1 Montgomery Modular Multiplication in Hard- ware

List of Symbols and Abbreviations
A (x) the x th word of vector A
Ax..y particular range of bits in a vector A from position x to position y
A (y)
x
bit position of the y th word of A
B bound of smoothness
D a parameter in improved standard continuation of ECM
DCLJ dividing factor for CLJ clock signal
DCLK dividing factor for CLK clock signal
FCLJ frequency of CLJ clock signal
FCLK frequency of CLK clock signal
KD decimation factor of CLK clock signal
KM decimation factor of CLJ clock signal
M modulus
MCLJ multiplication factor for CLJ clock signal
MCLK multiplication factor for CLK clock signal
S partial sum
TQ
time period of bit generation
TCLJ time period of CLJ clock signal
TCLK time period of CLK clock signal
X nultiplier
Y multiplicand
φ canonical homomorphism
φ() Euler tontien function