TeslaCrypt is “Crypto” malware that belongs to a family of malware that encrypts the compromised user files and adds the .ecc and .ezz extensions to the end of the encrypted file.
For more information on TeslaCrypt, characteristics, and mitigation, see the threat advisory (https://kc.mcafee.com/corporate/index?page=content&id=PD25854).
For more resources, visit the ServicePortal and search for Malware related content. Also visit the VSE Community at https://community.mcafee.com/community/business/system/vse.
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TeslaCrypt has been discontinued. It appears to have been replaced or superseded by CryptXXX.
The developers have announced the end of TeslaCrypt and have made the Master Decryption Key publicly available. There is a program (TeslaDecoder) which should be able to decrypt most or all of the files encrypted by this ransomware.
See for a screenshot, and a link to the BleepingComputer article which gives instructions on using TeslaDecoder.