Title, Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization. Booktitle, Advances in Cryptology – CRYPTO ’99, 19th Annual International. Download Citation on ResearchGate | Cryptanalysis of the HFE Public Key Finally, we develop a new relinearization method for solving such systems for any. Finally, we develop a new relinearization method for solving such systems for any constant ffl? Cryptanalysis of the HFE Public Key Cryptosystem ().

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We first review the basic idea of known attacks and then illustrate why the proposal is secure against these attacks.

Introduction Public key cryptography [ 1 ] built from the NP-hardness of solving multivariate quadratic equations over finite filed [ 23 ] was conceived as a plausible candidate to traditional factorization and discrete logarithm based public key cryptosystems due to its high performance and the resistance to quantum attacks [ 4 ].

So the HFE scheme is secure against linearization equations attack.

We analyze the security of the proposed HFE modified encryption scheme. So the adversary cannot derive from the publicly known map a kwy matrix. Retrieved from ” https: So the computational overhead is about bit operations.

Then two invertible affine transformations are applied to hide the special structure of the central map [ 25 ]. Let be a -order finite field with being a prime power.

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In certain cases those polynomials could be defined over both a ground and an extension field. We impose some restrictions on the plaintext space and can use the restriction to merge the coefficients of the linear part and the cryptoshstem part.

Please help improve this section by adding citations to reliable sources. Therefore, we cannot hope to derive linearization equations from the modified Xryptosystem scheme. The HFE scheme firstly defines a univariate map over an extension field: Considering the aforementioned discussions, we suggest choosing and.

Security We analyze the security of the publoc HFE modified encryption scheme. That’s why those schemes are often considered to be good candidates for post-quantum cryptography. Multivariate Quadratics involves a public and a private key. If we fail to derive a vector in form all the preimageswe output the symbol designating an invalid ciphertext. We define the quadratic part of asnamely, forNote that can be expressed as homogeneous quadratic polynomials over the base field ; then the application of two linear transformations on the input and output of will also yb homogeneous quadratic polynomials over the base field.

Conflicts of Interest The authors declare that they have no conflicts of interest.

Overall, the situation is now more stable and the strongest schemes have withstood the test of time. From Wikipedia, the free encyclopedia. So we define Now we show that the corresponding matrix is of not necessarily low rank.

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CiteSeerX — Cryptanalysis of the HFE Public Key Cryptosystem

So the proposed scheme reduces the public key size by bits. Notations Let be a -order finite field with being a prime power.

By setting we can express as bilinear equations about input and output of function: Suggested Parameters Considering the aforementioned discussions, we suggest choosing and. Signatures are generated using the private key and are verified using the public key as follows. Multivariate cryptography has been very productive in terms of design and cryptanalysis. The proposed HFE modification has the following features: Thus by solving the Cryptanqlysis problem we can determine the matrix and the coefficients of the linear transformation.

Multivariate cryptography

So both schemes have the same secret key sizes and decryption costs. If we lift to the extension field and find that the corresponding matrix is not of low rank, we can claim our proposal is secure against the MinRank attack [ 78 ]. However, the rank of the matrix is unknown, and hence the rank of the matrix is not relijearization low.

Last modified: February 10, 2020