Technologies for robust computation of elliptic curve digital signatures

A compute device for verification of elliptic curve digital signatures, the compute device comprising:

• an elliptic curve cryptography (ECC) engine, wherein the ECC engine is to:
• read a parameter value for each of a plurality of parameters of a elliptic curve digital signature algorithm verify operation from a data port of the ECC engine;
• read an opcode from an instruction port of the ECC engine, wherein the opcode is indicative of the elliptic curve digital signature algorithm verify operation;
• perform the elliptic curve digital signature algorithm verify operation in response to reading the second opcode, wherein to perform the elliptic curve digital signature algorithm verify operation comprises to:
• determine a first intermediate value u1;
• determine a second intermediate value u2;
• determine a smaller number of leading zeros of u1 and u2;
• perform, for each index location of u1 after the first bit after the smaller number of leading zeros, one or more elliptic curve operations, wherein to perform, for each index location of u1 after the first bit after the smaller number of leading zeros, the one or more elliptic curve operations comprises to:
• perform a point doubling operation when the bit value of the index location of u1 is 0 and the bit value of the index location of u2 is 0;
• perform a point doubling operation and a point addition operation when the bit value of the index location of u1 is 1 and the bit value of the index location of u2 is 0;
• perform a point doubling operation and a point addition operation when the bit value of the index location of u1 is 0 and the bit value of the index location of u2 is 1;
• and
• perform a point doubling operation and only one point addition operation when the bit value of the index location of u1 is 1 and the bit value of the index location of u2 is 1;
• and
• write result data to an output port of the ECC engine in response to performance of the elliptic curve digital signature algorithm verify operation.

One or more non-transitory computer-readable media comprising a plurality of instructions stored thereon that, when executed, causes an elliptic curve cryptography (ECC) engine of a compute device to:

• read a parameter value for each of a plurality of parameters of a elliptic curve digital signature algorithm sign operation from a data port of the ECC engine, wherein one parameter of the plurality of parameters is a scalar multiplier, wherein the scalar multiplier has one or more leading zeros;
• read an opcode from an instruction port of the ECC engine, wherein the opcode is indicative of the elliptic curve digital signature algorithm sign operation;
• perform the elliptic curve digital signature algorithm sign operation in response to reading the opcode, wherein to perform the elliptic curve digital signature algorithm sign operation comprises to:
• perform, for each bit of the scalar multiplier after the first bit after the one or more leading zeros, an elliptic curve point addition operation and an elliptic curve point doubling operation;
• and
• perform, for each leading zero of the one or more leading zeros, a dummy elliptic curve point addition operation and a dummy elliptic curve point doubling operation, wherein the dummy elliptic curve point operations and the dummy elliptic curve point doubling operations have no effect on result data of the elliptic curve digital signature algorithm sign operation;
• and
• write the result data to an output port of the ECC engine in response to performing the elliptic curve digital signature algorithm sign operation.

One or more non-transitory computer-readable media comprising a plurality of instructions stored thereon that, when executed, causes an elliptic curve cryptography (ECC) engine of a compute device to:

• read a parameter value for each of a plurality of parameters of a elliptic curve digital signature algorithm verify operation from a data port of the ECC engine;
• read an opcode from an instruction port of the ECC engine, wherein the opcode is indicative of the elliptic curve digital signature algorithm verify operation;
• perform the elliptic curve digital signature algorithm verify operation in response to reading the second opcode, wherein to perform the elliptic curve digital signature algorithm verify operation comprises to:
• determine a first intermediate value u1;
• determine a second intermediate value u2;
• determine a smaller number of leading zeros of u1 and u2;
• perform, for each index location of u1 after the first bit after the smaller number of leading zeros, one or more elliptic curve operations, wherein to perform, for each index location of u1 after the first bit after the smaller number of leading zeros, the one or more elliptic curve operations comprises to:
• perform a point doubling operation when the bit value of the index location of u1 is 0 and the bit value of the index location of u2 is 0;
• perform a point doubling operation and a point addition operation when the bit value of the index location of u1 is 1 and the bit value of the index location of u2 is 0;
• perform a point doubling operation and a point addition operation when the bit value of the index location of u1 is 0 and the bit value of the index location of u2 is 1;
• and
• perform a point doubling operation and only one point addition operation when the bit value of the index location of u1 is 1 and the bit value of the index location of u2 is 1;
• and
• write result data to an output port of the ECC engine in response to performance of the elliptic curve digital signature algorithm verify operation.