Sieve Method for Polynomial Linear Equivalence

Algorithm 2

Additive sieve: AddSieve 𝔽_𝑞,𝒮,𝒫,𝐱_𝑖,𝐱_𝑗,𝑆_𝑖,𝑆_𝑗.

(1)   Set the two sets 𝑆⁺_𝑖=Φ and 𝑆⁺_𝑗=Φ.

(2)   Compute 𝒫𝐱_𝑖+𝐱_𝑗.

(3)   for each 𝐲^(𝑖)∈𝑆_𝑖  do

(4)     for each 𝐲^(𝑗)∈𝑆_𝑗  do

(5)     Compute 𝒮𝐲^(𝑖)+𝐲^(𝑗).

(6)     if  𝒫𝐱_𝑖+𝐱_𝑗=𝑆𝐲^(𝑖)+𝐲^(𝑗)  then

(7)        Add 𝐲^(𝑖) to 𝑆⁺_𝑖, and 𝐲^(𝑗) to 𝑆⁺_𝑗, respectively.

(8)     end if

(9)     end for

(10) end for

(11) return  𝑆⁺_𝑖,𝑆⁺_𝑗.