Decomposition of masked values

A method of decomposing, using a mod 44 operation, an N bit Boolean share input, where N>12, the method comprising:

• reducing a number of bits in the N bit Boolean share input by adding a lower 11:0 bits of the input to an upper portion of the input left shifted by 2 bits to provide a first intermediate result having M bits;
• reducing a number of bits of the first intermediate result by adding a lower 6:0 portion of the intermediate result to an upper portion left shifted by 2 bits and subtracted from a multiple of 44 to provide a second intermediate result;
• adjusting the second intermediate result by adding and/or subtracting 44 to provide an output having a value within an interval of 0:43, the output being a mod 44 representation of the N bit Boolean share input;
• and
• generating a digital signature based on a digital signature operation using the output and a secret key.

A non-transitory computer readable medium storing processor-readable instructions that, when executed, cause a processor to decompose, using mod 44 operation, an N bit Boolean share input, where N>12, the non-transitory computer readable medium storing comprising the processor-readable instructions that cause the processor to:

• reduce a number of bits in the N bit Boolean share input by adding a lower 11:0 bits of the input to an upper portion of the input left shifted by 2 bits to provide a first intermediate result having M bits;
• reduce a number of bits of the first intermediate result by adding a lower 6:0 portion of the intermediate result to an upper portion left shifted by 2 bits and subtracted from a multiple of 44 to provide a second intermediate result;
• adjust the second intermediate result by adding or subtracting 44 to provide an output having a value within an interval of 0:43, the output being a mod 44 representation of the N bit Boolean share input;
• and
• generate a digital signature based on a digital signature operation using the output and a secret key.