TripleDecompositionProtocolInstance::TripleDecompositionProtocolInstance
( int braid_rank ,
quadruple< Word , Word , Word , Word > conjugators ,
quintuple< Word , Word , Word , Word , Word > privateKeyA ,
quintuple< Word , Word , Word , Word , Word > privateKeyB ) :
theRank( braid_rank ),
theConjugators( conjugators ),
thePrivateKeyA( privateKeyA ),
thePrivateKeyB( privateKeyB )
{
thePublicKeyA.first = DehornoyForm( braid_rank , privateKeyA.first * privateKeyA.fourth ).getDehornoyForm( );
thePublicKeyA.second = DehornoyForm( braid_rank , -privateKeyA.fourth * privateKeyA.second * privateKeyA.fifth ).getDehornoyForm( );
thePublicKeyA.third = DehornoyForm( braid_rank , -privateKeyA.fifth * privateKeyA.third ).getDehornoyForm( );
thePublicKeyB.first = DehornoyForm( braid_rank , privateKeyB.first * privateKeyB.fourth ).getDehornoyForm( );
thePublicKeyB.second = DehornoyForm( braid_rank , -privateKeyB.fourth * privateKeyB.second * privateKeyB.fifth ).getDehornoyForm( );
thePublicKeyB.third = DehornoyForm( braid_rank , -privateKeyB.fifth * privateKeyB.third ).getDehornoyForm( );
theSharedKey = ThRightNormalForm( braid_rank , privateKeyA.first * privateKeyB.first * privateKeyA.second * privateKeyB.second * privateKeyA.third * privateKeyB.third );
}
set<ThRightNormalForm>
ThRightNormalForm::computeCentralizer( ) const
{
const Permutation omega = Permutation::getHalfTwistPermutation( theRank );
set<ThRightNormalForm> result;
map< ThRightNormalForm , ThRightNormalForm > new_states;
map< ThRightNormalForm , ThRightNormalForm > unchecked_states;
map< ThRightNormalForm , ThRightNormalForm > checked_states;
if( theOmegaPower<0 ) {
ThRightNormalForm rep = *this;
rep.theOmegaPower = -theOmegaPower%2;
cout << "Power = " << rep.theOmegaPower << endl;
new_states[rep] = ThRightNormalForm( theRank );
} else
new_states[*this] = ThRightNormalForm( theRank );
/*
cout << endl << " init:" << endl;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
cout << (*new_states.begin( )).first;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
*/
while( !new_states.empty( ) ) {
{ // was unsupported by MSVC++
// checked_states.insert( unchecked_states.begin(), unchecked_states.end() );
map< ThRightNormalForm , ThRightNormalForm >::iterator m_it = unchecked_states.begin( );
for( ; m_it!=unchecked_states.end( ) ; ++m_it )
checked_states.insert( *m_it );
}
// process all new vertices:
unchecked_states = new_states;
new_states.clear( );
size_t counter = 0;
map< ThRightNormalForm , ThRightNormalForm >::const_iterator
it = unchecked_states.begin( );
for( ; it!=unchecked_states.end( ) ; ++it ) {
ThRightNormalForm cur_el = (*it).first;
ThRightNormalForm cur_conj = (*it).second;
/*
cout << endl << " cur_el:" << endl;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
cout << cur_el;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
*/
// cout << "c1" << endl;
// cout << cur_el << endl;
// set<Permutation> conjugators = getSimpleSummitConjugators( G , cur_el );
set<Permutation> conjugators = cur_el.getSimpleConjugators( );
// cout << "c2" << endl;
for( set<Permutation>::const_iterator conj_it = conjugators.begin( ) ; conj_it!=conjugators.end( ) ; ++conj_it ) {
ThRightNormalForm r_mult( theRank , 0 , list<Permutation>( 1 , *conj_it ) );
if( *conj_it==omega )
r_mult = ThRightNormalForm( theRank , 1 , list<Permutation>( 0 ) );
ThRightNormalForm new_el = -r_mult * cur_el * r_mult;
ThRightNormalForm new_conj = cur_conj * r_mult;
/*
cout << "**********************************************" << endl;
cout << endl << " new_el:" << endl;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
cout << new_el;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
cout << endl << " new_conj:" << endl;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
cout << new_conj;
cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
*/
// check whether we made a loop
map< ThRightNormalForm , ThRightNormalForm >::const_iterator
fit = new_states.find( new_el );
if( fit!=new_states.end( ) ) {
result.insert( new_conj * -(*fit).second );
continue;
}
fit = unchecked_states.find( new_el );
if( fit!=unchecked_states.end( ) ) {
result.insert( new_conj * -(*fit).second );
continue;
}
fit = checked_states.find( new_el );
if( fit!=checked_states.end( ) ) {
result.insert( new_conj * -(*fit).second );
continue;
}
cout << "Size = " << new_states.size( ) << "," << unchecked_states.size( ) << "," << checked_states.size( ) << " (" << result.size( ) << ")" << endl;
new_states[new_el] = new_conj;
// cout << cur_el << endl;
// cout << new_el;
// cout << "+++++++++++++++++++++++++++++++" << endl;
if( counter!=result.size( ) ) {
ofstream of( "out.txt" );
set<ThRightNormalForm>::iterator r_it = result.begin();
for( ; r_it!=result.end( ) ; ++r_it ) {
Word w = shortBraidForm( theRank , (*r_it).getShortWord() );
of << w << endl;
}
counter = result.size( );
}
if( new_el.theOmegaPower<0 ) {
cerr << "Fail" << endl;
exit(1);
}
}
}
}
cout << "+++++++++++++++++++++++++++++++" << endl;
set<ThRightNormalForm>::iterator r_it = result.begin( );
for( ; r_it!=result.end( ) ; ++r_it ) {
cout << *r_it << endl;
ThRightNormalForm n = -(*r_it) * (*this) * (*r_it);
if( n!=*this ) {
cout << "Error!" << endl;
exit( 23 );
}
}
return result;
}
