Abstract. We construct a signature scheme that is proved secure, without random oracles, under the strong RSA assumption. Unlike other efficient strong-RSA based schemes, the new scheme does not generate large prime numbers during signing. The public key size and signature size are competitive with other strong RSA schemes, but verification is less efficient. The new scheme adapts the prefix signing technique of Hohenberger and Waters (CRYPTO 2009) to work without generating primes. Keywords. Digital Signatures, Strong RSA.