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In 2017 Kyung-Ah Shim et al proposed a multivariate signature scheme called Himq-3 which is a submission to National Institute of Standards and Technology (NIST) standardization process of post-quantu...
Non-commutative cryptography studies cryptographic primitives and systems which are based on algebraic structures like groups, semigroups and noncommutative rings. We con-tinue to investigate inverse ...
Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups and non-commutative rings. Its inter-section with Multivariate cryptography contains...
The Multivariate Ring Learning with Errors (mm-RLWE) problem was introduced in 2015 by Pedrouzo-Ulloa, Troncoso-Pastoriza and Pérez-González. Instead of working over a polynomial residue ring with one...
Homomorphic encryption schemes allow to perform computations over encrypted data. In schemes based on RLWE assumption the plaintext data is a ring polynomial. In many use cases of homomorphic encrypti...
One of the most efficient post-quantum signature schemes is Rainbow whose harness is based on the multivariate quadratic polynomial (MQ) problem. ELSA, a new multivariate signature scheme proposed at ...
In this work we analyze the security of cubic cryptographic constructions with respect to rank weakness. We detail how to extend the big field idea from quadratic to cubic, and show that the same rank...
In August 2015 the cryptographic world was shaken by a sudden and surprising announcement by the US National Security Agency (NSA) concerning plans to transition to post-quantum algorithms. Since this...
Asymptotically faster quantum algorithms to solve multivariate quadratic equations.
We present here new multivariate schemes that can be seen as HFE generalization having a property called `Two-Face'. Particularly, we present five such families of algorithms named `Dob', `Simple Pat'...
Multivariate Public Key Cryptography is a leading option for security in a post quantum society. In this paper we propose a new encryption scheme, EFLASH, and analyze its efficiency and security.
The security of several post-quantum cryptosystems is based on the assumption that solving a system of multivariate (quadratic) polynomial equations p1=⋯=pm=0p1=⋯=pm=0 over a finite field ...
Total Break of the Fully Homomorphic Multivariate Encryption Scheme of 2017/458: Decryption can not be of low degree.
Efficient and secure third party computation has many practical applications in cloud computing. We develop new approach for building fully homomorphic encryption (FHE) schemes, by starting with the i...
Previously I proposed fully homomorphic public-key encryption (FHPKE) based on discrete logarithm problem which is vulnerable to quantum computer attacks. In this paper I propose FHPKE based on multiv...

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