16 lines
910 B
Markdown
16 lines
910 B
Markdown
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title = "Coppersmith's attack under the hood"
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date = 2022-05-03
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[taxonomies]
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tags = ["filler"]
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## Introduction
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Finding the roots of polynomials under {{ katex(body="\mathbb{R}") }} or {{ katex(body="\mathbb{Z}") }} is relatively easy, for example by using Newton's method. However, solving polynomials under {{ katex(body="\mathbb{Z}_ n")}} is much more difficult. Coppersmith's method is a method for solving these polynomials for small roots less than {{ katex(body="N^\frac{1}{k}") }} where {{ katex(body="k")}} is the degree of the polynomial.
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Coppersmith's method relies on **lattice reductions** to create polynomials which are solvable over the integers. Lattice reductions are an important technique for a multitude of attacks on different cryptographic schemes. For example, they can be used to reduce the Merkle-Hellman cryptosystem, Learning with Error, NTRU, and many others.
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