Exponent splitting for cryptographic operations

A system comprising:

• a first register and a second register to store elements of a mathematical group;
• and
• a processing device coupled to the first and second registers and to:
• receive a first share value and a second share value, wherein a combination of the first share value and the second share value corresponds to an exponent value;
• update a value of a first register using a first equation that is based on the first and second share values;
• update a value of a second register using a second equation that is based on the second share value;
• and
• select, by a processing device, one of the value of the first register or the value of the second register based on a bit value of the second share value.

A non-transitory computer readable medium including data that, when accessed by a processing device, cause the processing device to perform operations comprising:

• receiving a first share value and a second share value, wherein a combination of the first share value and the second share value corresponds to an exponent value;
• updating a value of a first register using a first equation that is based on the first and second share values;
• updating a value of a second register using a second equation that is based on the second share value;
• and
• selecting one of the value of the first register or the value of the second register based on a bit value of the second share value.

A method comprising:

• receiving a first share value and a second share value, wherein a combination of the first share value and the second share value corresponds to an exponent value;
• modifying a first register and a second register based on the first share value;
• modifying the first register and the second register based on the second share value;
• and
• selecting, by a processing device, one of a value of the first register or a value of the second register based on the modified first and second registers.