A cubic RSA code equivalent to factorization

The RSA public-key encryption system of Rivest, Shamir, and Adelman can be broken if the modulus, R say, can be factorized. However, it is still not known if this system can be broken without factorizing R. A version of the RSA scheme is presented with encryption exponent ℓ ≡ 3 (mod 6). For this modified version, the equivalence of decryption and factorization of R can be demonstrated.