Paper 2015/084

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.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
elliptic curve cryptographybilinear-pairing based cryptographyinputting parametersworking parametersembedding degree
Contact author(s)
liulh @ shmtu edu cn
History
2015-02-15: revised
2015-02-14: received
See all versions
Short URL
https://ia.cr/2015/084
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/084,
      author = {Zhengjun Cao and Lihua Liu},
      title = {On the Disadvantages of Pairing-based Cryptography},
      howpublished = {Cryptology ePrint Archive, Paper 2015/084},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/084}},
      url = {https://eprint.iacr.org/2015/084}
}
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