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Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully preserving the discrete logarithm $s$ between the two such as $F=s×O$.

The most well know example is moving elliptic curves into hyperelliptic curves but as far I’m aware this only work on extension fields of medium sized degree (and not over prime field). But of course, I’m more interested in curve over prime fields.
As an example outside hyperelliptic curve, is there a case that consider building a different curve defined on a field from different characteristic while preserving the same order in a subgroup ?

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully preserving the discrete logarithm between the two.

The most well know example is moving elliptic curves into hyperelliptic curves but as far I’m aware this only work on extension fields of medium sized degree (and not over prime field). But of course, I’m more interested in curve over prime fields.
As an example outside hyperelliptic curve, is there a case that consider building a different curve defined on a field from different characteristic while preserving the same order in a subgroup ?

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully preserving the discrete logarithm $s$ between the two such as $F=s×O$.

The most well know example is moving elliptic curves into hyperelliptic curves but as far I’m aware this only work on extension fields of medium sized degree (and not over prime field). But of course, I’m more interested in curve over prime fields.
As an example outside hyperelliptic curve, is there a case that consider building a different curve defined on a field from different characteristic while preserving the same order in a subgroup ?

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user2284570
user2284570
  • 87
  • 8

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully preserving theirthe discrete logarithm relationbetween the two.

The most well know example is moving elliptic curves into hyperelliptic curves but as far I’m aware this only work on extension fields of medium sized degree (and not over prime field). But of course, I’m more interested in curve over prime fields.
As an example outside hyperelliptic curve, is there a case that consider building a different curve defined on a field from different characteristic while preserving the same order in a subgroup ?

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully preserving their discrete logarithm relation.

The most well know example is moving elliptic curves into hyperelliptic curves but as far I’m aware this only work on extension fields of medium sized degree (and not over prime field). But of course, I’m more interested in curve over prime fields.
As an example outside hyperelliptic curve, is there a case that consider building a different curve defined on a field from different characteristic while preserving the same order in a subgroup ?

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully preserving the discrete logarithm between the two.

The most well know example is moving elliptic curves into hyperelliptic curves but as far I’m aware this only work on extension fields of medium sized degree (and not over prime field). But of course, I’m more interested in curve over prime fields.
As an example outside hyperelliptic curve, is there a case that consider building a different curve defined on a field from different characteristic while preserving the same order in a subgroup ?

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user2284570
user2284570
  • 87
  • 8

State of the art on attempts to solve the elliptic curve discrete logarithm problem through transfering the problem to a weaker curve

Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully preserving their discrete logarithm relation.

The most well know example is moving elliptic curves into hyperelliptic curves but as far I’m aware this only work on extension fields of medium sized degree (and not over prime field). But of course, I’m more interested in curve over prime fields.
As an example outside hyperelliptic curve, is there a case that consider building a different curve defined on a field from different characteristic while preserving the same order in a subgroup ?