Apparatus and method for modular multiplication

A method for modular multiplication, performed by an apparatus for modular multiplication, comprising:

• performing, by a first operation unit having a systolic structure, a first operation based on a structure of at least one of a serial multiplier, which scans all partial products, and a serial squarer-based multiplier, which calculates a difference between a square of a sum of input values and a square of a difference of the input values, and outputting, by the first operation unit, a result of the first operation in digit-serial format in order from a least significant digit to a most significant digit;
• performing, by a second operation unit having a systolic structure, a second operation based on a structure of at least one of the serial multiplier and the serial squarer-based multiplier, and outputting, by the second operation unit, a result of the second operation in digit-serial format in order from a least significant digit to a most significant digit;
• outputting a result of adding the result of the first operation and the result of the second operation;
• feeding an intermediate value stream back to the first operation unit, which is configured to calculate a product of the intermediate value stream and a zeta parameter;
• and
• outputting a High-Order Term as a result of Montgomery modular multiplication.