Such a government backed currency would be a variation on the current model of Bitcoin related Cryptocurrencies. It is difficult to see a country permitting independent mining of such a currency, or allowing a currency to circulate free of its control. The reason the gold standard was abandoned was the inability of central banks to ensure a degree of control over relative value. That freedom from control is the essential attribute of Cryptocurrencies as an asset, and is what makes them attractive. Any government backed cryptocurrency would essentially be a trackable medium of exchange, rather than the tradable assets we now see.