On Degrees of Modular Common Divisors and the Big Prime Algorithm

Algorithm 1

The polynomial reconstruction by modular image.

Input: For an unknown polynomial we know

the upper bound of absolute values of its coefficients,

and for arbitrarily large prime number we have the

modular image   .

Reconstruct the polynomial .

(01) Choose any prime .

(02) Set .

(03) Set .

(04) While

(05)  if

(06)    set ;

(07)  else

(08)    set ;

(10)  set .

(11) Output .