Abstract: Systems and methods for securing an Elliptic Curve Digital Signature Algorithm (ECDSA) nonce communicated between symmetric and asymmetric cryptographic co-processors in a heterogeneous system are discussed. In some embodiments, a processor may include: a symmetric portion configured to generate Boolean masked shares, wherein the Boolean masked shares constitute a nonce; and an asymmetric portion coupled to the symmetric portion, the asymmetric portion configured to produce an ECDSA signature based, at least in part, upon the nonce.

Abstract: Shuffling and sliding subgroup techniques are provided to shuffle an order of a plurality of data blocks. The techniques include selecting a first value for a starting position and a second value for a step size. A first iteration of the technique includes generating a first subgroup to include a first subset of the plurality of data blocks based on the first value and the second value and executing data operations associated therewith. Then, in each of one or more subsequent iterations based on whether all of the data blocks have been added to the shuffled order, subsequent subgroups are added to the shuffled order that each include a different subset of the plurality of data blocks that are shifted by one position from data blocks in the previously generated subgroup and executing data operations associated therewith.

Abstract: The present invention relates to a method for managing the memory of a secure microcircuit, including steps executed by the microcircuit of: forming a data block with executable code and/or data stored in a volatile memory of the microcircuit, and to be backed up outside the microcircuit, calculating a signature of the data block using a first signature key, inserting the calculated signature of the data block into a signature block, obtaining a current value of a non-volatile counter internal to the microcircuit, calculating a signature of the signature block associated with the current value of the internal counter, using a second signature key, and sending outside the microcircuit, the data block, the signature block and the signature of the signature block.

Abstract: Fast scalar multiplication operations are disclosed for use in an elliptic curve cryptographic system The operations use binary representations of a secret key and points on an elliptic curve defined over a prime field expressed in a coordinate system (e.g., Jacobian coordinates). The operations can be based on a modified Montgomery ladder that uses modified Meloni addition formulas. The operations can be more efficient than a double-and-add operation, and can be more resistant to side-channel attacks by hackers.

Abstract: Fast scalar multiplication operations are disclosed for use in an elliptic curve cryptographic system The operations use binary representations of a secret key and points on an elliptic curve defined over a prime field expressed in a coordinate system (e.g., Jacobian coordinates). The operations can be based on a modified Montgomery ladder that uses modified Meloni addition formulas. The operations can be more efficient than a double-and-add operation, and can be more resistant to side-channel attacks by hackers.