Ideal 9th-order Multigrades and Letac's Elliptic Curve

نویسنده

  • C. J. SMYTH
چکیده

By showing that the elliptic curve (x2 13)(y2 13) = 48 has infinitely many rational points, we prove that Letac's construction produces infinitely many genuinely different ideal 9th-order multigrades. We give one (not very small) new example, and, by finding the Mordell-Weil group of the curve, show how to find all examples obtainable by Letac's method.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A NEW PROTOCOL MODEL FOR VERIFICATION OF PAYMENT ORDER INFORMATION INTEGRITY IN ONLINE E-PAYMENT SYSTEM USING ELLIPTIC CURVE DIFFIE-HELLMAN KEY AGREEMENT PROTOCOL

Two parties that conduct a business transaction through the internet do not see each other personally nor do they exchange any document neither any money hand-to-hand currency. Electronic payment is a way by which the two parties transfer the money through the internet. Therefore integrity of payment and order information of online purchase is an important concern. With online purchase the cust...

متن کامل

Efficient elliptic curve cryptosystems

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

متن کامل

Meshing Error of elliptic cylinder gear based on tooth contact analysis

In order to study the dynamic meshing characteristics of the elliptic cylinder gear and obtain the meshing error of the gear transmission system, the two-dimensional static contact analysis of the gear tooth surface is carried out by using ANSYS software, and the key parts of the contact area of the tooth surface are determined. Then, the dynamic meshing model of the elliptic cylinder gear is e...

متن کامل

The new protocol blind digital signature based on the discrete logarithm problem on elliptic curve

In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind  digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve...

متن کامل

An efficient blind signature scheme based on the elliptic curve discrete logarithm problem

Elliptic Curve Cryptosystems (ECC) have recently received significant attention by researchers due to their high performance such as low computational cost and small key size. In this paper a novel untraceable blind signature scheme is presented. Since the security of proposed method is based on difficulty of solving discrete logarithm over an elliptic curve, performance of the proposed scheme ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010