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Fast Quantum Algorithm for Solving Multivariate Quadratic Equations
NSA Solving Multivariate Quadratic Equations
2017/12/25
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
FXL Grover reversibility
2017/12/19
Asymptotically faster quantum algorithms to solve multivariate quadratic equations.
Generic Zero-Knowledge and Multivariate Quadratic Systems
zero-knowledge proof post-quantum signature
2016/12/29
Zero-knowledge proofs are a core building block for a broad range of cryptographic protocols. This paper introduces a generic zero-knowledge proof system capable of proving the correct computation of ...
MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems
post-quantum cryptography multivariate public-key cryptosystem MQ problem
2016/1/3
Multivariate Quadratic polynomial (MQ) problem serve as the basis of security
for potentially post-quantum cryptosystems. The hardness of solving MQ problem depends
on a number of parameters, most i...
Generating S-Box Multivariate Quadratic Equation Systems And Estimating Algebraic Attack Resistance Aided By SageMath
polynomial quotient ring SAT solver Rijndael AES
2015/12/29
Methods are presented to derive with the aid of the computer
mathematics software system SageMath the Multivariate Quadratic
equation systems (MQ) for the input and output bit variables of a
crypto...
Extension Field Cancellation: a New Central Trapdoor for Multivariate Quadratic Systems
MQ multivariate quadratic public-key
2015/12/18
This paper introduces a new central trapdoor for multivariate quadratic (MQ)
public-key cryptosystems that allows for encryption, in contrast to time-tested MQ primitives
such as Unbalanced Oil and ...
Practical Cryptanalysis of a Public-Key Encryption Scheme Based on New Multivariate Quadratic Assumptions
cryptanalysis lattice techniques
2014/3/11
In this paper, we investigate the security of a public-key encryption scheme introduced by Huang, Liu and Yang (HLY) at PKC’12. This new scheme can be provably reduced to the hardness of solving a set...
Small Public Keys and Fast Verification for Multivariate Quadratic Public Key Systems
implementation / MQ Multivariate Quadratic UOV Unbalanced Oil and Vinegar
2012/3/28
Security of public key schemes in a post-quantum world is a challenging task---as both RSA and ECC will be broken then. In this paper, we show how post-quantum signature systems based on Multivariate ...
Small Public Keys and Fast Verification for Multivariate Quadratic Public Key Systems
MQ, Multivariate Quadratic UOV Unbalanced Oil and Vinegar
2011/6/9
Security of public key schemes in a post-quantum world is a challenging task---as both RSA and ECC will be broken then. In this paper, we show how post-quantum signature systems based on Multivariate ...
A New Scheme for Zero Knowledge Proof based on Multivariate Quadratic Problem and Quaternion Algebra
Multivariate Quadratic Quaternion Zero Knowledge Proof Authentication
2010/2/20
This paper introduces a new intractable security problem whose
intractability is due to the NP completeness of multivariate quadratic problem. This
novel problem uses quaternion algebra in conjuncti...
Algorithms to solve massively under-defined systems of multivariate quadratic equations
under-defined multivariate quadratic equations oil and vinegar signature scheme
2009/6/12
It is well known that the problem to solve a set of randomly chosen multivariate
quadratic equations over a finite field is NP-hard. However, when the number of
variables is much larger than the num...
A Public Key Block Cipher Based on Multivariate Quadratic Quasigroups
Public Key Cryptosystems Fast signature generation Multivariate Quadratic Polynomials
2009/6/5
We have designed a new class of public key algorithms based on quasigroup string trans-
formations using a specific class of quasigroups called multivariate quadratic quasigroups (MQQ). Our
public k...
Super°uous Keys in Multivariate Quadratic Asymmetric Systems
Multivariate Quadratic Equations Public Key Schemes Equivalent Keys
2009/4/3
In this article, we show that public key schemes based on multivariate
quadratic equations allow many equivalent, and hence super°uous private
keys. We achieve this result by investigating several t...
Applications of Multivariate Quadratic Public Key Systems
Multivariate Quadratic Equations Public Key Schemes Applications
2009/3/31
The original version was published in Sicherheit 2005: Sicherheit —Schutz und
Zuverl¨assigkeit, Beitr¨age der 2. Jahrestagung des Fachbereichs Sicherheit der
Gesellschaft f¨ur Informatik e.v. (GI), ...
Equivalent Keys in Multivariate Quadratic Public Key Systems
Public Key signature Hidden Field Equations Stepwise Triangular Systems
2009/3/19
Multivariate Quadratic public key schemes have been suggested back in 1985 by Matsumoto
and Imai as an alternative for the RSA scheme. Since then, several other schemes have
been proposed, for examp...