臺灣博碩士論文加值系統

在這篇論文裡，我們設計了一個可調式RSA和ECC﹝Elliptic Curve Cryptography﹞密碼處理器。為了使密碼處理器的面積不致於太大，所以我們將字元基礎﹝word-based﹞的架構運用在密碼處理器上。在字元基礎架構的作用下，除了可以大幅降低我們密碼處理器的面積，還可以使電路變成具有執行可擴充性金鑰長度﹝scalable key length﹞的能力。這種功能可以提供給使用者在運算時間和安全性上做一個選擇，如果覺得安全性重要的話，就選擇較長的金鑰長度來執行RSA或ECC的加解密，反之，就可以選較短的金鑰長度，來減少加解密的時間。
雖然字元基礎的架構，能帶來上述的好處，但其付出的代價是當金鑰長度增加時，運算時間會成平方比增加。對此問題，我們在其他地方做了一些速度上的補救。首先利用修改過的蒙哥馬利演算法﹝Modified Montgomery algorithm﹞來消除原始蒙哥馬利演算法中最後的化減﹝final reduction﹞，使得計算每個模數乘法之間不需額外的時間確認結果是否小於質數﹝prime﹞，來節省時脈週期﹝clock cycles﹞。除此之外，我們額外設計了一個預測位元硬體﹝parity prediction hardware﹞來加快計算模數乘法時的速度。最後我們的可調式RSA和ECC密碼處理器在TSMC CMOS 0.35μm元件庫﹝cell library﹞的合成下，用220MHz的速度執行512位元金鑰長度的RSA加解密，鮑率﹝baud rate﹞是276k位元/秒。在GF(p)時，160位元金鑰長度的ECC加解密，鮑率﹝baud rate﹞是73.3k位元/秒。在GF(2m)時，160位元金鑰長度的ECC加解密，鮑率﹝baud rate﹞是65.9k位元/秒。

With the rapid advance in communication technology, more and more applications such
as e-commerce and wireless networking are becoming possible. Protecting the sensitive
information when transmitted on the insecure communication channel is an essential issue
in such applications. Public-key cryptography such as the RSA algorithm or elliptic curve
cryptography plays a vital role in modern security system, because it can solve the problem
of key distribution and possess the signature property.
In this thesis we propose an asymmetric crypto-processor (ACP) core. The ACP core
can support scalable keys of length up to 2048 bits for both RSA and ECC in GF(p) or
GF(2
m
). In order to reduce silicon area, the word-based architecture is adopted in our ACP
core. This feature provides a trade-o between security and computation time. Since the
original Montgomery's multiplication algorithm needs nal reduction which will decrease the
speed, a modied Montgomery multiplication is used to eliminate the nal reduction in our
datapath. With moderate area overhead, the circuit can achieves an encryption rate of 276
Kbps for 512-bit RSA, 73.3 Kbps for 160-bit ECC in GF(p) and 65.9 Kbps for 160-bit ECC
in GF(2
m
), with a 220 MHz clock.

目　錄
摘要…………………………………………………………………1
誌謝…………………………………………………………………………2
目錄……………………………………………………………………………3
第一章　序論……………………………………………………………4
第二章 密碼學概論………………………………………………………5
第三章 模數指數演算法…………………………………………………6
第四章 可調式RSA和ECC密碼處理器核心設計…………………………7
第五章 非對稱式密碼處理器……………………………………………8
第六章 結論與未來展望…………………………………………………9
英文附錄……………………………………………………………………10

[1] R. L. Rivest, A. Shamir, and L. Adleman, \A method for obtaining digital signatures
and public-key cryptosystems," Communications of the ACM, vol. 21, pp. 120{126, Feb.
1978.
[2] W. DiÆe and M. E. Hellman, \New directions in cryptography," IEEE Trans. Informa-
tion Theory, vol. 22, pp. 644{654, Nov. 1976.
[3] V. S. Miller, \Use of elliptic curve in cryptography," in Advances in Cryptology|
Crypto'85 Proceedings, pp. 417{426, 1986.
[4] P. L. Montgomery, \Modular multiplication without trial division," Math. Computation,
vol. 44, no. 7, pp. 519{521, 1985.