## QUAD

swMATH ID: | 19553 |

Software Authors: | Berbain, Côme; Gilbert, Henri; Patarin, Jacques |

Description: | QUAD: A multivariate stream cipher with provable security. We present the stream cipher QUAD and the provable security arguments supporting its conjectured strength for suitable parameter values. QUAD was first proposed at Eurocrypt 2006 by {it C. Berbain} et al. [in: Advances in cryptology – EUROCRYPT 2006. 25th annual international conference on the theory and applications of cryptographic techniques, St. Petersburg, Russia, May 28 – June 1, 2006. Proceedings. Berlin: Springer. Lecture Notes in Computer Science 4004, 109–128 (2006; Zbl 1140.94322)]. It relies on the iteration of a set of multivariate quadratic polynomials over a finite field, typically GF(2) or a small extension. We show that in the binary case, the security of the keystream generation can be related, in the concrete security model, to the conjectured intractability of the MQ problem of solving a random system of m equations in n unknowns. We show furthermore that this security reduction can be extended to incorporate the key and IV setup and provide a security argument related to the whole stream cipher. We also briefly address software and hardware performance issues and show that if one is willing to pseudo-randomly generate the sets of quadratic polynomials underlying the cipher, this leads to surprisingly inexpensive hardware implementations of QUAD. |

Homepage: | http://www.sciencedirect.com/science/article/pii/S0747717108001831?via%3Dihub |

Keywords: | MQ problem; stream cipher; provable security; Gr”obner basis computation |

Related Software: | McEliece; eSTREAM; ZHFE; CUDA; SNOW; Scream; SWIFFT; SWATT; fhe; SageMath; MXL3; NIST Statistical Test Suite; LEX; Diehard; Grain; Trivium; FGb |

Referenced in: | 15 Publications |

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### Referenced by 40 Authors

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### Referenced in 6 Serials

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### Referenced in 6 Fields

15 | Information and communication theory, circuits (94-XX) |

3 | Number theory (11-XX) |

2 | Computer science (68-XX) |

2 | Quantum theory (81-XX) |

1 | Commutative algebra (13-XX) |

1 | Systems theory; control (93-XX) |