A system and method for providing cryptographic keys which are usable in a network of connected computer nodes applying a signature scheme. The method employs: generating a random secret key usable in the network of connected computer nodes; generating an exponent interval I having a plurality of exponent elements, the exponent interval having a specified first random limit, wherein each element of the plurality of exponent elements of the exponent interval has a unique prime factor tat is larger than a given security parameter; and, providing a public key comprising an exponent-interval description including The first random limit, and a public key value derived from the random secret key, such That the random secret key and a selected exponent value from the plurality of exponent elements in the exponent interval I are usable for deriving a signature value on a message to be sent within The network to a second computer node for verification.