Private Right of Action Against Theft of Trade Secrets Act of 2013 - Amends the Economic Espionage Act of 1996 to authorize any person who suffers injury by reason of a violation of prohibitions against the theft of trade secrets to maintain a civil action against the violator for appropriate compensatory damages and injunctive or other equitable relief.

Prohibits such an action unless it is begun within two years of the date of the act complained of or the date of the discovery of the damage.

Declares that the phrase "without authorization" in such Act's prohibitions shall not mean independent derivation or working backwards from a lawfully obtained known product or service to divine the process which aided its development or manufacture.