**On the Disadvantages of Pairing-based Cryptography**

*Zhengjun Cao and 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.

**Category / Keywords: **foundations / elliptic curve cryptography; bilinear-pairing based cryptography; inputting parameters; working parameters; embedding degree

**Date: **received 3 Feb 2015, last revised 14 Feb 2015

**Contact author: **liulh at shmtu edu cn

**Available format(s): **PDF | BibTeX Citation

**Version: **20150215:030037 (All versions of this report)

**Short URL: **ia.cr/2015/084

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