Method for protecting an electronic system with modular exponentiation-based cryptography against attacks by physical analysis
AssigneeCP8 Technologies
InventorLouis Goubin
Life of this patent
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Abstract
The invention concerns a method for protecting an electronic system implementing a cryptographic calculation process involving a modular exponentiation of a quantity (x), said modular exponentiation using a secret exponent (d), characterized in that said secret exponent is broken down into a plurality of k unpredictable values (d1, d2, . . . , dk), the sum of which is equal to said secret exponent.
Claims7
A method adapted to protect a smart card implementing a cryptographic process involving calculation of a modular exponentiation of a quantity (x), said modular exponentiation using a secret exponent (d), comprising breaking down said secret exponent (d) into unpredictable values (d1, d2, . . . , dk), wherein k is reater than 2, and at least one of said (k−1) values has a length at least equal to 64 bits, the sum of which is equal to said secret exponent (d) including:
- deriving (k−1) unpredictable values (d1, d2, . . . , dk-1), using a random generator;
- obtaining a final unpredictable value (dk) from the difference between the secret exponent (d) and the (k−1) unpredictable values (d1, d2, . . . , dk-1),
- creating k intermediate results by performing modular exponentiation on the quantity (x) using the k unpredictable values (d1, d2, . . . , dk−1, dk);
- and
- calculating a final results based on the k intermediate results, equal to the modular exponentiation of the quantity (x) using the secret exponent (d).
A method adapted to protect a smart card implementing a cryptographic process involving calculation of a modular exponentiation of a quantity (x), said modular exponentiation using a secret exponent (d), comprising:
- breaking down said secret exponent (d) into a plurality of k unpredictable values (d1, d2, . . . , dk), the sum of which is equal to said secret exponent;
- obtaining said unpredictable value (d1, d2, . . . , dk) by deriving (k−1) values by means of a random generator,
- wherein k is greater than 2, and at least one of said (k−1) values has a length at least equal to 64 bits, by raising the quantity (x) by an exponent comprising a final value and obtaining a set of results for each of said k values and calculating a product of the set of results and taking the difference between the secret exponent and the (k−1) values to derive the final value.
A smart card adapted to protect an electronic system comprising:
- means for a implementing a cryptographic process involving calculation of a modular exponentiation of a quantity (x), said modular exponentiation using a secret exponent (d), comprising:
- means for breaking down said secret exponent (d) into a plurality of k unpredictable values (d1, d2, . . . , dk), the sum of which is equal to said secret exponent, means for obtaining said unpredictable value (d1, d2, . . . , dk) by a random generator for deriving (k−1) values, wherein k is greater than 2, and at least one of said (k−1) values has a length at least equal to 64 bits, and means for taking the difference between the secret exponent and the (k−1) values to derive the final value.
Dependencies are inferred from the claim text.