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The '''[[Dirac delta function]]''' is a function introduced in 1930 by Paul Adrien Maurice Dirac in his seminal book on quantum mechanics. A physical model that visualizes a delta function is a mass distribution of finite total mass ''M''—the integral over the mass distribution. When the distribution becomes smaller and smaller,  while ''M'' is constant, the mass distribution shrinks to a ''point mass'', which by definition has zero extent and yet has a finite-valued integral equal to total mass ''M''. In the limit of a point mass the distribution becomes a Dirac delta function.  
A '''[[cypherpunk]]''' is an activist advocating widespread use of strong cryptography as a route to social and political change. Cypherpunks have been engaged in an active movement since the late 1980s, heavily influenced by the hacker tradition and by libertarian ideas. Many cypherpunks were quite active in the intense political and legal controversies around cryptography of the 90s, and most have remained active into the 21st century.


Heuristically, the Dirac delta function can be seen as an extension of the Kronecker delta from integral indices (elements of <font style="vertical-align: 13%"> <math>\mathbb{Z}</math></font>) to real indices (elements of <font style="vertical-align: 13%"><math>\mathbb{R}</math></font>). Note that the Kronecker delta acts as a "filter" in a summation:
The basic ideas are in this quote from the ''Cypherpunk Manifesto'':
:<math>
\sum_{i=m}^n \; f_i\; \delta_{ia} =
\begin{cases}
f_a & \quad\hbox{if}\quad  a\in[m,n] \sub\mathbb{Z}  \\
0  & \quad \hbox{if}\quad a \notin [m,n].
\end{cases}
</math>


In analogy, the Dirac delta function &delta;(''x''&minus;''a'')  is defined by (replace ''i'' by ''x'' and the summation over ''i'' by an integration over ''x''),
{{quotation|Privacy is necessary for an open society in the electronic age. ...
:<math>
\int_{a_0}^{a_1} f(x)  \delta(x-a) \mathrm{d}x =
\begin{cases}
f(a) & \quad\hbox{if}\quad  a\in[a_0,a_1] \sub\mathbb{R},  \\
0  & \quad \hbox{if}\quad a \notin [a_0,a_1].
\end{cases}
</math>


The Dirac delta function is ''not'' an ordinary well-behaved map  <font style="vertical-align: 12%"><math>\mathbb{R} \rightarrow \mathbb{R}</math></font>, but a distribution, also known as an ''improper'' or ''generalized function''. Physicists express its special character by stating that the Dirac delta function makes only sense as a factor in an integrand ("under the integral"). Mathematicians say that the delta function is a linear functional on a space of test functions.
We cannot expect governments, corporations, or other large, faceless organizations to grant us privacy ...


====Properties====
We must defend our own privacy if we expect to have any. ...
Most commonly one takes the lower and the upper bound in the definition of the delta function equal to <math>-\infty</math> and <math> \infty</math>, respectively. From here on this will be done.
 
:<math>
Cypherpunks write code. We know that someone has to write software to defend privacy, and ... we're going to write it. ... }}
\begin{align}
 
\int_{-\infty}^{\infty} \delta(x)\mathrm{d}x &= 1, \\
Many cypherpunks are technically quite sophisticated; they do understand ciphers and are capable of writing software. Some are or were quite senior people at major hi-tech companies and others are well-known researchers. However, the "punk" part of the name indicates an attitude:
\frac{1}{2\pi}\int_{-\infty}^{\infty} e^{ikx} \mathrm{d}k &= \delta(x) \\
 
\delta(x-a) &= \delta(a-x), \\
{{quotation|We don't much care if you don't approve of the software we write. We know that software can't be destroyed and that a widely dispersed system can't be shut down.}}
(x-a)\delta(x-a) &= 0, \\
 
\delta(ax) &= |a|^{-1} \delta(x) \quad (a \ne 0), \\
{{quotation|This is crypto with an attitude, best embodied by the group's moniker: Cypherpunks.}}
f(x) \delta(x-a) &= f(a) \delta(x-a), \\
 
\int_{-\infty}^{\infty} \delta(x-y)\delta(y-a)\mathrm{d}y &= \delta(x-a)
The first mass media discussion of cypherpunks was in a 1993 Wired article by Steven Levy titled ''Code Rebels'':
\end{align}
 
</math>
{{quotation|The people in this room hope for a world where an individual's informational footprints -- everything from an opinion on abortion to the medical record of an actual abortion -- can be traced only if the individual involved chooses to reveal them; a world where coherent messages shoot around the globe by network and microwave, but intruders and feds trying to pluck them out of the vapor find only gibberish; a world where the tools of prying are transformed into the instruments of privacy.}}
The physicist's proof of these properties proceeds by making proper substitutions into the integral and using the ordinary rules of integral calculus. The delta function as a Fourier transform of the unit function ''f''(''x'') = 1 (the second property) will be proved below.  
 
The last property is the analogy of the multiplication of two identity matrices,
{{quotation|There is only one way this vision will materialize, and that is by widespread use of cryptography. Is this technologically possible? Definitely. The obstacles are political -- some of the most powerful forces in government are devoted to the control of these tools. In short, there is a war going on between those who would liberate crypto and those who would suppress it. The seemingly innocuous bunch strewn around this conference room represents the vanguard of the pro-crypto forces. Though the battleground seems remote, the stakes are not: The outcome of this struggle may determine the amount of freedom our society will grant us in the 21st century. To the Cypherpunks, freedom is an issue worth some risk.}}
:<math>
 
\sum_{j=1}^n \;\delta_{ij}\;\delta_{jk} = \delta_{ik}, \quad i,k=1,\ldots, n.
The three masked men on the cover of that edition of Wired were prominent cypherpunks Tim May, Eric Hughes and John Gilmore.
</math>
 
''[[Dirac delta function|.... (read more)]]''
Later, Levy wrote a book ''Crypto: How the Code Rebels Beat the Government &mdash; Saving Privacy in the Digital Age'' covering the "crypto wars" of the 90s in detail. "Code Rebels" in the title is almost synonymuous with "cypherpunks".
 
The term "cypherpunk" is mildly ambiguous. In most contexts in means anyone advocating cryptography as a tool for social change. However, it can also be used to mean a participant in the cypherpunks mailing list described below. The two meanings obviously overlap, but they are by no means synonymous.
 
Documents exemplifying cypherpunk ideas include the ''Crypto Anarchist Manifesto'', the ''Cypherpunk Manifesto'' and the ''Ciphernomicon''.
 
== Cypherpunk issues ==
 
Through most of the 90s the cypherpunks mailing list had extensive discussions of the public policy issues related to cryptography and on the politics and philosophy of concepts such as anonymity, pseudonyms, reputation, and privacy. Of course these discussions are continuing elsewhere since the list shut down.
 
In at least two senses, people on the list were ahead of more-or-less everyone else. For one thing, the list was discussing questions about privacy, government monitoring, corporate control of information, and related issues in the early 90s that did not become major topics for broader discussion until ten years or so later. For another, at least some list participants were more radical on these issues than almost anyone else.
 
The list had a range of viewpoints and there was probably no completely unanimous agreement on anything. The general attitude, though, definitely put personal privacy and personal liberty above all other considerations.
''[[Cypherpunk|.... (read more)]]''

Revision as of 05:47, 17 September 2011

A cypherpunk is an activist advocating widespread use of strong cryptography as a route to social and political change. Cypherpunks have been engaged in an active movement since the late 1980s, heavily influenced by the hacker tradition and by libertarian ideas. Many cypherpunks were quite active in the intense political and legal controversies around cryptography of the 90s, and most have remained active into the 21st century.

The basic ideas are in this quote from the Cypherpunk Manifesto:

Privacy is necessary for an open society in the electronic age. ...

We cannot expect governments, corporations, or other large, faceless organizations to grant us privacy ...

We must defend our own privacy if we expect to have any. ...

Cypherpunks write code. We know that someone has to write software to defend privacy, and ... we're going to write it. ...

Many cypherpunks are technically quite sophisticated; they do understand ciphers and are capable of writing software. Some are or were quite senior people at major hi-tech companies and others are well-known researchers. However, the "punk" part of the name indicates an attitude:

We don't much care if you don't approve of the software we write. We know that software can't be destroyed and that a widely dispersed system can't be shut down.

This is crypto with an attitude, best embodied by the group's moniker: Cypherpunks.

The first mass media discussion of cypherpunks was in a 1993 Wired article by Steven Levy titled Code Rebels:

The people in this room hope for a world where an individual's informational footprints -- everything from an opinion on abortion to the medical record of an actual abortion -- can be traced only if the individual involved chooses to reveal them; a world where coherent messages shoot around the globe by network and microwave, but intruders and feds trying to pluck them out of the vapor find only gibberish; a world where the tools of prying are transformed into the instruments of privacy.

There is only one way this vision will materialize, and that is by widespread use of cryptography. Is this technologically possible? Definitely. The obstacles are political -- some of the most powerful forces in government are devoted to the control of these tools. In short, there is a war going on between those who would liberate crypto and those who would suppress it. The seemingly innocuous bunch strewn around this conference room represents the vanguard of the pro-crypto forces. Though the battleground seems remote, the stakes are not: The outcome of this struggle may determine the amount of freedom our society will grant us in the 21st century. To the Cypherpunks, freedom is an issue worth some risk.

The three masked men on the cover of that edition of Wired were prominent cypherpunks Tim May, Eric Hughes and John Gilmore.

Later, Levy wrote a book Crypto: How the Code Rebels Beat the Government — Saving Privacy in the Digital Age covering the "crypto wars" of the 90s in detail. "Code Rebels" in the title is almost synonymuous with "cypherpunks".

The term "cypherpunk" is mildly ambiguous. In most contexts in means anyone advocating cryptography as a tool for social change. However, it can also be used to mean a participant in the cypherpunks mailing list described below. The two meanings obviously overlap, but they are by no means synonymous.

Documents exemplifying cypherpunk ideas include the Crypto Anarchist Manifesto, the Cypherpunk Manifesto and the Ciphernomicon.

Cypherpunk issues

Through most of the 90s the cypherpunks mailing list had extensive discussions of the public policy issues related to cryptography and on the politics and philosophy of concepts such as anonymity, pseudonyms, reputation, and privacy. Of course these discussions are continuing elsewhere since the list shut down.

In at least two senses, people on the list were ahead of more-or-less everyone else. For one thing, the list was discussing questions about privacy, government monitoring, corporate control of information, and related issues in the early 90s that did not become major topics for broader discussion until ten years or so later. For another, at least some list participants were more radical on these issues than almost anyone else.

The list had a range of viewpoints and there was probably no completely unanimous agreement on anything. The general attitude, though, definitely put personal privacy and personal liberty above all other considerations. .... (read more)

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