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-[[bundlechap]]
-== Bundled programs ==
-
-Several binaries and curve parameters are bundled with the PBC library,
-such as <<pbcintro, the `pbc` program>>.
-
-The `param` subdirectory contains pairing parameters one might use in
-a real cryptosystem. Many of the test programs read the parameters
-from files such as these on standard input, for example:
-
-  $ benchmark/benchmark < param/c159.param
-  $ example/bls < param/e.param
-
-[[pbcref]]
-=== Pairing-based calculator ===
-
-The `pbc` subdirectory contains the pairing-based calculator, `pbc`,
-which is loosely based on `bc`, a well-known arbitrary precision
-calculator.
-
-See `pairing_test.pbc` for an example script. Some differences: the assignment
-operator is `:=`, and newlines are ordinary whitespace and not statement
-terminators.
-
-If started with the `-y` option, the syntax is compatible with `bc`: newlines
-are treated as statement terminators and `=` is assignment. Additionally,
-`pbc` displays a prompt. This mode may be easier for beginners.
-
-Initially, the variables G1, G2, GT and Zr are represent groups associated with
-a particular A pairing.
-
-An element is represented with a tree of integers, such as `[[1,2], 3]`, or
-`4`.
-
-Assignments such as `variable := expression;` return the value of the variable.
-
-The arithmetic operators `+, -, /, *, ^` have the standard precedence.
-The C comparison operators and ternary operator are available.
-
-Each statement should be terminated by a semicolon.
-
-Comments are the same as in (original) C, or begin with "#" and end at a
-newline.
-
-Some of the pbc functions:
-
-+init_pairing_A()+::
-Set the variables G1, G2, GT and Zr to the groups in a particular A pairing:
-+
-  init_pairing_A();
-+
-Other sample pairings can be used by replacing `A` with one of `D, E, F, G`.
-
-+rnd(+'G'+)+::
-Returns a random element of an algebraic structure 'G', e.g:
-+
-  g := rnd(Zr);
-+
-Synonym: `random`.
-
-+pairing(+'g, h'+)+::
-Returns the pairing applied to 'g' and 'h'.
-The element 'g' must be an element of G1 and 'h' of G2, e.g:
-+
-  pairing(rnd(G1), rnd(G2));
-
-'G'+(+'g'+)+::
-Maps an element 'g' to element of the field 'G', e.g:
-+
-  Zr(123);
-  GT([456, 789]);
-
-=== Parameter generation ===
-
-Programs that generate pairing parameters are located in the `gen`
-subdirectory. Some of the programs are already functional enough to be used to
-find parameters for real applications. I need to write more documentation
-first; for now, read the source!
-
-*listmnt*::
-  Searches for discriminants D that lead to MNT curves with subgroups
-  of prime order.
-
-*genaparam*, *gena1param*, *gendparam*, *geneparam*, *genfparam*, *gengparam*::
-  Prints parameters for a curve suitable for computing pairings of a given type.
-  The output can be fed to some of the other test programs.  The programs
-  `gendparam` and `gengparam` should be given a discriminant as the first
-  argument.
-
-*hilbertpoly*::
-  Prints the Hilbert polynomial for a given range of discriminants. Computing
-  the Hilbert polynomial is an intermediate step when generating type D
-  parameters.
-
-=== Example cryptosystems ===
-
-In the `example` subdirectory there are various programs that read curve
-parameters on standard input and perform computations that would be required in
-a typical implementation of a pairing-based cryptosystem. Sample schemes
-include:
-
--   Boneh-Lynn-Shacham short signatures
--   Hess identity-based signatures
--   Joux tripartite Diffie-Hellman
--   Paterson identity-based signatures
--   Yuan-Li identity-based authenticated key agreement
--   Zhang-Kim identity-based blind/ring signatures
--   Zhang-Safavi-Naini-Susilo signatures
-
-More work would be required to turn these programs into real applications.
-
-=== Benchmarks ===
-
-I use the programs in the `benchmark` subdirectory to measure running times of
-pairings, and also RSA decryptions.
-
-The `benchmark` program takes pairing parameters on standard input and reports
-the average running time of the pairing over 10 runs, while `timersa` estimates
-the time required to perform one 1024-bit RSA decryption.