A survey and refinement of repairable threshold schemes

Laing, Thalia M.; Stinson, Douglas R.

doi:10.1515/jmc-2017-0058

Cited by 7 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All of that said, Errx security does imply robustness whenever the latter can be achieved. Auth and Errx have little in common with repairable threshold schemes [25,32], which allow a party to reconstruct a missing share by interacting with fellow shareholders. In scenarios we care about, shareholders may not have the ability to interact with one another prior to recovery.…”

Section: Privmentioning

confidence: 99%

“…In this section we contrast these goals. Then we contrast Auth with robustness [15,31] and, finally, with repairability [25,32].…”

Section: A Relationsmentioning

confidence: 99%

“…Repairable threshold schemes [25,32] allow a party to reconstruct a missing share by interacting with fellow shareholders. In our applications, we do not anticipate that shareholders have any desire or ability to interact with one another prior to recovery.…”

Section: A3 Comparison With Repairabilitymentioning

confidence: 99%

See 2 more Smart Citations

Reimagining Secret Sharing: Creating a Safer and More Versatile Primitive by Adding Authenticity, Correcting Errors, and Reducing Randomness Requirements

Bellare

Dai

Rogaway

2020

Proceedings on Privacy Enhancing Technologies

View full text Add to dashboard Cite

Aiming to strengthen classical secret-sharing to make it a more directly useful primitive for human endusers, we develop definitions, theorems, and efficient constructions for what we call adept secret-sharing. Our primary concerns are the properties we call privacy, authenticity, and error correction. Privacy strengthens the classical requirement by ensuring maximal confidentiality even if the dealer does not employ fresh, uniformly random coins with each sharing. That might happen either intentionally—to enable reproducible secretsharing— or unintentionally, when an entropy source fails. Authenticity is a shareholder’s guarantee that a secret recovered using his or her share will coincide with the value the dealer committed to at the time the secret was shared. Error correction is the guarantee that recovery of a secret will succeed, also identifying the valid shares, exactly when there is a unique explanation as to which shares implicate what secret. These concerns arise organically from a desire to create general-purpose libraries and apps for secret sharing that can withstand both strong adversaries and routine operational errors.

show abstract

Section: Privmentioning

confidence: 99%

“…In this section we contrast these goals. Then we contrast Auth with robustness [15,31] and, finally, with repairability [25,32].…”

Section: A Relationsmentioning

confidence: 99%

See 1 more Smart Citation

Reimagining Secret Sharing: Creating a Safer and More Versatile Primitive by Adding Authenticity, Correcting Errors, and Reducing Randomness Requirements

Bellare

Dai

Rogaway

2020

Proceedings on Privacy Enhancing Technologies

View full text Add to dashboard Cite

show abstract

“…133 As many critics have noted, West is deliberately invoking 'Conradian resonances' here. 134 Just like Marlow in Heart of Darkness (1899), George locates darkness and 'the horror' not in the depths of Africa but in the imperial centre of London. Marlow confronts two women 'guarding the door of Darkness, knitting black wool as for a warm pall'; similarly, George recalls how he was introduced to Evadne by an elderly widow, Mrs Mary Ellerker, who sat 'in the black-panelled drawing-room amidst the jungle of shiny mahogany furniture' and in 'a mass of darkness': 'This horror obsessed him'.…”

Section: Whirling Dissipating Energy: Scientific Discoursementioning

confidence: 99%

Rebecca West, the Forgotten Vorticist?

Mourant¹

2019

Modernist Cultures

View full text Add to dashboard Cite

The inclusion of Rebecca West's short story ‘Indissoluble Matrimony’ in the first issue of BLAST (1914) has much to tell us about the intellectual debts the Vorticist movement owed to West and to the feminist periodical culture with which she was associated. West composed her story in 1912–13, years when she was highly active as both contributor to and literary editor of Dora Marsden's The Freewoman (1911–12) and The New Freewoman (1913). In this article, I examine how the ‘energy’ promoted across BLAST aligned with feminist political conceptions of energy in Marsden's journals, and how these ideas were also shaped by early twentieth-century understandings of the universe, including theories of vortex motion, the ether, electromagnetism and thermodynamics. By paying close attention to the theme and metaphor of energy in ‘Indissoluble Matrimony’, this article traces patterns of influence between West, Marsden, Ezra Pound and Wyndham Lewis that reveal intersections between avant-guerre feminism and the Vorticist avant-garde.

show abstract

“…Reconstruction is easily accomplished using the Lagrange interpolation formula (see, e.g., [7, §11.5.1]). The problem of share repairability has been considered by several authors in recent years (see Laing and Stinson [5] for a survey on this topic). The problem setting is that a certain player P ℓ (in a (τ, n)-threshold scheme, say) loses their share.…”

Section: Introduction To Combinatorial Repairabilitymentioning

confidence: 99%

A network reliability approach to the analysis of combinatorial repairable threshold schemes

Kacsmar¹,

Stinson²

2019

Advances in Mathematics of Communications

View full text Add to dashboard Cite

A repairable threshold scheme (which we abbreviate to RTS ) is a (τ, n)-threshold scheme in which a subset of players can "repair" another player's share in the event that their share has been lost or corrupted. This will take place without the participation of the dealer who set up the scheme. The repairing protocol should not compromise the (unconditional) security of the threshold scheme. Combinatorial repairable threshold schemes (or combinatorial RTS ) were recently introduced by Stinson and Wei [8]. In these schemes, "multiple shares" are distributed to each player, as defined by a suitable combinatorial design called the distribution design. In this paper, we study the reliability of these combinatorial repairable threshold schemes in a setting where players may not be available to take part in a repair of a given player's share. Using techniques from network reliability theory, we consider the probability of existence of an available repair set, as well as the expected number of available repair sets, for various types of distribution designs. * D.R. Stinson's Research is supported by NSERC discovery grant RGPIN-03882.Corollary 3.4. A 3-(v, k, 1)-design can be used as a distribution design to produce an RTS with threshold τ if k ≥ τ (τ − 1) + 1.Remark 3.5. In order to obtain τ = 3, we require k ≥ 7 in Corollary 3.4; to obtain τ = 4, we require k ≥ 13, etc. ReliabilityIn our analysis, to compute the reliability metrics for repair sets, we employ the use of cutsets from network reliability theory (see Colbourn [2] for basic results and terminology relating to network reliability). When using BIBDs as distribution designs, we were able to easily compute reliability formulas in Section 2 without the use of this methodology because the sets C j were disjoint. However, it is advantageous to use cutsets to analyze the reliability of the RTS constructed using distribution designs with t ≥ 3.In this section, for brevity, we will conflate the notion of players and blocks and express all our arguments in terms of blocks of the distribution design (X, B).Definition 3.6. A cutset for a block B is a minimal subset of blocks B ′ such that a repair is not possible if all the blocks in B ′ are not available. A cutset fails if every block in the cutset is not available.Lemma 3.7. Let B = {x 1 , . . . , x k } be a block in the distribution design. Then the sets C j , for 1 ≤ j ≤ k, are the cutsets. Example 3.8. Here are the blocks in an 3-(8, 4, 1)-design: A 1 = {1, 2, 3, 4} A 2 = {5, 6, 7, 8} B 1 = {1, 2, 5, 6} B 2 = {1, 2, 7, 8} B 3 = {1, 3, 5, 7} B 4 = {1, 3, 6, 8} B 5 = {1, 4, 5, 8} B 6 = {1, 4, 6, 7} B 7 = {3, 4, 7, 8} B 8 = {3, 4, 5, 6} B 9 = {2, 4, 6, 8} B 10 = {2, 4, 5, 7} B 11 = {2, 3, 6, 7} B 12 = {2, 3, 5, 8} Suppose A 1 wants to repair their share. Then, the relevant cutsets are

show abstract

A survey and refinement of repairable threshold schemes

Cited by 7 publications

References 14 publications

Reimagining Secret Sharing: Creating a Safer and More Versatile Primitive by Adding Authenticity, Correcting Errors, and Reducing Randomness Requirements

Reimagining Secret Sharing: Creating a Safer and More Versatile Primitive by Adding Authenticity, Correcting Errors, and Reducing Randomness Requirements

Rebecca West, the Forgotten Vorticist?

A network reliability approach to the analysis of combinatorial repairable threshold schemes

Contact Info

Product

Resources

About