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    $\begingroup$ Are you asking using Grover's Against FrodoKem or Against the symmetric key encryption that FrodoKem produced? What symmetric encryption is under usage after FrodoKem? Consider it like RSA-KEM ( Key Encapsulation Mechanism) + AES-GCM (Data Encapsulation Mechanism (DEM)). Grover will beat AES-128 in a near future but not AES-256. $\endgroup$
    – kelalaka
    Commented Nov 12, 2021 at 12:29
  • $\begingroup$ Thank you @kelalaka. What about breaking FrodoKEM it self? Is it possible with Grover's algorithm? $\endgroup$
    – C.S.
    Commented Nov 12, 2021 at 12:40
  • $\begingroup$ Of course it is not clear that how one can run the $\sqrt{2^n}$ Grover Oracles calls in the real life. What is the cost of ( timexmoney ) of preparing the next Oracle... $\endgroup$
    – kelalaka
    Commented Nov 12, 2021 at 12:51
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    $\begingroup$ A simple Grover time analysis is here and the parallel Grover machine inefficiency is here $\endgroup$
    – kelalaka
    Commented Nov 12, 2021 at 14:46