## The Stability Theory of Stream CiphersSecure message transmission is of extreme importance in today's information-based society. Stream encryption is a practically important means to this end. This monograph is devoted to a new aspect of stream ciphers, namely the stability theory of stream ciphers, with the purpose of developing bounds on complexity which can form part of the basis for a general theory of data security and of stabilizing stream-cipher systems. The approach adopted in this monograph is new. The topic is treated by introducing measure indexes on the security of stream ciphers, developing lower bounds on these indexes, and establishing connections among them. The treatment involves the stability of boolean functions, the stability of linear complexity of key streams, the period stability of key streams, and the stability of source codes. Misleading ideas about stream ciphers are exposed and new viewpoints presented. The numerous measure indexes and bounds on them that are introduced here, the approach based on spectrum techniques, andthe ten open problems presented will all be useful to the reader concerned with analyzing and designing stream ciphers for securing data. |

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### Contents

I | 1 |

II | 5 |

III | 7 |

IV | 8 |

V | 10 |

VI | 13 |

VIII | 15 |

IX | 17 |

XXV | 100 |

XXVI | 105 |

XXVII | 108 |

XXVIII | 117 |

XXIX | 120 |

XXX | 121 |

XXXI | 125 |

XXXII | 130 |

X | 29 |

XI | 30 |

XIII | 33 |

XIV | 35 |

XV | 41 |

XVI | 48 |

XVII | 53 |

XVIII | 61 |

XIX | 81 |

XX | 82 |

XXI | 85 |

XXII | 88 |

XXIII | 89 |

XXIV | 95 |

XXXIII | 131 |

XXXIV | 135 |

XXXV | 138 |

XXXVI | 139 |

XXXVII | 143 |

XXXVIII | 146 |

XXXIX | 153 |

XL | 159 |

XLI | 162 |

XLII | 169 |

XLIII | 172 |

XLIV | 176 |

XLV | 180 |

### Other editions - View all

The Stability Theory of Stream Ciphers Cunsheng Ding,Guozhen Xiao,Weijuan Shan No preview available - 2014 |

### Common terms and phrases

additive stream cipher BAA attack bent functions Berlekamp-Massey algorithm best affine approximation binary additive stream binary ML-sequence binary sequences Boolean function cipher of Fig ciphertext clock-controlled complexity and sphere complexity of binary complexity of sequences correlation immunity correlation-immune cryptographic cryptology denotes Ding divides driving LFSR feedback polynomial filter function finite state machine follows from Lemma follows from Theorem GF(q Hamming weight Hence irreducible polynomial key stream LFSR linear complexity linear-complexity stability lower bounds Massey's algorithm measure indexes minimal polynomial nonlinear order Noticing Open Problem output sequence periodic sequence periodic with period plaintext plexity positive integer probability of agreement Proceedings Proof prove quence reciprocal polynomial Research Report Ruep 86 Rueppel running key Section sequence of period sequences with period shortest LFSR SML function source code sphere complexity stability of linear vector Walsh transforms weight complexity weight period WH(w Xiao XIDU