Computation of a 30750-bit binary field discrete logarithm

نویسندگان

چکیده

This paper reports on the computation of a discrete logarithm in finite field F 2 30750 \mathbb {F}_{2^{30750}} , breaking by large margin previous record, which was set January 2014 9234"> 9234 {F}_{2^{9234}} . The present made essential use elimination step quasi-polynomial algorithm due to Granger, Kleinjung and Zumbrägel, is first large-scale experiment truly test successfully demonstrate its potential when applied recursively, it leads stated complexity. It required equivalent about alttext="2900"> 2900 encoding="application/x-tex">2900 core years single an Intel Xeon Ivy Bridge processor running at 2.6 GHz, comparable approximately alttext="3100"> 3100 encoding="application/x-tex">3100 expended for record prime fields, bit-length alttext="795"> 795 encoding="application/x-tex">795 demonstrates just how much easier problem this level computational effort. In order make feasible we introduced several innovative techniques small degree irreducible elements, meant that avoided performing any costly Gröbner basis computations, contrast all records since early 2013. While such computations are crucial alttext="upper L left-parenthesis one fourth plus o 1 right-parenthesis right-parenthesis"> L ( 1 4 + o stretchy="false">) encoding="application/x-tex">L(\frac 4 + o(1)) complexity algorithms, they were simply too slow our purposes. Finally, should serve as serious deterrent cryptographers who still proposing rely security fields applications, despite existence two algorithms prospect even faster being developed.

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Computation of a 768-Bit Prime Field Discrete Logarithm

This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the factorization of a 768-bit RSA modulus, and briefly discusses the cryptologic relevance of the result.

متن کامل

A Kilobit Hidden SNFS Discrete Logarithm Computation

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software. Our chosen prime p looks random, and p−1 has a 160-bit pri...

متن کامل

Solving a 676-Bit Discrete Logarithm Problem in GF(36n)

Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The ηT pairing on supersingular curves over GF(3) is particularly popular since it is efficiently implementable. Taking into account the Menezes-Okamoto-Vanstone (MOV) attack, the discrete logarithm problem (DLP) in GF(3) becomes a concern for the security of cryptosystems using ηT pairing...

متن کامل

Statistical Analysis of Binary Functional Graphs of the Discrete Logarithm

The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively difficult. Therefore, we focus on the statistical analysis of certain properties of the graph of the discrete logarithm. We discovered the expected value and...

متن کامل

Solving the Discrete Logarithm of a 113-Bit Koblitz Curve with an FPGA Cluster

Using FPGAs to compute the discrete logarithms of elliptic curves is a well-known method. However, until to date only CPU clusters succeeded in computing new elliptic curve discrete logarithm records. This work presents a high-speed FPGA implementation that was used to compute the discrete logarithm of a 113-bit Koblitz curve. The core of the design is a fully unrolled, highly pipelined, self-s...

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

ژورنال

عنوان ژورنال: Mathematics of Computation

سال: 2021

ISSN: ['1088-6842', '0025-5718']

DOI: https://doi.org/10.1090/mcom/3669