IRDETO B.V.

A method for performing an elliptic curve cryptographic process to generate output data based on input data, the elliptic curve cryptographic process based on an elliptic curve over a finite field, wherein the generation of the output data comprises generating, based on a predetermined point V of the elliptic curve and a positive R-bit integer k, a first point of the elliptic curve that is based, at least in part, on the point kV of the elliptic curve, wherein k=Σ r=0 R−1 2 r b r and, for each r=0, 1, . . . , R−1, b r is the bit value of k at bit position r of k, wherein the method comprises: storing, according to a partition of the R bit positions for k into T groups of bit positions P t (t=0, 1, . . . , T−1), a corresponding lookup table L t having, for each of the 2 |P t | possible options for assigning to the |P t | bit positions s∈P t a respective bit value x s , a corresponding point of the elliptic curve that is based, at least in part, on the point (Σ s∈P t 2 s x s )V of the elliptic curve; obtaining k; and determining the first point as Σ t=0 T−1 l t , where l t is the point of the elliptic curve that corresponds, in lookup table L t , to the option for assigning to the |P t | bit positions s∈P t the corresponding bit value b s .

A method for performing an elliptic curve cryptographic process to generate output data based on input data, the elliptic curve cryptographic process based on an elliptic curve over a finite field, wherein the generation of the output data comprises generating, based on a predetermined point V of the elliptic curve and a positive R-bit integer k, a first point of the elliptic curve that is based, at least in part, on the point kV of the elliptic curve, wherein k=Σ r=0 R−1 2 r b r and, for each r=0,1, . . . , R−1, b r is the bit value of k at bit position r of k, wherein the method comprises: storing, according to a partition of the R bit positions for k into T groups of bit positions P t (t=0, 1, . . . , T−1), a corresponding lookup table L t having, for each of the 2 |P t | possible options for assigning to the |P t | bit positions s ∈ P t a respective bit value x s , a corresponding point of the elliptic curve that is based, at least in part, on the point (Σ s∈P t 2 s x s )V of the elliptic curve; obtaining k; and determining the first point as Σ t=0 T−1 l t , where l t is the point of the elliptic curve that corresponds, in lookup table L t , to the option for assigning to the |P t | bit positions s ∈ P t the corresponding bit value b s .

A method of obfuscated performance of a predetermined function, wherein for the predetermined function there is a corresponding plurality of first functions so that, for a set of inputs for the function, a corresponding set of outputs may be generated by (a) representing the set of inputs as a corresponding set of values, wherein each value comprises at least part of each input of a corresponding plurality of the inputs, (b) generating a set of one or more results from the set of values, where each result is generated by applying a corresponding first function to a corresponding set of one or more values in the set of values, and (c) forming each output as either a part of a corresponding one of the results or as a combination of at least part of each result of a corresponding plurality of the results; wherein the method comprises: obtaining, for each value in the set of values, one or more corresponding transformed versions of said value, wherein a transformed version of said value is the result of applying a bijection, that corresponds to said transformed version, to said value; and generating a set of transformed results corresponding to the set of results, wherein each transformed result corresponds to a respective result and is generated by applying a second function, that corresponds to the first function that corresponds to the respective result, to a transformed version of the one or more values of the respective set of one or more values for the corresponding first function.