Paper 2011/570
Degree of regularity for HFE
Jintai Ding and Thorsten Kleinjung
Abstract
In this paper, we prove a closed formula for the degree of regularity of the family of HFE (HFE Minus) multivariate public key cryptosystems over a finite field of size $q$. The degree of regularity of the polynomial system derived from an HFE system is less than or equal to \begin{eqnarray*} \frac{(q1)(\lfloor \log_q(D1)\rfloor +a)}2 +2 & & \text{if $q$ is even and $r+a$ is odd,} \\ \frac{(q1)(\lfloor \log_q(D1)\rfloor+a+1)}2 +2 & & \text{otherwise.} \end{eqnarray*} Here $q$ is the base field size, $D$ the degree of the HFE polynomial, $r=\lfloor \log_q(D1)\rfloor +1$ and $a$ is the number of removed equations (Minus number). This allows us to present an estimate of the complexity of breaking the HFE Challenge 2: \vskip .1in \begin{itemize} \item the complexity to break the HFE Challenge 2 directly using algebraic solvers is about $2^{96}$. \end{itemize}
Metadata
 Available format(s)
 Category
 Publickey cryptography
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 multivariatedegree of regularity
 Contact author(s)
 jintai ding @ gmail com
 History
 20111025: received
 Short URL
 https://ia.cr/2011/570
 License

CC BY
BibTeX
@misc{cryptoeprint:2011/570, author = {Jintai Ding and Thorsten Kleinjung}, title = {Degree of regularity for {HFE}}, howpublished = {Cryptology ePrint Archive, Paper 2011/570}, year = {2011}, note = {\url{https://eprint.iacr.org/2011/570}}, url = {https://eprint.iacr.org/2011/570} }