Computation of Complex Primes Using Elliptic Curves: Application for Cryptosystem Design
نویسندگان
چکیده
منابع مشابه
Knapsack Cryptosystem on Elliptic Curves
—The LLL algorithm is strong algorithm that de-crypts the additional type Knapsack cryptosystem. However, the LLL algorithm is not applicable in the addition in the group that rational points of elliptic curves on finite fields do. Therefore, we think the Knapsack cryptosystem constructed on elliptic curves. By using the pairing for the decryption, it is shown to be able to make the computation...
متن کاملPairing computation for elliptic curves
This paper presents the first study of pairing computation on curves with embedding degree 15. We show that pairing computation on these curves has loop length r and we use a twist of degree 3 to perform most of the operations in Fp or Fp5 . Furthermore, we present an original arithmetic for extension fields of degree 5. Key-words: Pairing based cryptography, Pairing computation, Arithmetic, In...
متن کاملA nonlinear cryptosystem based on elliptic curves *
We propose a new system that is applicable to public key cryptography. The system is a variant of the Discrete Logarithm Problem (DLP) with the elements of a certain group, formed with points of an elliptic curve, and the elements of a certain finite field related to the curve. The nonlinear term refers to the coefficient that we use as the problem to solve because it is obtained with a nonline...
متن کاملThe main conjecture for CM elliptic curves at supersingular primes
At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is ...
متن کاملThe anticyclotomic Main Conjecture for elliptic curves at supersingular primes
The Main Conjecture of Iwasawa theory for an elliptic curve E over Q and the anticyclotomic Zp-extension of an imaginary quadratic field K was studied in [BD2], in the case where p is a prime of ordinary reduction for E. Analogous results are formulated, and proved, in the case where p is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Communications, Network and System Sciences
سال: 2012
ISSN: 1913-3715,1913-3723
DOI: 10.4236/ijcns.2012.51001