Input: a group containing two PU partition modes, denoted by p = (p1, p2), a basis vector b = (b1, b2), and a secret digit s in a (22 + 3 − 1)-ary notational system Output: the modified group of p, denoted by p′ 1. F = p ⋅ b = p1 × b1 + p2 × b2 2. if s ≥ F 3. d = s-F 4. else if s < F 5. d = 22 + 3 − 1 − |s − F| 6. end if 7. ptemp = (p1 + d1, p2 + d2) 8. if (any element of ptemplarger than 7 or smaller than 0) 9. for i=0:1:7 10. for j = 0:1:7 11. record all the $${\mathbf{p}}_l=\left({p}_{l_1},{p}_{l_2}\right)=\left(i,j\right)$$that makes i × b1 + j × b2 =  = s, and store them in one set 12. $$\mathbf{P}=\left\{{\mathbf{p}}_l=\left({p}_{l_1},{p}_{l_2}\right),l\in \Big\{1,2,\cdots, k\Big\}\right\}$$ 13. end for 14. end for 15. for l=1:1:k 16. calculate the Manhattan Distance md of each element in P from p, i.e. $$\left|{\mathbf{p}}_l-\mathbf{p}\right|=\left|{p}_{l_1}\hbox{-} {p}_1\right|+\left|{p}_{l_2}\hbox{-} {p}_2\right|$$ 17. end for 18. $${\mathbf{p}}^{\prime }=\underset{{\mathbf{p}}_l}{\arg \min}\left(\left|{p}_{l_1}-{p}_1\right|+\left|{p}_{l_2}-{p}_2\right|\right)$$ 19. else if 20. p′ = ptemp 21. end if 