Score:1

Challenges like RSA factoring challenge

ru flag

RSA factoring challenge is a famous one and is still not completely solved.

Are there similar challenges for

  1. Discrete log over $\mathbb Z_p^*$?
  2. Discrete log over Elliptic curves?
  3. LWE?
  4. LPN?
Score:4
ru flag
  1. Not that I am aware of.

  2. See the Certicom ECC challenge

  3. See the Darmstadt LWE challenge (part of a larger set of lattice challenges)

  4. Closest is probably the decoding challenge, though this is not generic LPN. If you like opening cans of worms, see also this thread.

fgrieu avatar
ng flag
As to 1, I know no challenge for Discrete log over $\mathbb Z_p^*$ either. But it is possible to extend RFC 2409's [Oakley groups](https://www.rfc-editor.org/rfc/rfc2409#section-6) to create more, say by steps of 32 bits starting from the existing 768-bit one; and then any nothing-up-my-sleeves value in $[1,p)$ makes a good challenge for the DLP; e.g. $\lfloor2^{\lfloor\log_2 p\rfloor}\sqrt3\rfloor$.
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