Datasets:
Improve dataset card: Add task category, tags, sample usage, update language and license info (#2)
Browse files- Improve dataset card: Add task category, tags, sample usage, update language and license info (c0343aae366a926f62a7896e8afb45d57b00a952)
Co-authored-by: Niels Rogge <nielsr@users.noreply.huggingface.co>
README.md
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---
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license: mit
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pretty_name: UQ
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---
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- [Data Instances](#data-instances)
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- [Data Fields](#data-fields)
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- [Data Splits](#data-splits)
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- [Dataset Creation](#dataset-creation)
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- [Curation Rationale](#curation-rationale)
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- [Source Data](#source-data)
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'question_id': '5',
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'site': 'crypto',
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'title': 'Finding $x$ such that $g^x\\bmod p<p/k$?',
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'body': "In a Schnorr group as used for DSA, of prime modulus $p$, prime order $q$, generator $g$ (with $p/g$ small), how can we efficiently exhibit an $x$ with $0<x<q$ such that $g^x\\bmod p<p/k$, for sizable $k$ but $k\\ll\\sqrt q$
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'link': 'https://crypto.stackexchange.com/questions/48503/finding-x-such-that-gx-bmod-pp-k',
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'tags': ['discrete-logarithm', 'group-theory'],
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'votes': 19,
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| **Business** | Quantitative Finance | 2 |
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| **Total** | - | **500** |
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## Additional Information
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### Licensing Information
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The
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### Citation Information
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---
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language:
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- en
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license: mit
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pretty_name: UQ
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task_categories:
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- question-answering
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tags:
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- stack-exchange
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- llm-evaluation
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- benchmark
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- reasoning
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- factuality
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---
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- [Data Instances](#data-instances)
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- [Data Fields](#data-fields)
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- [Data Splits](#data-splits)
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- [Sample Usage](#sample-usage)
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- [Dataset Creation](#dataset-creation)
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- [Curation Rationale](#curation-rationale)
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- [Source Data](#source-data)
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'question_id': '5',
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'site': 'crypto',
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'title': 'Finding $x$ such that $g^x\\bmod p<p/k$?',
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'body': "In a Schnorr group as used for DSA, of prime modulus $p$, prime order $q$, generator $g$ (with $p/g$ small), how can we efficiently exhibit an $x$ with $0<x<q$ such that $g^x\\bmod p<p/k$, for sizable $k$ but $k\\ll\\sqrt q$ ?
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I see that for small $k$, it is enough to try incremental values of $x$ until finding an $x$ that fits, with expected cost $O(k)$ modular multiplications in $\\mathbb Z_p^*$. Is there better?
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Assume $p$ is an $l$-bit prime; $q$ is an $n$-bit prime with $q$ dividing $p-1$; and $g=h^{(p-1)/q}$ for some (random?) $h$ in $\\mathbb Z_p^*$. For concrete values, assume $l\\approx1024$, $n\\approx160$, $k\\approx2^{64}$.
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Update: I'm expecting the problem to be hard, and thus that the more difficult problem of exhibiting $x$ with $g^x\\bmod p$ in a range of width $p/k$ must be hard.\
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\",
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'link': 'https://crypto.stackexchange.com/questions/48503/finding-x-such-that-gx-bmod-pp-k',
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'tags': ['discrete-logarithm', 'group-theory'],
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'votes': 19,
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| **Business** | Quantitative Finance | 2 |
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| **Total** | - | **500** |
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## Sample Usage
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You can load the data from [🤗 uq-project/uq](https://huggingface.co/datasets/uq-project/uq) via:
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```python
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# pip install -q datasets
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from datasets import load_dataset
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dataset = load_dataset("uq-project/uq", split="test")
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```
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## Additional Information
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### Licensing Information
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The dataset is licensed under the MIT License.
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### Citation Information
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