The failure of McEliece PKC based on Reed-Muller codes

نویسندگان

  • I. V. Chizhov
  • M. A. Borodin
چکیده

This paper describes new algorithm for breaking McEliece cryptosystem, built on ReedMuller binary code RM(r,m), which receives the private key from the public key. The algorithm has complexity O(n+nlog2n) bit operations, where n = 2, d = GCD(r,m−1). In the case of GCD(r,m − 1) limitation, attack has polynomial complexity. Practical results of implementation show that McEliece cryptosystems, based on the code with length n = 65536 bits, can be broken in less than 7 hours on a personal computer.

برای دانلود 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

The failure of McEliece PKC based on Reed - Muller codes . May 8 , 2013

This paper describes new algorithm for breaking McEliece cryptosystem, built on ReedMuller binary code RM(r,m), which receives the private key from the public key. The algorithm has complexity O(n+nlog2n) bit operations, where n = 2, d = GCD(r,m−1). In the case of GCD(r,m − 1) limitation, attack has polynomial complexity. Practical results of implementation show that McEliece cryptosystems, bas...

متن کامل

Punctured Reed-Muller code-based McEliece cryptosystems

The authors propose new McEliece cryptosystems based on punctured Reed–Muller (RM) codes. They successfully show that the commonly known attacks, such as the Minder–Shokrollahi attack, the Chizhov–Borodin attack, and the square code attack, are ineffective against the proposed RM code-based McEliece cryptosystem. We developed an optimal puncturing scheme to prevent the above-mentioned attacks f...

متن کامل

On McEliece’s result about divisibility of the weights in the binary Reed-Muller codes

First, we give an alternative proof of the famous McEliece’s result about divisibility of the weights of the binary Reed-Muller codes fully relying on knowledge for Boolean functions. Second, we prove that any binary Reed-Muller code RM(r, m) contains codeword such that the highest power of 2 dividing its weight is exactly 2[(m−1)/r].

متن کامل

Quantum Fourier sampling, Code Equivalence, and the quantum security of the McEliece and Sidelnikov cryptosystems

The Code Equivalence problem is that of determining whether two given linear codes are equivalent to each other up to a permutation of the coordinates. This problem has a direct reduction to a nonabelian hidden subgroup problem (HSP), suggesting a possible quantum algorithm analogous to Shor’s algorithms for factoring or discrete log. However, in Dinh et al. [2011] we showed that in many cases ...

متن کامل

A New Class of Public Key Cryptosystems Constructed Based on Reed-Solomon Codes, K(XII)SE(1)PKC. – Along with a presentation of K(XII)SE(1)PKC over the extension field

In this paper, we present a new class of public key cryptosystem based on Reed-Solomon codes, a member of the code based PKC(CBPKC), referred to as K(XII)SE(1)PKC. We show that K(XII)SE(1)PKC can be secure against the various attacks. Particularly we present a member of K(XII)SE(1)PKC constructed based on the Reed-Solomon code over the extension field F28 , which is extensively used in the pres...

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

برای دانلود 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

عنوان ژورنال:
  • IACR Cryptology ePrint Archive

دوره 2013  شماره 

صفحات  -

تاریخ انتشار 2013