Elliptic curve cryptography scheme with simple side-channel attack countermeasure
AssigneeInfosec Global Inc.
InventorsVladimir SOUKHAREV, Basil HESS
Life of this patent
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Abstract
There is provided an elliptic curve cryptographic scheme for permitting secure communications between two or more cryptographic correspondent devices, with a simple side-channel attack countermeasure. The cryptographic scheme includes: transforming a point to Jacobian projective coordinates; constant-time scalar multiplication of the point by a parameter; and transforming the resultant of the scalar multiplication to affine coordinates. The scalar multiplication including: performing iteratively to the value of the parameter either one of: doubling of the point and multiplying any two random field elements; or mixed addition of the point.
Claims19
An elliptic curve cryptography scheme resistant to simple side channel attacks for permitting secure communications between two or more cryptographic correspondent devices, each of the cryptographic correspondent devices comprising a processor and a memory, the memory configured to store a plurality of instructions which when executed by the processor cause the processor to implement the cryptographic scheme, the cryptographic scheme comprising:
- generating a Jacobian projective coordinate representation of a point;
- performing scalar multiplication of the point by a parameter, the scalar multiplication comprising:
- performing iteratively in relation to the value of the parameter, for each iteration, either one of:
- doubling of the point and performing a dummy operation;
- or
- mixed addition of the point;
- and
- transforming the resultant of the scalar multiplication to affine coordinates.
A method for a simple side-channel attack countermeasure for scalar multiplication of a point by a parameter in an elliptic curve cryptographic scheme, the elliptic curve cryptographic scheme permitting secure communications between two or more cryptographic correspondent devices, each of the cryptographic correspondent devices comprising a processor and a memory, the memory configured to store a plurality of instructions which when executed by the processor cause the processor to implement the cryptographic scheme, the method comprising:
- generating a Jacobian projective coordinate representation of the point;
- performing iteratively in relation to the value of the parameter, for each iteration, either one of:
- if doubling of the point is viable:
- doubling of the point to produce a new value for the point;
- and
- performing a dummy operation;
- or
- otherwise, performing mixed addition on the point to produce a new value for the point;
- and
- transforming the point to affine coordinates.
A system for implementing an elliptic curve cryptographic scheme on a correspondent device, the elliptic curve cryptographic scheme comprising a countermeasure resistant to a simple side-channel attack, the elliptic curve cryptographic scheme permitting secure communications between two or more cryptographic correspondent devices, each of the cryptographic correspondent devices comprising a processor and a memory, the memory configured to store a plurality of instructions which when executed by the processor cause the processor to implement the cryptographic scheme, the elliptic curve cryptographic scheme comprising scalar multiplication of a point by a parameter, the system comprising:
- a representation generation module for generating a Jacobian projective coordinate representation of the point;
- a determination module for performing iteratively in relation to the value of the parameter, for each iteration, either one of:
- if doubling of the point is viable:
- doubling of the point to produce a new value for the point;
- and
- performing a dummy operation;
- or
- otherwise, performing mixed addition on the point to produce a new value for the point;
- and
- a transformation module for transforming the point to affine coordinates.
Dependencies are inferred from the claim text.