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### Citations

528 | Establishing Pairwise Keys in Distributed Sensor Networks
- Liu, Ning
- 2003
(Show Context)
Citation Context ...eds can be further reduced if instead of taking a large value for b, we compute a long key by concatenating several n b-bit keys, e.g. a 128 bits long key from 4 32-keys. This technique is applied in =-=[12]-=- to generate a 128-bit key by concatenating 8 keys generated from polynomials in F216+ 1. Each of the n b-bit keys is generated from a different keying material so, in the system initialization step, ... |

261 | Perfectly-secure key distribution for dynamic conferences
- Blundo, Santis, et al.
- 1993
(Show Context)
Citation Context ...) that is symmetric, that is, f(X, Y ) = f(Y, X). Each node with identifier η receives a secret keying material - a function - KMη(X) = f(X, η) such that KMη(η ′ ) = f(η, η ′ ) for any other η ′ . In =-=[2]-=-, Blundo et al. choose the secret function f(X, Y ) to be a symmetric bivariate polynomial over a finite field of degree α in each variable and show that their scheme offers information-theoretic secu... |

53 |
The Art of Computer Programming, Volume 2 (3rd Ed.): Seminumerical Algorithms
- Knuth
- 1997
(Show Context)
Citation Context ...registers R0 (lower 8-bit word) and R1 (higher 8-bit word). In Algorithm 1 we show the key generation algorithm which we have implemented in the ATmega128L. The underlying method is the Horner’s Rule =-=[11]-=-. To compute each intermediate value 〈Rj〉N = 〈Rj+1 × η ′ + KM j〉N with j = α − 1, . . . , 0. (4) without performing the modN reduction we take advantage of N’s specific form, N = 2 (α+2)b −1 and the s... |

50 |
On the key predistribution systems: A practical solution to the key distribution problem
- Matsumoto, Imai
- 1987
(Show Context)
Citation Context ... own secret keying material and the identity of the other node to generate a common pairwise key. The key distribution problem - as discussed in this paper - was first described by Matsumoto and Imai =-=[1]-=-. They propose that a TTP chooses a secret function f(X, Y ) that is symmetric, that is, f(X, Y ) = f(Y, X). Each node with identifier η receives a secret keying material - a function - KMη(X) = f(X, ... |

34 | Tinypbc: Pairings for authenticated identity-based non-interactive key distribution in sensor networks
- Oliveira, Aranha, et al.
(Show Context)
Citation Context ...work: Table 3 compares our generic HIMMO implementation with a polynomial scheme [2,12], the previous broken attempt of creating an scheme with the full collusion resistance property [3] and pairings =-=[13]-=-. The results are taken from those works when implemented and evaluated in the AVR ATmega128L MCU as in our experiments. HIMMO’s performance is as the one of a polynomial scheme of degree 40 with the ... |

27 | A random perturbation-based scheme for pairwise key establishment in sensor networks
- Zhang, Tran, et al.
- 2007
(Show Context)
Citation Context ...n-theoretic security if an attacker knows the secret keying material of c colluding nodes whenever c ≤ α. If c ≥ α+1, an attacker can recover f(X, Y ) by means of Lagrange interpolation. Zhang et al. =-=[3]-=- proposed a “noisy” versionof [2] aiming at being fully-collusion resistant. This scheme was generalized and broken by Albrecht et al. [4] in different ways including error-correcting and lattice tec... |

17 |
Secret linear congruential generators are not cryptographically secure
- Stern
- 1987
(Show Context)
Citation Context ...structed if the qis are secret. Secondly, for c = m(α + 1), the lattice dimension is m(m + 1)(α + 1) so by 5 Note that even for m = 1 the secrecy of the qis can make an attack infeasible. The work in =-=[8]-=- shows that a polynomial of degree α = 1 can be recovered even if the module is secret. Results for degree α > 1 are unknown. Ntaking m relatively large, the lattice becomes too big for practical app... |

16 | Attacking cryptographic schemes based on perturbation polynomials
- Albrecht, Gentry, et al.
- 2009
(Show Context)
Citation Context ...er f(X, Y ) by means of Lagrange interpolation. Zhang et al. [3] proposed a “noisy” versionof [2] aiming at being fully-collusion resistant. This scheme was generalized and broken by Albrecht et al. =-=[4]-=- in different ways including error-correcting and lattice techniques. Their idea was to provide node η with a polynomial KMη(X) = f(X, η) + s1,ηp1(X) + s2,ηp2(X) of degree α where p1(X) and p2(X) are ... |

13 | Sparse polynomial approximation in finite fields
- Shparlinski
- 2001
(Show Context)
Citation Context ...) Hiding Information corresponds to the Noisy Polynomial Interpolation Problem of recovering an unknown polynomial f(X) ∈ Zq[X] from approximate values of f(η) at polynomially many points η ∈ Zq, see =-=[5]-=- and [6]. In HIMMO, these approximations are with respect to the LSBs. Hiding Information (HI) Problem: Let KM (X) ∈ ZN[X] be a polynomial of degree at most α, and let Kη = 〈〈KM (X = η)〉N〉 2b, the las... |

11 | Reconstructing noisy polynomial evaluation in residue rings
- Blackburn, Gomez-Perez, et al.
(Show Context)
Citation Context ... identifiers are small affects the requirements on the HIMMO parameters or can even allow for a better attack. A more general open question about the noisy polynomial reconstruction is posed in paper =-=[7]-=-. Independently of the above results that already provide us secure parameters, this approach cannot be applied always because the common key generated between two nodes can differ a value ∆ specified... |

7 |
8-bit AVR Microcontroller with 128 KBytes
- Atmel
(Show Context)
Citation Context ...Tmega128L. Later, we describe the performance results. 4.1 Optimized HIMMO on ATmega128L We have implemented HIMMO in the low-power 8-bit ATmega128L microcontroller based on the AVR RISC architecture =-=[9]-=-. The ATmega128L has 32 8-bit general-purpose registers (R0 to R31) of which six of them can be used in pairs as indirect address registers (X=R27:R26, Y=R29:R28 and Z=R31:R30) [10]. The program code ... |

4 |
Noisy interpolation of sparse polynomials in finite fields
- Shparlinski, Winterhof
- 2005
(Show Context)
Citation Context ... Information corresponds to the Noisy Polynomial Interpolation Problem of recovering an unknown polynomial f(X) ∈ Zq[X] from approximate values of f(η) at polynomially many points η ∈ Zq, see [5] and =-=[6]-=-. In HIMMO, these approximations are with respect to the LSBs. Hiding Information (HI) Problem: Let KM (X) ∈ ZN[X] be a polynomial of degree at most α, and let Kη = 〈〈KM (X = η)〉N〉 2b, the last b bits... |