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## K.: Signatures for network coding (2006)

Venue: | In: International Journal on Information and Coding |

Citations: | 79 - 1 self |

### Citations

753 | Short signature from the Weil pairing
- Boneh, Lynn, et al.
- 2001
(Show Context)
Citation Context ...ther method by which an adversary can foil our system is by forging a signature. Our scheme for the signature is essentially the Aggregate Signature version of the Boneh-Lynn-Shacham signature scheme =-=[BLS04]-=-. In that paper it is shown that forging a signature is at least as hard as solving the so-called computational co-Diffie-Hellman problem on the elliptic curve. The only known way to solve this proble... |

489 | Network coding for large scale content distribution - GKANTSIDIS, P |

461 | Practical network coding - Chou, Wu, et al. - 2003 |

374 | Reducing elliptic curve logarithms to logarithms in a finite fields - Menezes, Okamoto, et al. - 1991 |

238 |
The Arithmetic of Elliptic Curves, Graduate Texts
- Silverman
- 1986
(Show Context)
Citation Context ...detecting pollution of packets. 2. Background on elliptic curves In this section we briefly review some facts about elliptic curves over finite fields, the reader should consult Chapters III and V of =-=[Sil86]-=- for proofs of the number theoretic claims. Let Fq be a finite field where q is a power of a prime relatively prime to 2 and 3. An elliptic curve E over Fq (sometimes abbreviated as E/Fq), is a projec... |

222 | Elliptic Curves over Finite Fields and Computation of Square Roots Mod - Schoof - 1985 |

202 | Elliptic curves and primality proving”, - Atkin, Morain - 1993 |

137 | On-the-fly verification of rateless erasure codes for efficient content distribution
- KROHN, FREEDMAN, et al.
(Show Context)
Citation Context ...upted if at least one of the incoming packets is corrupted. The question of how to prevent pollution attacks in the network coding scheme remained open and was the subject of the paper by Krohn et al =-=[KFM04]-=- in the generalized setting of rateless erasure codes (see also [GR06]). They show that a construction based on homomorphic hashing works to detect the polluted packets. This scheme, however, assumes ... |

122 | New explicit conditions of elliptic curve traces for FRreduction - Miyaji, Nakabayashi, et al. |

109 | Cooperative security for network coding file distribution
- GKANTSIDIS, P
(Show Context)
Citation Context ...n of how to prevent pollution attacks in the network coding scheme remained open and was the subject of the paper by Krohn et al [KFM04] in the generalized setting of rateless erasure codes (see also =-=[GR06]-=-). They show that a construction based on homomorphic hashing works to detect the polluted packets. This scheme, however, assumes that there is a separate secure channel which is used to transmit the ... |

99 | Incremental cryptography: the case of hashing and signing,”
- Bellare, Goldreich, et al.
- 1994
(Show Context)
Citation Context ...biri = 0? It is clear that the latter probability is 1 p . Thus with high probability we can solve for the discrete log of Q. One can also conclude the above proposition from the proof presented in =-=[BGG94]-=- (see Appendix A of that paper). The proof in that paper deals with finite fields but the argument applies equally well to the case of elliptic curves. We have shown that producing hash collisions in ... |

92 |
N.Koblitz, “The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm,”
- Balasubramanian
- 1998
(Show Context)
Citation Context ...t of order k in F∗p. 6 extension of F`. This is where the additional constraint that ` ≡ −1 mod p is used. Since ` ≡ −1 mod p the order of ` in F∗p is 2. Now a theorem of Koblitz-Balasubramanian (see =-=[BK98]-=-, Theorem 1) shows that in this case the entire p-torsion is defined over a degree 2 extension of the base field, in other words E[p] ⊆ E(F`2). Now we have an elliptic curve E/F` and we know that it h... |

71 |
Short programs for functions on curves. Unpublished manuscript
- Miller
- 1986
(Show Context)
Citation Context ...ate em(S, T ) in O(log2+ q) bit operations for all S, T in E[m]. If it is clear from the context we may drop the subscript m when writing em. The algorithm for computing em was proposed by Miller in =-=[Mil86]-=-. See the paper by Eisenträger et al ([ELM04]) for a description of Miller’s algorithm and also a deterministic variant for computing the square of the Weil pairing. 3. The signature scheme 3.1. Netw... |

62 | Constructing Elliptic Curves with Prescribed Embedding Degrees - Barreto, Lynn, et al. |

35 | Building scalable and robust peer-to-peer overlay networks for broadcasting using network coding,” - Jain, Lovasz, et al. - 2007 |

18 | Constructing elliptic curves with a known number of points over a prime field, High primes and misdemeanours: lectures in honour of the 60th birthday of H - Agashe, Lauter, et al. - 2004 |

10 | Algorithms in number theory, Handbook of Theoretical Computer Science Vol.A - Lenstra, Lenstra - 1971 |

8 | Improved Weil and Tate pairings for elliptic and hyperelliptic curves, Algorithmic Number Theory
- Eisenträger, Lauter, et al.
- 2004
(Show Context)
Citation Context ...r all S, T in E[m]. If it is clear from the context we may drop the subscript m when writing em. The algorithm for computing em was proposed by Miller in [Mil86]. See the paper by Eisenträger et al (=-=[ELM04]-=-) for a description of Miller’s algorithm and also a deterministic variant for computing the square of the Weil pairing. 3. The signature scheme 3.1. Network Coding. We briefly describe the standard n... |

1 |
K.; Computing modular polynomials, Lond
- Charles, Lauter
- 2005
(Show Context)
Citation Context .... 5.1. Finding a suitable elliptic curve. In general, if we have an elliptic curve E over a finite field K, then the p-torsion points are defined over an extension of degree Θ(p2) of the field K (see =-=[CL05]-=- Lemma 2.2). It is crucial for our scheme to have the p-torsion points defined over a small degree extension field so that the operations can be carried out in polynomial time. In this section we disc... |