Cryptography Reference
In-Depth Information
Mathematics and the Real World
The gradual development and refinement of the digital signature model
provides a useful window from which to examine the cryptographic
research community's conceptualization of their mathematical practices.
In the aftermath of the publication of “New Directions,” these practices
sat at the intersection of several trends: Diffie and Hellman's call for
increased mathematization of the field; the practical concerns that have
historically given the field its identity, that is, the construction of effective
systems that afford confidential communications; and Simmons's program
for a broader disciplinary identity, centered on the design of digital ana-
logues to paper-based security protocols. The challenges in reconciling
these divergent trends registered, among other symptoms, as a certain
ambivalence in dealing with the relationship between mathematics and
the “real world” and the role of models in mediating that relationship. At
times, that world seems immediately and self-evidently at hand, as in Diffie
and Hellman's succinct definition of the signature, a definition whose
fundamental features were never challenged or improved upon again. At
other times, it seems reluctant and remote, forcibly summoned through
the scenarios that justify, with various degrees of realism, the practical
utility of the mathematical objects created by cryptographers. Both cases
reveal a problematic encounter with the practice of modeling, and the
attendant issue of representation . Even though modeling clearly formed an
integral dimension of cryptographic practice, by and large, cryptographers
did not and could not explicitly articulate its specific possibilities and
constraints.
This issue shouldn't necessarily come as a surprise. Models have remained
a largely tacit dimension of scientific practice. The twelve-volume Encyclo-
pedia of Mathematics entry is content to define modeling as “a (rough)
description of some class of events of the outside world, expressed using
mathematical symbolism.” 55 Philosophers Mary Morgan and Margaret
Morrison point out that “there appear to be no general rules for model
construction in the way that we can find detailed guidance on principle
of experimental design or on methods of measurement.” 56 Indeed, it is
only in last decade that historians, philosophers, and sociologists of science
have begun examining models with the same degree of attention they
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