Blinding techniques for protection of private keys in message signing based on elliptic curve cryptography

A computer program product, comprising a tangible machine-readable storage medium having encoded therein executable code of one or more software programs, wherein the one or more software programs when executed by at least one processing device perform the following steps:

• obtaining a private key of a message signer to generate a signature for a message;
• selecting a random integer as an internal private key in a predefined range based at least in part on an order of an elliptic curve;
• computing an internal public key as a point on the elliptic curve using (a) a scalar multiply operation based at least in part on (i) the internal private key blinded using a random blinding value and (ii) a base point of the elliptic curve, and (b) a first inverse value for the random blinding value added to a result of the scalar multiply operation;
• generating a first part of the signature for the message based at least in part on the point of the elliptic curve;
• generating a second part of the signature for the message based at least in part on a second inverse value of the selected random integer generated from a message-dependent value of the message and the first part of the signature;
• and
• forming a signed version of the message using the first part of the signature and the second part of the signature.

An apparatus, comprising:

• a memory;
• and
• at least one processing device, coupled to the memory, operative to implement the following steps:
• obtaining a private key of a message signer to generate a signature for a message;
• selecting a random integer as an internal private key in a predefined range based at least in part on an order of an elliptic curve;
• computing an internal public key as a point on the elliptic curve using (a) a scalar multiply operation based at least in part on (i) the internal private key blinded using a random blinding value and (ii) a base point of the elliptic curve, and (b) a first inverse value for the random blinding value added to a result of the scalar multiply operation;
• generating a first part of the signature for the message based at least in part on the point of the elliptic curve;
• generating a second part of the signature for the message based at least in part on a second inverse value of the selected random integer generated from a message-dependent value of the message and the first part of the signature;
• and
• forming a signed version of the message using the first part of the signature and the second part of the signature.