### Abstract

A cryptographic primitive is leakage-resilient, if it remains secure even if an adversary can learn a bounded amount of arbitrary information about the computation with every invocation. As a consequence, the physical implementation of a leakage-resilient primitive is secure against every side-channel as long as the amount of information leaked per invocation is bounded. In this paper we prove positive and negative results about the feasibility of constructing leakage-resilient pseudorandom functions and permutations (i.e. block-ciphers). Our results are three fold: 1. We construct (from any standard PRF) a PRF which satisfies a relaxed notion of leakage-resilience where (1) the leakage function is fixed (and not adaptively chosen with each query.) and (2) the computation is split into several steps which leak individually (a "step" will be the invocation of the underlying PRF.) 2. We prove that a Feistel network with a super-logarithmic number of rounds, each instantiated with a leakage-resilient PRF, is a leakage resilient PRP. This reduction also holds for the non-adaptive notion just discussed, we thus get a block-cipher which is leakage-resilient (against non-adaptive leakage). 3. We propose generic side-channel attacks against Feistel networks. The attacks are generic in the sense that they work for any round functions (e.g. uniformly random functions) and only require some simple leakage from the inputs to the round functions. For example we show how to invert an r round Feistel network over 2n bits making 4•(n+1) ^{r-2} forward queries, if with each query we are also given as leakage the Hamming weight of the inputs to the r round functions. This complements the result from the previous item showing that a super-constant number of rounds is necessary.

Original language | English (US) |
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Title of host publication | Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings |

Pages | 21-40 |

Number of pages | 20 |

Volume | 6223 LNCS |

DOIs | |

State | Published - 2010 |

Event | 30th Annual International Cryptology Conference, CRYPTO 2010 - Santa Barbara, CA, United States Duration: Aug 15 2010 → Aug 19 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 6223 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 30th Annual International Cryptology Conference, CRYPTO 2010 |
---|---|

Country | United States |

City | Santa Barbara, CA |

Period | 8/15/10 → 8/19/10 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings*(Vol. 6223 LNCS, pp. 21-40). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6223 LNCS). https://doi.org/10.1007/978-3-642-14623-7_2

**Leakage-resilient pseudorandom functions and side-channel attacks on feistel networks.** / Dodis, Yevgeniy; Pietrzak, Krzysztof.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings.*vol. 6223 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6223 LNCS, pp. 21-40, 30th Annual International Cryptology Conference, CRYPTO 2010, Santa Barbara, CA, United States, 8/15/10. https://doi.org/10.1007/978-3-642-14623-7_2

}

TY - GEN

T1 - Leakage-resilient pseudorandom functions and side-channel attacks on feistel networks

AU - Dodis, Yevgeniy

AU - Pietrzak, Krzysztof

PY - 2010

Y1 - 2010

N2 - A cryptographic primitive is leakage-resilient, if it remains secure even if an adversary can learn a bounded amount of arbitrary information about the computation with every invocation. As a consequence, the physical implementation of a leakage-resilient primitive is secure against every side-channel as long as the amount of information leaked per invocation is bounded. In this paper we prove positive and negative results about the feasibility of constructing leakage-resilient pseudorandom functions and permutations (i.e. block-ciphers). Our results are three fold: 1. We construct (from any standard PRF) a PRF which satisfies a relaxed notion of leakage-resilience where (1) the leakage function is fixed (and not adaptively chosen with each query.) and (2) the computation is split into several steps which leak individually (a "step" will be the invocation of the underlying PRF.) 2. We prove that a Feistel network with a super-logarithmic number of rounds, each instantiated with a leakage-resilient PRF, is a leakage resilient PRP. This reduction also holds for the non-adaptive notion just discussed, we thus get a block-cipher which is leakage-resilient (against non-adaptive leakage). 3. We propose generic side-channel attacks against Feistel networks. The attacks are generic in the sense that they work for any round functions (e.g. uniformly random functions) and only require some simple leakage from the inputs to the round functions. For example we show how to invert an r round Feistel network over 2n bits making 4•(n+1) r-2 forward queries, if with each query we are also given as leakage the Hamming weight of the inputs to the r round functions. This complements the result from the previous item showing that a super-constant number of rounds is necessary.

AB - A cryptographic primitive is leakage-resilient, if it remains secure even if an adversary can learn a bounded amount of arbitrary information about the computation with every invocation. As a consequence, the physical implementation of a leakage-resilient primitive is secure against every side-channel as long as the amount of information leaked per invocation is bounded. In this paper we prove positive and negative results about the feasibility of constructing leakage-resilient pseudorandom functions and permutations (i.e. block-ciphers). Our results are three fold: 1. We construct (from any standard PRF) a PRF which satisfies a relaxed notion of leakage-resilience where (1) the leakage function is fixed (and not adaptively chosen with each query.) and (2) the computation is split into several steps which leak individually (a "step" will be the invocation of the underlying PRF.) 2. We prove that a Feistel network with a super-logarithmic number of rounds, each instantiated with a leakage-resilient PRF, is a leakage resilient PRP. This reduction also holds for the non-adaptive notion just discussed, we thus get a block-cipher which is leakage-resilient (against non-adaptive leakage). 3. We propose generic side-channel attacks against Feistel networks. The attacks are generic in the sense that they work for any round functions (e.g. uniformly random functions) and only require some simple leakage from the inputs to the round functions. For example we show how to invert an r round Feistel network over 2n bits making 4•(n+1) r-2 forward queries, if with each query we are also given as leakage the Hamming weight of the inputs to the r round functions. This complements the result from the previous item showing that a super-constant number of rounds is necessary.

UR - http://www.scopus.com/inward/record.url?scp=77956996186&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956996186&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14623-7_2

DO - 10.1007/978-3-642-14623-7_2

M3 - Conference contribution

AN - SCOPUS:77956996186

SN - 3642146228

SN - 9783642146220

VL - 6223 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 21

EP - 40

BT - Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings

ER -