  In 1994, Jim Massey proposed the guessing entropy as a measure of the
difficulty that an attacker has to guess a secret used in a cryptographic
system, and established a well-known inequality between entropy and guessing
entropy. Over 15 years before, in an unpublished work, he also established a
well-known inequality for the entropy of an integer-valued random variable of
given variance. In this paper, we establish a link between the two works by
Massey in the more general framework of the relationship between discrete
(absolute) entropy and continuous (differential) entropy. Two approaches are
given in which the discrete entropy (or R\'enyi entropy) of an integer-valued
variable can be upper bounded using the differential (R\'enyi) entropy of some
suitably chosen continuous random variable. As an application, lower bounds on
guessing entropy and guessing moments are derived in terms of entropy or
R\'enyi entropy (without side information) and conditional entropy or Arimoto
conditional entropy (when side information is available).
