Rashi on Genesis
ועל חרבך—The phrase is equivalent to בחרבך BY THY SWORD. The word על is sometimes used instead of the prefix ב, as (Ezekiel 33:26) “Ye stand by your sword (על חרבכם)”, which is the same as בחרבכם; (Exodus 6:26) “by their hosts (על צבאותם), which is the same as בצבאותם.
Ramban on Genesis
AND ON THY SWORD (‘VE’AL CHARBECHA’) YOU SHALL LIVE. The meaning of ve’al charbecha is as if it were written, becharbecha (by thy sword). A similar case is the verse, For man does not live ‘al halechem’ (on bread) alone,238Deuteronomy 8:3. which means belechem (by bread). Now the blessing is not that he live on the booty he takes from his enemies by the sword, for he has already given him of the fat places of the earth and of the dew of heaven by which he shall live. Instead, the purport of the blessing is that he survive his battles and be victorious, and not fall by the sword of an enemy. It is for this reason that immediately following this he said, And thou shall serve thy brother, meaning, “but you will not prevail over him. Instead, he will prevail over you.”
Rashbam on Genesis
ועל חרבחך תחיה, a reference to Esau’s vocation as a hunter, promising him success with his hunting tools.