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Doing a digital signature with RSA alone on a long message would be too slow (presumably using cipher block chaining). Suppose we could do division

Doing a digital signature with RSA alone on a long message would be too slow (presumably using cipher block chaining). Suppose we could do division quickly. Would it be reasonable to compute an RSA based digital signature on a long message by first finding what the message equals, mod n, and then signing the result of the division mod n ?

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