Secret sharing: fundamental role of remainder?
Secret sharing, Shapeshifting and Embodiment (Part #4)
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The sense of a "secret" is a focus of the preoccupation of Derrida in relation to literature, as noted by Joseph G. Kronick (Derrida and the Future of Literature, 1999):
... literature is the reserve or remainder that cannot be taken up or totalized within its institution... As trace, literature remarks a relation to an outside, an absolute past or remainder, which, like a secret, cannot be re-presented in a present but holds in a reserve a promise, a future that is to come... (p. 10). This is why Derrida likes literature, or rather something about it; "this would be in place of the secret." There, in place of the secret, is the non-place which allows us to think of the other. It is where "what remains is nothing -- but the remainder, not even of literature." The remainder is what shelters the other, that which is never presentable. Literature is such a reserve. (p. 22)
This highlights the question of how any such secret might be effectively shared, especially when distribtion of the trace of it in literature is already subject to access restrictions (cost, language, copyright, etc) to say nothing of information overload and limited attention span.
Detecting the "elephant": The quantitative and qualitative considerations relating to remainder are usefully interrelated through the manner in which a secret may be protected and held. Whilst this is fundamental to issues of cryptography, that challenge has been fruitfully illustrated by the traditional tale of the blind men and the elephant. The point has been specifically argued using that tale with respect to internet security by Martin Burkhart (Enabling Collaborative Network Security with Privacy-Preserving Data Aggregation, ETH Zurich, 2011). The challenge of secret sharing then consists of recovering a "secret" from a set of "shares", each containing partial information about the secret.
Remainder theorem: In mathematics, a focus on "remainder" is articulated through the so-called Chinese Remainder Theorem (CRT), said to be one of the jewels of mathematics as a combination of beauty and utility (C Ding and D Pei, Chinese Remainder Theorem: applications in computing, coding, cryptography, 1996). This is about congruences in number theory and its generalizations in abstract algebra. In its most basic form it is concerned with determining n, given the remainders generated by division of n by several numbers. (For example what is the single lowest number if repeatedly divided by 3 gives a remainder of 2; when divided by 5 gives a remainder of 3; and when divided by 7 gives a remainder of 2?)
In secret sharing, each of the shares is represented in a congruence, and the solution of the system of congruences using the theorem is the secret to be recovered. In secret sharing using the Chinese Remainder Theorem uses special sequences of integers that guarantee the impossibility of recovering the secret from a set of shares with less than a certain cardinality. Shamir's Secret Sharing is an algorithm in cryptography is a form of secret sharing, where a secret is divided into parts, giving each participant its own unique part, where some of the parts or all of them are needed in order to reconstruct the secret.
Sustainability as a "secret": The widespread and unexpected variety of references to the "Holy Grail" in relation to issues of governance was explored in earlier papers (In Quest of Sustainability as Holy Grail of Global Governance, 2011; In-forming the Chalice as an Integrative Cognitive Dynamic, 2011). In the latter, using the elephant tale, the question was raised as to whether the "Chalice" of sustainable governance posed the same cognitive challenges as the "elephant" (The Chalice as an "elephant", 2011). In this sense the "secret" of sustainable governance might need to be derived from a set of disparate set of cognitive skills usefully to be explored and understood in the light of "secret sharing" according to the Chinese Remainder Theorem. In a separate argument, the organization of these skills into a fruitful set was discussed (Eliciting a 12-fold Pattern of Generic Operational Insights: recognition of memory constraints on collective strategic comprehension, 2011; Enabling a 12-fold Pattern of Systemic Dialogue for Governance, 2011).
NB: See main paper for Conclusion and References
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