Various embodiments relate to a method for masked decoding of a polynomial a using an arithmetic sharing a to perform a cryptographic operation in a data processing system using a modulus q, the method for use in a processor of the data processing system, including: subtracting an offset δ from each coefficient of the polynomial a; applying an arithmetic to Boolean (A2B) function on the arithmetic shares of each coefficient ai of the polynomial a to produce Boolean shares âi that encode the same secret value ai; and performing in parallel for all coefficients a shared binary search to determine which of coefficients ai are greater than a threshold t to produce a Boolean sharing value {circumflex over (b)} of the bitstring b where each bit of b decodes a coefficient of the polynomial a.