Ensuring the efficiency of snark proving involves matching the fields of definition for arithmetic and snark computation. The mismatch between these fields can lead to inefficiencies. One solution is to find two elliptic curves where the statement elliptic is defined over the field used for snark computation. This issue has occurred in various curve implementations like Japetto, Zexe, MNT4, and MNT6. Ideally, finding a cycle allows using one elliptic curve for both statement and snark elliptical, but for efficiency or specific applications, using separate curves is preferred. Recursion can be applied for this purpose and other scenarios.

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