Method for strengthening the implementation of ECDSA against power analysis

A computing device operative to execute a method of computing a digital signature on a message m, said signature being computed by a signer having a private key d and a public key dG, where G is a generator of a cryptographic group, said device comprising:

• a memory;
• a secure memory for storing the plurality of parts;
• and,
• a processor operative to:
• a) split said private key d into a plurality of private key parts;
• b) combine said plurality of private key parts with a random value Δ generated for that computed digital signature to obtain updated private key parts;
• c) generate an ephemeral private key k;
• d) obtain a first signature component r from an ephemeral public key kG;
• e) compute a value e derived from said message m by application of a cryptographic function;
• f) compute a second signature component s utilizing, said plurality of updated private key parts, said ephemeral private key k, said first signature component r, and said value e.

A computing device operative to execute a method of computing a public key corresponding to a private key k in a cryptosystem, wherein the cryptosystem uses a generator G, the device comprising:

• a memory;
• and,
• a processor operative to:
• a) represent a masking value β as a plurality of values which may be combined to obtain said masking value, each of said plurality of values updated by a random value π for each computation of said public key;
• b) combine each of said plurality of updated values with said private key k to obtain a plurality of private key components;
• c) combine each of said plurality of private key components with said generator G to obtain a plurality of public key components;
• and,
• d) combine said public key components to obtain said public key.

A computing device operative to execute a method for masking a secret value k used in a cryptographic operation, said device comprising:

• a memory;
• a processor operative to:
• generate a masking value β;
• split said masking value β into a plurality of components;
• apply each of said plurality of components to said secret value k in performing said cryptographic operation to generate a signature component;
• and
• update said plurality of components by applying a random value π to each said plurality of components such that said plurality of components, when combined, equal said masking value β.