CONTENTS - Emerald

8 Theoretical Cryptology
041801 `Homomorphic threshold schemes, k-arcs and Lenstra's constant'
S Barwick, Y Desmedt, P Wild, Cirencester 93 pp 95{102
Homomorphic threshold schemes have the property that if shares ai can be used
to reconstruct the secret A and bi to reconstruct B, then ai bi can reconstruct A B.
previous schemes, de ned over an arbitrary nite Abelian group, had the restriction
that the number of shares was limited by the smallest prime factor of the group order.
The authors show that this restriction can be overcome by considering the group as a
module over some suitable extension of the integers.
041802 `Graph Decompositions and Secret Sharing Schemes'
C Blundo, A De Santis, DR Stinson, U Vaccaro, Journal of Cryptology v 8 no 1 (1995)
pp 39{64
The authors survey the information rate of the graph of a secret sharing scheme.
They look at upper bounds based on entropy arguments, and lower bounds from graph
decompositions; the latter case involves linear programming. Some general results are
proved on the information rate of paths, cycles and trees, and speci c results are given
for the 30 connected graphs on ve vertices or less.
041803 `A Perfect Threshold Secret Sharing Scheme to Identify Cheaters'
M Carpentieri, Designs, Codes and Cryptography v 5 no 3 (May 95) pp 183{187
The author discusses the evolution os secret sharing schemes which detect attempts
to cheat, and presents a perfect and unconditionally secure (k; n) threshold scheme each
of whose participants' secret amounts to k +2(n,1) elements of a nite eld rather
than the previous n +2k,3.
041804 `Disenrollment capability of conditionally secure sharing schemes'
C Charnes, J Pieprzyk, ISITA 94 pp 225{227
The paper gives the construction of a secret sharing scheme, using a modi cation
of Shamir's scheme, whose security relies on the di culty of the discrete logarithm
problem. Shareholders use their 'initial conditions' to recalculate new shares if the
exiting ones are invalidated.
041805 `Zero-Knowledge Proofs of Computational Power in the Shared
String Model'
ADeSantis, T Okamoto, G Persiano, Asiacrypt 94 pp 160{170
The authors formalise the concept of non-interactive zero knowledge proofs of computational
power, and give some implementations for certain types of dense random
self-reducible and uniformly generatable problems.
041806 `Multiplicative non-abelian sharing schemes and their application
to threshold cryptography'
Y Desmedt, G de Crescenzo, M Burmester, Asiacrypt 94 pp 2{13
The authors show multiplicative secret sharing schemes which can be used with
threshold signatures which are based on non-Abelian groups to produce perfect zeroknowledge
threshold proofs of knowledge.
041807 `Comment -multistage secret sharing based on one-way function'
L Harn, Electronics Letters v 31 no 4 (16/2/95) p 262
The author shows a slight improvement inascheme of He and Dawson (below).
041808 `Multisecret sharing scheme based on one-way functions'
J He, E Dawson, Electronics Letters v 31 no 2 (19/1/95) pp 93{95
Multistage secret sharing schemes can be used to reconstruct a number of secrets
in order given just one share per participant. The authors show how to generalise this
so that secrets can be reconstructed in any order.
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