Recently there has been a significant progress on the tower number field sieve (TNFS) method, reducing the complexity of the discrete logarithm problem (DLP) in finite field extensions of composite degree. These new variants of the TNFS attacks have a major impact on pairing-based cryptography and particularly on the selection of the underlying elliptic curve groups and extension fields. In this paper we revise the criteria for selecting pairing-friendly elliptic curves considering these new TNFS attacks in finite extensions of composite embedding degree. Additionally we update the criteria for finite extensions of prime degree in order to meet today’s security requirements
