Analysis on Bleichenbacher's Forgery Attack

In 2006, Bleichenbacher presented a new forgery attack against the signature scheme RSASSA-PKCS1-v1_5. The attack allows an adversary to forge a signature on almost arbitrary messages, if an implementation is not proper. Since the example was only limited to the case when the public exponent is 3 and the bit-length of the public composite is 3072, a potential threat is not known. This paper analyzes Bleichenbacher's forgery attack and shows applicable composite sizes for given exponents. We also propose two extended attacks with numerical examples