# Please review proxy re-signature on Elliptic Curve [closed]

I want to implement proxy re-signature on elliptic curve.

I've been thinking about ideas like the one below, but are there any problems?

Key Generate:

• $$a =$$ alice's secret key
• $$aG$$ = alice's public key
• $$b =$$ bob's secret key
• $$bG =$$bob's secret key
• $$rk_{ab} = aP * b^{-1} = a/bG$$

First Sign:

• $$Pm$$ is hashed point
• $$k =$$ random
• $$r = ka^{-1}$$
• $$z = e(G, G)$$
• $$s = z^kPm$$

Resign:

• $$r' = rk_{ab} * r = a/bP * ka^{-1} = k*1/b*G$$
• $$s' = s$$

Verification:

• $$t = e(bG, r) = e(G, G)^k = z^k$$
• Check $$tPm == s'$$
• Reviewing full scheme design is off-topic for this site. But you may break down specific components of the formula, and assumptions to make it on-topic. And the best way to get this started, I think, would be to annotate each step of your scheme with comments that explains what they achieves, both mathematically and security-wise/logically. Commented Feb 16, 2023 at 5:16
• e(aG, r) = z^k, So Anyone can generate a new signature via z^k . Commented Mar 8, 2023 at 3:30