Suppose there's a secret value x, an elliptic curve with the (public) generator G, and a sequence of secret values a1, a2, ..., an. The attacker knows the results of the following expressions: a1*x*G, a2*x*G, ..., an*x*G.

Is there any known weakness that'd allow the attacker to restore x based on this information? Maybe if n is becoming large enough (say, thousands/millions)? (To clarify: The attacker can not control the choice of a1...an.)

  • $\begingroup$ What is the source of this question? Anybody can create these points even with the knowledge of $a_i$. So what is the point of making them secret? $\endgroup$ – kelalaka Dec 23 '20 at 0:16

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