The ESIGN signature scheme was initially proposed in 1985. Since then, several variants have been proposed, but only a few have been formally supported using the methodology of provable security. In addition, these schemes are different from the ESIGN-PSS signature scheme submitted to ISO/IEC-14888-2 for standardization. It is believed that ESIGN-PSS is secure against the chosen-message attack, however, there has not yet been any report verifying this belief. This paper presents the security proofs of ESIGN-PSS and a variant of this scheme, denoted ESIGN-PSS-R, which is a signature scheme comprising the ESIGN signature mechanism and the PSS-R mechanism.