Chapter 3. Pairing functions

Table of Contents

Initializing pairings
Applying pairings
Other pairing functions

An application should first initialize a pairing object. This causes PBC to setup curves, groups and other mathematical miscellany. After that, elements can be initialized and manipulated for cryptographic operations.

Parameters for various pairings are included with the PBC library distribution in the param subdirectory, and some are suitable for cryptographic use. Some programs in the gen subdirectory may be used to generate parameters (see Chapter 7, Bundled programs). Also, see the PBC website for many more pairing parameters.

Pairings involve three groups of prime order. The PBC library calls them G1, G2, and GT, and calls the order r. The pairing is a bilinear map that takes two elements as input, one from G1 and one from G2, and outputs an element of GT.

The elements of G2 are at least as long as G1; G1 is guaranteed to be the shorter of the two. Sometimes G1 and G2 are the same group (i.e. the pairing is symmetric) so their elements can be mixed freely. In this case the pairing_is_symmetric function returns 1.

Bilinear pairings are stored in the data type pairing_t. Functions that operate on them start with pairing_.

Initializing pairings

To initialize a pairing from an ASCIIZ string:

pairing_t pairing;
pairing_init_set_str(pairing, s);  // Where s is a char *.

The string s holds pairing parameters in a text format. The param subdirectory contains several examples.

Alternatively, call:

pairing_t pairing;
pairing_init_pbc_param(pairing, param);

where param is an initialized pbc_param_t (see Chapter 5, Param functions).

int pairing_init_set_str(pairing_t pairing, const char *s)

Initialize pairing from parameters in a ASCIIZ string str Returns 0 on success, 1 on failure.

int pairing_init_set_buf(pairing_t pairing, const char *s, size_t len)

Same, but read at most len bytes. If len is 0, it behaves as the previous function. Returns 0 on success, 1 on failure.

void pairing_init_pbc_param(struct pairing_s *pairing, pbc_param_t p)

Initialize a pairing with pairing parameters p.

void pairing_clear(pairing_t pairing)

Free the space occupied by pairing. Call whenever a pairing_t variable is no longer needed. Only call this after all elements associated with pairing have been cleared, as they need information stored in the pairing structure.