PMI+, 低成本智慧卡密碼系統實作

Abstract

PMI 是去年在 “International Workshop on Practice and Theory in Public Key Cryptography” 的會議上，由辛辛那提大學的丁津泰教授所提出來的密碼系統，而PMI+則是PMI為了避免“differential”的攻擊方式所作的改進。在我的論文內，我將會提出兩種在低成本智慧卡（無輔助運算器）上實作PMI+的方式，一種採取傳統的實作方式並提出最佳化的方法，另一種採取金字塔般的方式來實作PMI+中會用到的Galois Field，在此我們特別稱為Composite Galois Field。 後者的實作方式使得在Galois Field 內的運算速度大為提升，並且也可以配合傳統的實作方式來做最佳化，目前實作成果在一般以8051為架構 的CPU下（１０MHz），每次加密大小為84/96bit的區塊只需要2.5/5.3 秒，我們可以宣稱PMI+的解密速度快於RSA-1024，而且不需要任何的輔助運算器。

PMI is a cryptosystem brought up by Prof. Jintai Ding, a professional of Cincinnati University, on the 2004 International Workshop on Practice and Theory in Public Key Cryptography. PMI+ is a further modification from PMI system to avoid the differential cryptanalysis. This thesis is about two kinds of implementations of PMI+ on a low-cost smart card without co-processor. One implementation takes traditional method to construct the field and another takes tower-like method to build the field named Composite Galois Field. Composite Galois Field has great performance of decryption than traditional one. It takes 2.5/5.3 seconds per 84/96-bit block on a 8051 based CPU at 10-MHz. We may say that PMI(84, 96) without co-processor beats RSA-1024 with co-processor.