COMPUTER SCIENCE EN

# Attacker who has access to all secrets of n or less

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42 M. Ramkumar Thus, while deterministic KPSs fail in a catastrophic manner, probabilistic KPSs fail gracefully. In this chapter we restrict ourselves to one representative scheme from each class - Blom’s deterministic KPS 10 and the ( n, p )-secure key subset and symmetric certificates (KSSC) 12 scheme. 3.2.2. Blom’s Deterministic Scheme The symmetric key generation scheme (SKGS) proposed by Blom 10 is based on maximum distance separation (MDS) codes over a finite-field - for ex- ample, the finite-field formed by the set of integers Z q = { 0 , 1 , . . ., q 1 } (where q is a prime). The KDC chooses (1) a public primitive element α Z q ; (2) ( n + 1) × ( n + 1) symmetric matrix D with ( n +1 2 ) independent values (secrets) chosen randomly from Z q . Corresponding to a node with ID A Z q the KDC computes g A = [ g A (0) , g A (1) , . . . , g A ( n )] T , g A ( i ) = α i × A . S A = Dg A = d A = [ s A 0 , s A 1 , . . . s A n ] T (5) The k = n + 1 secrets S A are then provided to A over a secure channel. Nodes A and B (with secrets d A = [ s A 0 · · · s A n ] T and d B = [ s B 0 · · · s B n ] T respectively) can compute K AB = ( d A ) T g B = ( d B ) T g A (as D is a sym- metric matrix). In other words, A and B compute K AB as K AB = n i =0 s A i α iB mod q by A n i =0 s B i α iA mod q by B (6) An n -secure SKGS is unconditionally secure as long as n or less nodes pool their secrets together. However, an attacker who has access to secrets assigned to more than n nodes can solve for all P = ( n +1 2 ) secrets chosen by the KDC, and thus compute any pairwise secret.
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• Spring '12
• Kushal Kanwar
• Public key infrastructure, ........., Public-key cryptography, Pretty Good Privacy

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