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author | 2015-09-04 09:25:34 +0200 | |
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committer | 2015-09-04 09:25:34 +0200 | |
commit | 3baeb11a8fbcfcdbc31976d421f17b85503b3ecd (patch) | |
tree | 04891d88c1127148f1b390b5a24414e85b270aee /moon-abe/pbc-0.5.14/doc/elementfns.txt | |
parent | 67c5b73910f5fc437429c356978081b252a59480 (diff) |
init attribute-based encryption
Change-Id: Iba1a3d722110abf747a0fba366f3ebc911d25b25
Diffstat (limited to 'moon-abe/pbc-0.5.14/doc/elementfns.txt')
-rw-r--r-- | moon-abe/pbc-0.5.14/doc/elementfns.txt | 111 |
1 files changed, 111 insertions, 0 deletions
diff --git a/moon-abe/pbc-0.5.14/doc/elementfns.txt b/moon-abe/pbc-0.5.14/doc/elementfns.txt new file mode 100644 index 00000000..cadf78b0 --- /dev/null +++ b/moon-abe/pbc-0.5.14/doc/elementfns.txt @@ -0,0 +1,111 @@ +== Element functions == + +Elements of groups, rings and fields are stored in the +element_t+ data type. +Variables of this type must be initialized before use, and should be cleared +after they are no longer needed. + +The +element_+ functions must be used with caution. Just as division by zero +does not make sense for integers, some operations may not make sense for +particular elements. For example, in a ring, one cannot in general invert +elements. + +Another caveat is that many of these functions assume their arguments come from +the same ring, group or field. No implicit type casting is performed. + +For debug builds, turn on run-time checks by defining `PBC_DEBUG` before +including `pbc.h`: + + #define PBC_DEBUG + #include <pbc.h> + +Also, when `PBC_DEBUG` is defined, the following macros are active. +Normally they are replaced with empty statements. + +include::gen/debug.txt[] + +=== Initializing elements === + +When an element is initialized it is associated with an algebraic structure, +such as a particular finite field or elliptic curve group. + +We use G1 and G2 to denote the input groups to the pairing, and GT for the +output group. All have order r, and Zr means the ring of integers modulo r. +G1 is the smaller group (the group of points over the base field). With +symmetric pairings, G1 = G2. + +include::gen/einit.txt[] + +=== Assigning elements === + +These functions assign values to elements. When integers are assigned, +they are mapped to algebraic structures canonically if it makes sense +(e.g. rings and fields). + +include::gen/eassign.txt[] + +=== Converting elements === + +include::gen/econvert.txt[] + +=== Element arithmetic === + +Unless otherwise stated, all +element_t+ arguments to these functions must have +been initialized to be from the same algebraic structure. When one of these +functions expects its arguments to be from particular algebraic structures, +this is reflected in the name of the function. + +The addition and multiplication functions perform addition and multiplication +operations in rings and fields. For groups of points on an ellitpic curve, such +as the G1 and G2 groups associated with pairings, both addition and +multiplication represent the group operation (and similarly both 0 and 1 +represent the identity element). It is recommended that programs choose and +one convention and stick with it to avoid confusion. + +In contrast, the GT group is currently +implemented as a subgroup of a finite field, so only multiplicative operations +should be used for GT. + +include::gen/earith.txt[] + +=== Exponentiating elements === + +Exponentiation and multiexponentiation functions. If it is known in advance +that a particular element will be exponentiated several times in the future, +time can be saved in the long run by first calling the preprocessing function: + + element_pp_t g_pp; + element_pp_init(g_pp, g); + element_pp_pow(h, pow1, g_pp); // h = g^pow1 + element_pp_pow(h, pow2, g_pp); // h = g^pow2 + element_pp_pow(h, pow3, g_pp); // h = g^pow3 + element_pp_clear(g_pp); + +include::gen/epow.txt[] + +=== Comparing elements === + +These functions compare elements from the same algebraic structure. + +include::gen/ecmp.txt[] + +=== Element I/O === + +Functions for producing human-readable outputs for elements. +Converting elements to and from bytes are discussed later. + +include::gen/eio.txt[] + +=== Random elements === + +Only works for finite algebraic structures. Effect on polynomial rings, fields +of characteristic zero, etc. undefined. + +See <<randomref>> for how PBC gets random bits. + +include::gen/erandom.txt[] + +=== Element import/export === + +Functions for serializing and deserializing elements. + +include::gen/etrade.txt[] |