This paper explores the idea of exposing sections of the private key in public-key cryptosystems whose security is based on the intractability of factorising large integers, such as RSA. While substantial work has been done in the area of partial key exposure, the aim has been to investigate the implications of inadvertant partial exposure of the private key. We focus instead on the potential advantages of deliberately revealing portions of the private key, and so, term our scheme "partial hiding". Significant segments of the key are made publicly available, greatly reducing the amount of data which must be securely hidden. This allows us to use biometric readings to protect the secret portion of the private key. We use iris recognition with error-correcting codes for this purpose. We propose an implementation of this system for RSA, and consider the potential risks and advantages of such a scheme.