two number theory questions

[Steve Zhang]

Hi, 

I have two number theory questions:

Question #1:

Assume that p is a large prime and g is a generator.

Given y=g^b mod p but no b (that is, b is unknown), are there efficient algorithms to compute z=g^{b^{-1}} mod p?

Question #2:

Assume that p is a large prime and g is a generator.

Given y=g^{b^2} mod p but no b (that is, b is unknown), are there efficient algorithms to compute z=g^b mod p? How about computing y from z (b is still unknown)? 

Thank you.

Steve



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