What does it mean to be secure? Hopes, Fears, and Software Obfuscation,
by Boaz Barak, CACM March 2016, vol. 59, no. 3, pages 88-96,
http://dx.doi.org/10.1145/2757276

Excerpt regarding "security through simplicity",
starting on page 95, middle column:

The history of cryptography is littered with the figurative corpses of
cryptosystems believed secure and then broken, and sometimes with the actual
corpses of people (such as Mary, Queen of Scots) that have placed their
faith in these cryptosystems.  But something changed in modern times. In 1976
Diffie and Hellman proposed the notion of public key cryptography and gave
their famous Diffie-Hellman key exchange protocol, which was followed soon
after by the RSA cryptosystem. In contrast to cryptosystems such as Enigma,
the description of these systems is simple and completely public. Moreover, by
being public key systems, they give more information to potential attackers,
and since they are widely deployed on a scale more massive than ever before,
the incentives to break them are much higher. Indeed, it seems reasonable
to estimate that the amount of manpower and computer cycles invested in
cryptanalysis of these schemes today every year dwarves all the cryptanalytic
efforts in pre-1970 human history. And yet (to our knowledge) they remain
unbroken.

How can this be? I believe the answer lies in a fundamental shift from
"security through obscurity" to "security through simplicity." To understand
this consider the question of how could the relatively young and unknown
Diffie and Hellman (and later Rivest, Shamir and Adleman) convince the
world they have constructed a secure public key cryptosystem, an object so
paradoxical that most people would have guessed could not exist (and indeed a
concept so radical that Merkle's first suggestion of it was rejected as an
undergraduate project in a coding theory course). The traditional approach
toward establishing something like that was "security through obscurity"
- keep all details of the cryptosystem secret and have many people try to
cryptanalyze it in-house, in the hope that any weakness would be discovered
by them before it is discovered by your adversaries. But this approach was
of course not available to Diffie and Hellman, working by themselves without
many resources, and publishing in the open literature.

Of course the best way would have been to prove a mathematical theorem
that breaking their system would necessarily take a huge number of
operations. Thanks to the works of Church, Turing, and Godel, we now
know that this statement can in fact be phrased as a precise mathematical
assertion.  However, this assertion would in particular imply that P != NP
and hence proving it seems way beyond our current capabilities. Instead,
what Diffie and Hellman did (aided by Ralph Merkle and John Gill) was to
turn to "security by simplicity" - base their cryptosystem on a simple and
well-studied mathematical problem, such as inverting modular exponentiation
or factoring integers, that has been investigated by mathematicians for ages
for reasons having nothing to do with cryptography. More importantly, it is
plausible to conjecture there simply does not exist an efficient algorithm to
solve these clean well-studied problems, rather than it being the case that
such an algorithm has not been found yet due to the problem's cumbersomeness
and obscurity. Later papers, such as the pioneering works of Goldwasser and
Micali, turned this into a standard paradigm and ushered in the age of modern
cryptography, whereby we use precise definitions of security for our very
intricate and versatile cryptosystems and then reduce the assertion that
they satisfy these definitions into the conjectured hardness of a handful
of very simple and well-known mathematical problems.