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## On the Asymptotic Idealness of the Asmuth-Bloom Threshold Secret Sharing Scheme

### Citations

78 |
A modular approach to key safeguarding,”
- Asmuth, Bloom
- 1983
(Show Context)
Citation Context ...nder the responsibility of the Managing Authority for the Sectoral Operational Programme for Human Resources Development 2007-2013 [grant POSDRU/CPP 107/DMI 1.5/S/78342] Asmuth-Bloom threshold scheme =-=[1]-=- and also proposes some asymptotically perfect and ideal variants of it. Another variant of the Asmuth-Bloom threshold scheme was proposed in [7] which provides better security than the original Asmut... |

51 | Chinese remaindering with errors.
- Goldreich, Ron, et al.
- 1999
(Show Context)
Citation Context ...er some security degree and, in order to study it, Quisquater et al. [6] have introduced the concepts of asymptotic perfectness and asymptotic idealness. They also proved that the threshold scheme in =-=[3]-=- is asymptotically ideal (and, therefore, asymptotically perfect) provided that it uses sequences of consecutive primes and the secret is uniformly chosen from the secret space. This result was later ... |

37 |
Chinese Remainder Theorem:
- Ding, Pei, et al.
- 1999
(Show Context)
Citation Context ... . 2 The Asmuth-Bloom secret sharing scheme and variations Given a finite non-empty set I of positive integers and the integers bi and mi for all i ∈ I, the Chinese Remainder Theorem (CRT, for short) =-=[8]-=- states that the system of congruences x ≡ bi mod mi, i ∈ I (1) has a unique solution modulo ∏ i∈I mi, if mi and mj are co-prime for any i, j ∈ I with i 6= j. One of the applications of CRT is the des... |

24 |
How to share a secret,” in
- Mignotte
- 1983
(Show Context)
Citation Context ...f congruences x ≡ bi mod mi, i ∈ I (1) has a unique solution modulo ∏ i∈I mi, if mi and mj are co-prime for any i, j ∈ I with i 6= j. One of the applications of CRT is the design of threshold schemes =-=[2, 1, 3]-=-. In this paper we will focus on the threshold scheme in [1] and some of its variants. As all of them are based on sequences of positive integers with special properties, we begin with a few notations... |

9 | Threshold cryptography based on Asmuth-Bloom Secret sharing,”
- Kaya, Selcuk
- 2007
(Show Context)
Citation Context ...ically perfect and its information rate goes asymptotically to 2 [4]; – the Asmuth-Bloom (t + 1, n)-threshold scheme based on (n − 1, Θ)-compact sequences of co-primes is asymptotically ideal [4]. In =-=[7]-=-, Kaya and Selcuk have conjectured that replacing the Asmuth-Bloom sequences of co-primes by extended Asmuth-Bloom sequences of co-primes may increase the security of the Asmuth-Bloom threshold scheme... |

8 |
On the security of the threshold scheme based on the chinese remainder theorem,” in
- Quisquater, Preneel, et al.
- 2002
(Show Context)
Citation Context ...nce and collecting the remainders. The CRT-based threshold schemes proposed so far are neither perfect nor ideal. However, they offer some security degree and, in order to study it, Quisquater et al. =-=[6]-=- have introduced the concepts of asymptotic perfectness and asymptotic idealness. They also proved that the threshold scheme in [3] is asymptotically ideal (and, therefore, asymptotically perfect) pro... |

1 |
Drăgan, “Compact sequences of co-primes and their applications to the security of CRT-based threshold schemes
- Barzu, Ţiplea, et al.
- 2013
(Show Context)
Citation Context ...ically ideal (and, therefore, asymptotically perfect) provided that it uses sequences of consecutive primes and the secret is uniformly chosen from the secret space. This result was later improved in =-=[4]-=- by showing that the asymptotic idealness of this scheme is achieved for a subclass of compact sequences of co-primes [4]. Compact sequences of co-primes capture very well the idea of sequence of numb... |

1 | A necessary and sufficient condition for the asymptotic idealness of the GRS threshold secret sharing scheme - Ţiplea, Drăgan |