US 2017/0346633 A1 · COMPUTING A SECURE ELLIPTIC CURVE SCALAR MULTIPLICATION USING AN UNSECURED AND SECURE ENVIRONMENT

Abstract

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 m2 random values ki, where i is an integer index; randomly select m1−m2 values ki for the indices m2<i≦m1; select m1 mask values δi; compute m1 residues ci based upon random residues ai, δπ(i)−1, and kπ(i), wherein π(i) is a random permutation; compute m1 elliptic curve points Gi based upon random residues ai and an elliptic point to be multiplied; receive m1 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 δi 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 m1 residues ci and elliptic curve points Gi; compute m1 elliptic curve points Pi based upon the m1 residues ci and elliptic curve points Gi; send the m1 elliptic curve points Pi to the secure processor.

Claims24

Dependent claims

A system for securely computing an elliptic curve scalar multiplication in an unsecured environment, comprising:

a secure processor including secure memory, the secure processor configured to:
split a secure scalar K into m2 random values ki, where i is an integer index;
randomly select m1−m2 values ki for the indices m2<i≦m1;
select m1 mask values δi;
compute m1 residues ci based upon random residues ai, δπ(i)−1, and kπ(i), wherein π(i) is a random permutation;
compute m1 elliptic curve points Gi based upon random residues ai and an elliptic point to be multiplied;
receive m1 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 δi from the portion of the received elliptic curve points;
a memory device;
and
an unsecure processor in communication with the memory device, the processor being configured to:
receive m1 residues ci and elliptic curve points Gi;
compute m1 elliptic curve points Pi based upon the m1 residues ci and elliptic curve points Gi;
send the m1 elliptic curve points Pi to the secure processor.

12 more elements

A non-transitory machine-readable storage medium encoded with instructions for securely computing an elliptic curve scalar multiplication using a secure processor and an unsecure processor, comprising:

instructions for execution by the secure processor including:
instructions for splitting a secure scalar K into m2 random values ki, where i is an integer index;
instructions for randomly selecting m1−m2 values ki for the indices m2<i≦m1;
instructions for selecting m1 mask values δi;
instructions for computing m1 residues ci based upon random residues ai, δπ(i)−1, and kπ(i), wherein π(i) is a random permutation;
instructions for computing m1 elliptic curve points Gi based upon random residues ai and an elliptic point to be multiplied;
instructions for receiving m1 elliptic curve points;
and
instructions for computing the elliptic curve scalar multiplication by combining a portion of the received elliptic curve points and removing the mask values δi from the portion of the received elliptic curve points;
and
instructions for execution by the unsecure processor including:
instructions for receiving m1 residues ci and elliptic curve points Gi;
instructions for computing m1 elliptic curve points Pi based upon the m1 residues ci and elliptic curve points Gi;
instructions for sending the m1 elliptic curve points Pi to the secure processor.

11 more elements

Dependencies are inferred from the claim text.

Computing a secure elliptic curve scalar multiplication using an unsecured and secure environment

Life of this patent

Computing a secure elliptic curve scalar multiplication using an unsecured and secure environment

Life of this patent

Abstract

Claims24