Towards the Verification of The AKS Primality Test in ACL2

نویسندگان

  • Cynthia Campos
  • Francois Modave
  • Steve Roach
چکیده

In this paper we present a recursive implementation of the Agrawal, Kayal and Saxena primality testing algorithm, which is the first unconditional deterministic polynomial time primality testing algorithm. Since the algorithm’s proof of correctness makes use of informal notation and omits many key steps, we present the progress made toward using ACL2 to verify the algorithm’s correctness. In particular, we focus on verifying that if n is prime, then the AKS algorithm will return PRIME.

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

An Empirical Study towards Refining the AKS Primality Testing Algorithm

The AKS (Agrawal-Kayal-Saxena) algorithm is the first ever deterministic polynomialtime primality-proving algorithm whose asymptotic run time complexity is O(log n), where > 0. Despite this theoretical breakthrough, the algorithm serves no practical use in conventional cryptologic applications, as the existing probabilistic primality tests like ECPP in conjunction with conditional usage of sub-...

متن کامل

Primality Proving via One round in Ecpp and One Iteration

On August 2002, Agrawal, Kayal and Saxena announced the first deterministic and polynomial time primality testing algorithm. For an input n, the AKS algorithm runs in heuristic time Õ(log n). Verification takes roughly the same amount of time. On the other hand, the Elliptic Curve Primality Proving algorithm (ECPP) runs in random heuristic time Õ(log n) ( Õ(log n) if the fast multiplication is ...

متن کامل

A Potentially Fast Primality Test

The running time is O(r log n). It can be shown by elementary means that the required r exists in O(log n). So the running time is O(log n). Moreover, by Fouvry’s Theorem [8], such r exists in O(log n), so the running time becomes O(log n). In [10], Lenstra and Pomerance showed that the AKS primality test can be improved by replacing the polynomial x − 1 in equation (1.1) with a specially const...

متن کامل

Some remarks and questions about the AKS algorithm and related conjecture

We show that AKS-algorithm for primality testing ( see [1]) can be modified to run in Õ(log n) time. We present some remarks and ask two questions related to this algorithm.

متن کامل

A Note On the Storage Requirement for AKS Primality Testing Algorithm

We remark that AKS primality testing algorithm needs about 1,000,000,000 G (gigabyte) storage space for a number of 1024 bits. Such storage requirement is hard to meet in practice. To the best of our knowledge, it is impossible for current operating systems to write and read data in so huge storage space. Thus, the running time for AKS algorithm should not be simply estimated as usual in terms ...

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 2004