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Anonymous Internet Banking is the name given to the proposed use of strong financial cryptography to make electronic bank secrecy (or more precisely pseudonymous banking) possible. The bank issues currency in the form of electronic tokens that can be converted on presentation to the bank to some other currency. This concept has a long history in which free banking institutions have issued their own paper currency often backed by a physical commodity. Financial cryptography (FC) is the use of cryptography in applications with strong financial motivation. ...
Bank secrecy (or bank privacy) is a legal principle under which banks are allowed to protect personal information about their customers, through the use of numbered bank accounts or otherwise. ...
Pseudonymity is a word derived from pseudonym, meaning false name, and describes a state of disguised identity resulting from the use of a pseudonym (also called nym). ...
Free banking is a theory of banking which involves only market forces, with a conspicuous absence of central banks and any banking regulations, with only the general commercial laws applicable. ...
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The Concept
Abraham wishes to send Zelda the secret documents. Abraham requests a padlock from Zelda. Zelda sends an open padlock but keeps the key. Abraham padlocks the secret docs in a box and sends them to her. [edit]
The underlying mathematics Let N=PQ where P, Q are large primes with a few additional properties, and thus N is a composite number. Computing the cube root of a number, A, modulo some large composite N is hard, at least compared to computing the cube of A modulo N. In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. ...
A composite number is a positive integer which has a positive divisor other than one or itself. ...
In computing, the modulo operation finds the remainder of division of one number by another. ...
Example: Suppose we're mod 55. Calculating the cube of something is easy, e.g.,
73(mod 55) = 343(mod 55) = 343 − (6 * 55) = 13.
But finding the cube root is tough; solve for x:
x3(mod 55) = 6
However if the factorization of N into two primes is known then both can be done with ease. In the following example all arithmetric is done modulo N.
We have two people, Alice and Bob. For simplicity we shall assume they are using the same bank. Alice wants to transfer $100 to Bob anonymously.
Only the bank has the ability to calculate cube roots, so the bank charges $100 for the service of finding the cube root of a number. The bank pays anyone who can calculate the cube root of an arbitrary number $100.
Bob asks the bank for several random numbers in anticipation that someone will want to pay him money. The bank remembers which numbers he was given so that it knows when Bob manages to calculate a cube root of one of them.
When Alice wants to pay Bob $100 she asks for one of these numbers R from Bob. She multiplies it by w cubed (W) and pays the bank $100 to cube root it. The bank returns the answer which is wr (where r is the cube root of R) so Alice divides it by w and sends Bob r. Bob now knows the cube root of R and can tell the bank what it is. The bank pays him $100.
Different composites N can be used for different denominations of currency so this system doesn't take appreciably longer for large transactions.
Note that if neither Alice nor Bob wishes the bank to know that they performed a transaction with each other then it is hard for the bank to find out. However, in order to ensure this is the case many people need to be making transactions at the same time. Otherwise the bank can figure it out by the timing of the transactions, using Traffic analysis. Traffic analysis is the process of intercepting and examining messages in order to deduce information from patterns in communication. ...
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See also [edit] In cryptography, RSA is an algorithm for public-key encryption. ...
In cryptography, a blind signature is a form of digital signature in which the content of a message is disguised (blinded) before it is signed. ...
The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...
A bearer bond or bearer security is a certificate that represents a bond obligation of, or stock in, a corporation or other intangible property. ...
Electronic money (also known as electronic cash, electronic currency, digital currency, digital money or internet money) refers to money which is exchanged only electronically. ...
External links - End of ordinary money, part 1, part 2
- David Chaum's Scientific American article on Achieving Electronic Privacy
- Untraceable Digital Cash, Information Markets, and BlackNet by Timothy C. May
- Robert A. Hettinga's http://www.shipwright.com/
- A large collection of links - Libertarian Views on Money - its Creation and Control
- J. Orlin Grabbe homepage, DMT network (warning: erotic pictures!)
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