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A bike from 1978 is likely to use 'nutted' bolts - in other words, the mounting bolts go all the way through the frame and fork, and are tightened with a standard nut. Most rim brakes in the last few decades use 'recessed' mounting, in which the back the nut is recessed into counterbores in the frame/fork.
However, there are a few modern dual pivot brakes available with 'nutted' bolts (exposed nuts). Several models are made by Tektro, which are decent quality. The difficulty might be the brake reach - 'nutted' brake calipers are most commonly found on medium and long reach brakes, but not for short reach. If you're bike takes medium or long reach brakes, then you can probably find replacements that bolt right up. If you bike requires short reach brakes, then there are still ways to deal with it, but they take a bit more ingenuity.
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