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Title:
On the Disadvantages of Pairing-based Cryptography
Authors: Zhengjun Cao, Lihua Liu
Abstract:Pairing-based cryptography (PBC) has many elegant properties. It is claimed that PBC can offer a desired security level with smaller parameters as the general elliptic curve cryptography (ECC). In the note, we remark that this view is misleading. Suppose that an elliptic curve E is defined over the field F_q. Then ECC is working with elements which are defined over F_q. But PBC is working with the functions and elements defined over F_{q^k}, where k is the embedding degree. The security of PBC depends directly on the intractable level of either elliptic curve discrete log problem (ECDLP) in the group E(F_q) or discrete log problem (DLP) in the group F_{q^k}^*. That means PBC protocols have to work in a running environment with parameters of 1024 bits so as to offer 80 bits security level. The shortcoming makes PBC lose its competitive advantages significantly.
ePrint: https://eprint.iacr.org/2015/084
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