| 摘要 |
Methods and apparatus for modular arithmetic operations with respect to a modulus p include representing operands as a series of s w-bit numbers, wherein <maths id="MATH-US-00001" num="00001"> <MATH OVERFLOW="SCROLL"> <MROW> <MI>s</MI> <MO>=</MO> <MROW> <MROW> <MO>⌈</MO> <MFRAC> <MI>k</MI> <MI>w</MI> </MFRAC> <MO>⌉</MO> </MROW> <MO>.</MO> </MROW> </MROW> </MATH> </MATHS> Operations are executed word by word and a carry, borrow, or other bit or word is obtained from operations on most significant words of the operands. Depending on the value of this bit or word, an operation-specific correction factor is applied. Cryptographic systems include computer executable instructions for such methods. Bit-level operations are generally avoided and the methods and apparatus are applicable to systems based on, for example, public-key cryptographic algorithms defined over the finite field GF(p). |
