PMI+, 低成本智慧卡密碼系統實作

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。

關鍵字

智慧卡；密碼系統

並列摘要

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.

並列關鍵字

smartcard ； PMI+

參考文獻

[SCS01] Sheueling Chang Shantz , From Euclid’s GCD to Montgomery Multiplication to the Great Divide, SML. Technical Report SMLI TR-2001-95, Sun Microsystems Laboratories, 2001

[Ding04] J. Ding, A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation, PKC 2004, LNCS 2947, pp.305–318.

[DGW+05] J. Ding, J. Gower, D. Schmidt, C.Wolf, and Z. Yin. Complexity Estimates for the F4 attack on the Perturbed Matsumoto-Imai Cryptosystem, 2004 manuscript.

[FGS05] P.-A. Fouque, L. Granboulan, and J. Stern, Differential Cryptanalysis for Multivariate Schemes, Eurocrypt 2005.

[Gua97] J. GUAJARDO, Efficient Algorithms for Elliptic Curve Cryptosystems, Master's Thesis, Worcester Polytechnic Institute, May 1997

國際替代計量

PMI+, 低成本智慧卡密碼系統實作

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