Practical FHE

• by Shai Halevi

• Moving Values Between Slots

  • 暗号文 $a\in R_p=Z_p[X]/{\Phi }_m(X)$
  • $a\cong [{\alpha }_1,\cdots ,{\alpha }_{\ell }]$, ${\alpha }_j=a({\zeta }^{t_j})$
  • BGV scheme はautomorphism ${\kappa }_j:a(X)\to a(X^j)$ を使った
  • ex.
    • $b={\kappa }_5(a)=a(X^5)$
    • $b({\zeta }^{5^j})=a(({\zeta }^{5^j}{)}^{5)}=a({\zeta }^{5^{j+1}})$
    • if $a\cong [{\alpha }_1,\cdots ]$, $b\cong [{\alpha }_2,\cdots ]$
  • $Z_{63}^{\ast }/⟨2⟩$ は5で生成され, 巡回群

• Operation Cost
  

• LinTrans: hypercube上の1D-変換

• 多項式の効率的な計算: Paterson-Stockmeyer procedureで可能

参考文献

• https://heat-project.eu/School/Shai%20Halevi/Practical%20(F)HE-II.pptx