# Further Observations on SIMON and SPECK Block Cipher Families

## Abstract

**:**

## 1. Introduction

## 2. Preliminary Notations and Definitions

## 3. Linear and Differential Properties of SIMON

**Theorem**

**1.**

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Remark**

**1.**

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Remark**

**2.**

## 4. Linear and Differential Properties of SPECK

**Theorem**

**5.**

**Theorem**

**6.**

**Remark**

**3.**

**Remark**

**4.**

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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x | $\mathit{Varibits}$ | $\mathit{Doublebits}$ | $\mathit{Varibits}\oplus \mathit{Doublebits}$ | $\mathit{Adjacent}\phantom{\rule{0.166667em}{0ex}}\mathit{Parity}:\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathit{x}\oplus {\mathit{S}}^{1}\left(\mathit{x}\right)$ |
---|---|---|---|---|

0 | 0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 | 0 |

2 | 1 | 0 | 1 | 1 |

3 | 1 | 0 | 1 | 1 |

4 | 1 | 0 | 1 | 1 |

5 | 1 | 1 | 0 | 1 |

6 | 1 | 0 | 1 | 0 |

7 | 1 | 0 | 1 | 0 |

r | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

${\mathcal{N}}_{d}\left(r\right)$ | 0 | 16 | 32 | 152 | 432 | 1216 | 2960 | 6318 |

${\mathcal{N}}_{l}\left(r\right)$ | 0 | 32 | 416 | 2816 | 10,560 | 21,504 | 21,504 | 8192 |

$\mathit{r}$ | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |

${\mathcal{N}}_{d}\left(r\right)$ | 411,472 | 16,320 | 15,344 | 8344 | 2496 | 400 | 32 | |

${\mathcal{N}}_{l}\left(r\right)$ | 510 | 0 | 0 | 0 | 0 | 0 | 0 |

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Dehnavi, S.M.
Further Observations on SIMON and SPECK Block Cipher Families. *Cryptography* **2019**, *3*, 1.
https://doi.org/10.3390/cryptography3010001

**AMA Style**

Dehnavi SM.
Further Observations on SIMON and SPECK Block Cipher Families. *Cryptography*. 2019; 3(1):1.
https://doi.org/10.3390/cryptography3010001

**Chicago/Turabian Style**

Dehnavi, Seyed Mojtaba.
2019. "Further Observations on SIMON and SPECK Block Cipher Families" *Cryptography* 3, no. 1: 1.
https://doi.org/10.3390/cryptography3010001