VORRICHTUNG ZUR ERZEUGUNG VON ANTEILEN, WIEDERHERSTELLUNGSVORRICHTUNG, GEHEIMES BERECHNUNGSSYSTEM, VERFAHREN ZUR ERZEUGUNG VON ANTEILEN, WIEDERHERSTELLUNGSVERFAHREN, PROGRAMM UND AUFZEICHNUNGSMEDIUM

摘要

A share [x]_iof plaintext x in accordance with Shamir's secret sharing scheme is expressed by N shares [x₀]_i, ..., [x_N-1]_i, and each share generating device A_iobtains a function value r_i= P_m(i(-))(S_i) of a seed s_i, obtains a first calculated value ζ_i= λ(i, i(-))[x_i(-)]_i+r_iusing a Lagrange coefficient λ(i, i(-)), a share [x_i(-)]_i, and the function value r_i, and outputs the first calculated value ζ_ito a share generating device A_i(-). Each share generating device A_iaccepts a second calculated value ζ_i(+), obtains a third calculated value z_i= λ(i, i(+))[x_i]_i+ζ_i(+)using a Lagrange coefficient λ(i, i(+)), a share [x_i]_i, and the second calculated value ζ_i(+), and obtains information containing the seed s_iand the third calculated value z_ias a share SS_iof the plaintext x in secret sharing and outputs the share SS_i.