>The cryptographic definition of constant-time postdates the algorithmic one by decades, i think.
The normal usage of the phrase "constant time" predates CS by centuries, and it is much closer in usage to the crypto version than the complexity version.
Crypto uses the term "constant time" to mean same time for any input, while the general CS community uses O(1) to mean bounded time and also often uses complexity to hide log N terms. It also allows variable time, as long as it's bounded (and that sometimes allows hiding terms like log N or log log N...).
A good example is most algorithms treat addition as a constant time operation, but, for example, addition of indices for lookups is not constant time when inputs are unbounded. So if you compute an index by addition and ignore the logN time to do the addition, then you fudged. Yet this is commonplace in complexity theory, which models many basic operations as constant time when they are not for unbounded inputs.
For example, a "constant time" hash table operation, which often indexes arbitrarily large indices with addition, ignores the log N needed to add arbitrarily large indices.
Thus crypto uses the phrase in the more precise, centuries old usage.
The normal usage of the phrase "constant time" predates CS by centuries, and it is much closer in usage to the crypto version than the complexity version.
Crypto uses the term "constant time" to mean same time for any input, while the general CS community uses O(1) to mean bounded time and also often uses complexity to hide log N terms. It also allows variable time, as long as it's bounded (and that sometimes allows hiding terms like log N or log log N...).
A good example is most algorithms treat addition as a constant time operation, but, for example, addition of indices for lookups is not constant time when inputs are unbounded. So if you compute an index by addition and ignore the logN time to do the addition, then you fudged. Yet this is commonplace in complexity theory, which models many basic operations as constant time when they are not for unbounded inputs.
For example, a "constant time" hash table operation, which often indexes arbitrarily large indices with addition, ignores the log N needed to add arbitrarily large indices.
Thus crypto uses the phrase in the more precise, centuries old usage.