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Your password is not kept on the browser, it is only used when logging into your account to decrypt the data in the encrypted state below.
{"success":true,"encrypted":"{\"pbkdf2_iterations\":\"10000\",\"payload\":\"3d0646083ac0ecc7945d5217d2dfd258b59969c13c82bb18b7351048cf510017s2GXQ5N/IQJ8ALd3T0s8549TidVDYkS2MEAwrnNP9qHifZrzoUDKkh+qf986bbChn2kr4+r0w99bILulCpMaaXppe9kLpcSKit+TN3+kIeo=\"}"}
When you switch to any other device, GalacticTrade provides you with the following encrypted data and asks you to prove your identity by decrypt it in your browser.
In case you lose your password, you can regain access to your account from any device with the "mnenomic" backup offered during registration or your "secret key" that you can access in Settings -> Security.