5 research outputs found
Quantum Cryptography II: How to re-use a one-time pad safely even if P=NP
When elementary quantum systems, such as polarized photons, are used to
transmit digital information, the uncertainty principle gives rise to novel
cryptographic phenomena unachievable with traditional transmission media, e.g.
a communications channel on which it is impossible in principle to eavesdrop
without a high probability of being detected. With such a channel, a one-time
pad can safely be reused many times as long as no eavesdrop is detected, and,
planning ahead, part of the capacity of these uncompromised transmissions can
be used to send fresh random bits with which to replace the one-time pad when
an eavesdrop finally is detected. Unlike other schemes for stretching a
one-time pad, this scheme does not depend on complexity-theoretic assumptions
such as the difficulty of factoring.Comment: Original 1982 submission to ACM Symposium on Theory of Computing with
spelling and typographical corrections, and comments by the authors 32 years
later. Submitted to Natural Computin
Quantum Cryptography II: How to re-use a one-time pad safely even if P=NP
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g.acommunications channel on which it is impossible in principle to eavesdrop without a high probability of being detected. With such a channel, a one-time pad can safely be reused many times as long as no eavesdrop is detected, and, planning ahead, part of the capacity of these uncompromised transmissions can be used to send fresh random bits with which to replace the one-time pad when an eavesdrop finally is detected. Unlike other schemes for stretching a one-time pad, this scheme does not depend on complexity-theoretic assumptions such as the difficulty of factoring
APL and the Grzegorczyk Hierarchy
We show in this paper that the set of "traditional" APL 1-liners (using arithmetic functions only) compute precisely the set of functions in the class E4 of Grzegorczyk hierarchy (the class immediately above the elementary functions). We also show that if we extend the set of 1-liners to include either the "execute" operator, or 1 line programs with gotos, then any partial recursive function can be computed