Security of Ramp Schemes

Blakley, G. R.; Meadows, Catherine

doi:10.1007/3-540-39568-7_20

Cited by 272 publications

(206 citation statements)

References 10 publications

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“…Robust ramp secret sharing scheme. A (t, r, N )-ramp secret sharing scheme [7,13] is a secret sharing scheme with two thresholds, t and r, such that any t or less shares do not leak any information about the secret while any r or more shares reconstruct the secret and if the number a of shares is in between t and r, an a−t r−t fraction of information of the secret will be leaked. We define a robust ramp secret sharing scheme as a ramp secret sharing scheme with an additional (ρ, δ)-robustness property which requires that the probability of reconstructing a wrong secret, if up to t+ ρ(r −t) shares are controlled by an active adversary, is bounded by δ.…”

Section: Our Workmentioning

confidence: 99%

Detecting Algebraic Manipulation in Leaky Storage Systems

Lin

Wang

2016

Lecture Notes in Computer Science

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Abstract. Algebraic Manipulation Detection (AMD) Codes detect adversarial noise that is added to a coded message which is stored in a storage that is opaque to the adversary. We study AMD codes when the storage can leak up to ρ log |G| bits of information about the stored codeword, where G is the group that contains the codeword and ρ is a constant. We propose ρ-AMD codes that provide protection in this new setting. We define weak and strong ρ-AMD codes that provide security for a random and an arbitrary message, respectively. We derive concrete and asymptotic bounds for the efficiency of these codes featuring a rate upper bound of 1 − ρ for the strong codes. We also define the class of ρ LV -AMD codes that provide protection when leakage is in the form of a number of codeword components, and give constructions featuring a family of strong ρ LV -AMD codes that asymptotically achieve the rate 1 − ρ. We describe applications of ρ-AMD codes to, (i) robust ramp secret sharing scheme and, (ii) wiretap II channel when the adversary can eavesdrop a ρ fraction of codeword components and tamper with all components of the codeword.

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Section: Our Workmentioning

confidence: 99%

Detecting Algebraic Manipulation in Leaky Storage Systems

Lin

Wang

2016

Lecture Notes in Computer Science

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“…But, in the case of ramp access structures such that some subsets of V are allowed to have intermediate properties between the qualified and forbidden sets, it is possible to decrease the coding rate ρ i to less than 1. The SSSs having the ramp access structure are called ramp schemes [17,18]. In this section, we treat the construction of ramp SSSs based on the multiple assignment maps.…”

Section: Example 14mentioning

confidence: 99%

“…Especially, in the case of (k, L, n)-threshold SSSs, the optimal ramp SSS attaining ρ i = 1/L for all i can easily be constructed [17,18]. Any common share V i must also satisfy that ρ i ≥ 1/L.…”

Section: Remark 15mentioning

confidence: 99%

Optimal Multiple Assignments Based on Integer Programming in Secret Sharing Schemes with General Access Structures

Iwamoto¹,

Yamamoto²,

Ogawa³

2007

IEICE Transactions on Fundamentals of Electronics, Communicatio

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It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m, m)-threshold scheme by using the so-called cumulative map or from a (t, m)-threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, we propose a new method to construct a SSS from a (t, m)-threshold scheme for any given general access structure. In the proposed method, integer programming is used to distribute optimally the shares of (t, m)-threshold scheme to each participant of the general access structure. From the optimality, it can always attain lower coding rate than the cumulative maps except the cases that they give the optimal distribution. The same method is also applied to construct SSSs for incomplete access structures and/or ramp access structures.

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“…For example, it is easy to see that we no longer lose the factor t in the security of our reduction in Theorem 2. As for the ef£ciency, instead of using an AONT (which is essentially an (n − 1, n)-secret sharing scheme), we can now use any (n/2, n)-"ramp" secret sharing scheme [6]. This means that n shares reconstruct the secret, but any n/2 shares yield no information about the secret.…”

Section: Theorem 1 ([18 29 24]) For Any N and T One Can Ef£cientlmentioning

confidence: 99%

Key-Insulated Public Key Cryptosystems

Dodis

Katz

et al. 2002

Lecture Notes in Computer Science

278

213

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Abstract. Cryptographic computations (decryption, signature generation, etc.) are often performed on a relatively insecure device (e.g., a mobile device or an Internet-connected host) which cannot be trusted to maintain secrecy of the private key. We propose and investigate the notion of key-insulated security whose goal is to minimize the damage caused by secret-key exposures. In our model, the secret key(s) stored on the insecure device are refreshed at discrete time periods via interaction with a physically-secure -but computationally-limiteddevice which stores a "master key". All cryptographic computations are still done on the insecure device, and the public key remains unchanged. In a (t, N )-keyinsulated scheme, an adversary who compromises the insecure device and obtains secret keys for up to t periods of his choice is unable to violate the security of the cryptosystem for any of the remaining N − t periods. Furthermore, the scheme remains secure (for all time periods) against an adversary who compromises only the physically-secure device.We focus primarily on key-insulated public-key encryption. We construct a (t, N )-key-insulated encryption scheme based on any (standard) public-key encryption scheme, and give a more ef£cient construction based on the DDH assumption. The latter construction is then extended to achieve chosen-ciphertext security.

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Security of Ramp Schemes

Cited by 272 publications

References 10 publications

Detecting Algebraic Manipulation in Leaky Storage Systems

Detecting Algebraic Manipulation in Leaky Storage Systems

Optimal Multiple Assignments Based on Integer Programming in Secret Sharing Schemes with General Access Structures

Key-Insulated Public Key Cryptosystems

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