication device comprises:

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Rennes, France

Cédric Murdica