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I am wondering if the inversion of multiplication of polynomials is equally hard as the discrete logarithm problem used for key exchange. Or are there algorithms that weaken such an usage. I understand that it is somewhat easy to factorize if one omits the division by an irreducible polynomial.

I cannot find any comparison for the hardness of

  • multiplicative inverse in GF(2^n) mod (some irreducible polynomial)
  • Diffie Hellman using exponents of g^x mod p
  • elliptic curves

Only for the last two I was able to find some comparison which favors elliptic curves over the discrete logarithm problem as the key length is about 1/12 as opposed to Diffie Hellman for the same security.

kwasmich
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1 Answers1

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The inverse is easy, it can be done by the extended Euclidean algorithm, thus polynomial in complexity compared to the others which are exponential.

kodlu
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