How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
How to construct random functions
Journal of the ACM (JACM)
A simple unpredictable pseudo random number generator
SIAM Journal on Computing
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Asymmetric cryptography with S-Boxes
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
An Improved Pseudo-random Generator Based on Discrete Log
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Solving Underdefined Systems of Multivariate Quadratic Equations
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Cryptanalysis of Stream Ciphers with Linear Masking
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
An efficient pseudo-random generator provably as secure as syndrome decoding
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
About the XL algorithm over GF(2)
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Compact FPGA implementations of QUAD
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
Multivariates Polynomials for Hashing
Information Security and Cryptology
Syndrome Based Collision Resistant Hashing
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Security Analysis of Multivariate Polynomials for Hashing
Information Security and Cryptology
An efficient forward private RFID protocol
Proceedings of the 16th ACM conference on Computer and communications security
More efficient DDH pseudorandom generators
Designs, Codes and Cryptography
Dial C for cipher: le chiffrement était presque parfait
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Efficient implementations of multivariate quadratic systems
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
On building hash functions from multivariate quadratic equations
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Analysis of multivariate hash functions
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
Cryptanalysis of the TRMS signature scheme of PKC'05
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Lightweight privacy preserving authentication for RFID using a stream cipher
FSE'10 Proceedings of the 17th international conference on Fast software encryption
Fast exhaustive search for polynomial systems in F2
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
ACISP'10 Proceedings of the 15th Australasian conference on Information security and privacy
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
On the provable security of an efficient RSA-Based pseudorandom generator
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
KFC - The Krazy Feistel Cipher
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Searching for compact algorithms: CGEN
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
General fault attacks on multivariate public key cryptosystems
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Public-Key identification schemes based on multivariate cubic polynomials
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Public-Key cryptography from new multivariate quadratic assumptions
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
On the security of IV dependent stream ciphers
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
Perfect block ciphers with small blocks
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
On the complexity of solving quadratic Boolean systems
Journal of Complexity
Zero-Knowledge for multivariate polynomials
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Linear recurring sequences for the UOV key generation revisited
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
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We introduce a practical stream cipher with provable security named QUAD. The cipher relies on the iteration of a multivariate quadratic system of m equations in n m unknowns over a finite field. The security of the keystream generation of QUAD is provably reducible to the conjectured intractability of the MQ problem, namely solving a multivariate system of quadratic equations. Our recommended version of QUAD uses a 80-bit key, 80-bit IV and an internal state of n = 160 bits. It outputs 160 keystream bits (m = 320) at each iteration until 240 bits of keystream have been produced.