Efficient Lattice-Based Signcryption in Standard Model

Algorithm 1

InvertG(b).

Input:

  Vector 𝐛∈ℤ^𝑘, where 𝐛^𝐭=[𝑏₀,…,𝑏_𝑘−1].

Output:

  Scalar 𝑠∈ℤ_𝑞 and a vector 𝐞∈ℤ^𝑘.

(1)  𝑠←0;

(2)  for 𝑗=𝑘−1; 𝑘≥0; step −1  do

(3)   if  (𝑏_𝒾−2^𝒾⋅𝑠)∈[−𝑞/4,𝑞/4)mod𝑞  then

(4)   𝑡=0;

(5)   else

(6)   𝑡=1;

(7)   end if

(8)   𝑠=𝑠+𝑡⋅2^{𝑘−1−𝑗};

(9)   𝑒_𝒾=𝑏_𝒾−2^𝒾⋅𝑠∈[−𝑞/4,𝑞/4);

(10)  end for

(11)  Output 𝑠∈ℤ_𝑞 and 𝐞=(𝑒₀,…,𝑒_𝑘−1)∈[−𝑞/4,𝑞/4)^𝑘⊂ℤ^𝑘.