The genitive is always used with some prepositions and verbs, but it is also used for many other things including 1) the attribute genitive (functioning as an adjective), 2) the possessive genitive ("belonging to"), 3) the partitive genitive ("which is part of"), 4) the apposition genitive (same thing as head noun, i.e. "which is"), 5) the descriptive genitive ("described by'), 6) the genitive of comparison ("than" when used with "more," "less," etc.), 7) subjective genitive ("or") with participle ("coming of the son" becomes "the son comes" , 8) objective gentive as the object of a transitive verb and preposition depends on action of verb often in prefix ("in," ‘for’, ‘about’, ‘concerning’, ‘toward’ or ‘against’) ("blasphemy of the spirit" to "blasphemy against the spirit"), 9) absolute: a participle and noun at the beginning of a sentence ("while") 8) of time ("during," "within") of a word indicating time. -- The form of this word requires the addition of extra words in English to capture its meaning.  The most common is the "of" of possession, but it can also mean "belonging to," "part of," "which is," "than" (in comparisons), or  "for," "concerning" or "about" with transitive verbs. 

The genitive absolute is a noun and a genitive particle at the beginning of a sentence, the action happening at the same time as the action of the sentence. Best translation with a "while" or a "during." A present participle is used with simultaneous actions. With an aorist participle, the event in the main clause occurs after the event in the participial clause. The perfect participle describes a situation which was already in existence and which still prevailed at the time of the action of the main verb.

when -- This is from a special word construction that indicates things happening at the same time as the following clause. A "while" or "during" is more accurate.

while -- This is from a special word construction that indicates things happening at the same time as the following clause.