縮短嵌入體變換多變量公開金鑰密碼系統的金鑰長度

Abstract

Shortening the public key of the Multivariate Public-Key Cryptographic(MPKC) schemes [20] is the most active issue in recent MPKC research. In this article we extend the results of PTBW11 [20] which is applied only to single field schemes, we show a method shortening the public key of embedded field transformation schemes like Hidden Field Equations(HFE) [17]. We also explain how the structure of central map restricts the short form of public key. This restriction only depends on the structure of central map so all MPKC schemes are affected. The affine map S can also participate in shortening the public key although the capacity and efficiency is not as well as central map because the resulting equations for solving S are not on-to in the big field. Unlike S, the affine map T gives a better result in the key shortening process. As a proof of concept, we propose a short public-key version of HFE- signature scheme and quantify the reduction in public key size in the end.