I'm studying Lightning network and I use c-lightning. I can Get a new address with newaddr method, but I can't find private key. My address is bcrt1qmckts70jsq2u5886lgcq2yn7xjmp97t09zlrg, how can I retrieve it's public key? Where Can I find it's private key?

$ bitcoin-cli validateaddress bcrt1qmckts70jsq2u5886lgcq2yn7xjmp97t09zlrgj                                                              │
{                                                                                                                                       │
  "isvalid": true,                                                                                                                      │
  "address": "bcrt1qmckts70jsq2u5886lgcq2yn7xjmp97t09zlrgj",                                                                            │
  "scriptPubKey": "0014de2cb879f28015ca1cfafa3005127e34b612f96f",                                                                       │
  "isscript": false,                                                                                                                    │
  "iswitness": true,                                                                                                                    │
  "witness_version": 0,                                                                                                                 │
  "witness_program": "de2cb879f28015ca1cfafa3005127e34b612f96f"                                                                         │

lightningd doesn't offer simple RPC commands to dump keys.

If you really need to access the keys the simplest way would be to derive them directly from the hsm_secret.

Keys for onchain transactions (since you mentioned newaddr. The other derivations are more involved) are derived using BIP32 unhardened derivation from m/0/0.
The root seed is derived from the hsm_secret with :

root_seed = hkdf_sha256(hsm_secret, salt=NULL, info="bip32 seed")

There exist tools such as the hsmtools (which currently only derive keys for the commitment transactions but might be extended in the furure) or jb55's clightning-dumpkeys which take care of the derivation for you.

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