Can encryption replace the need for paper records of votes cast?
No. The security problems encryption solves are important, but there are other voting security problems that encryption does not solve. For some more information, please see: http://www.schneier.com/crypto-gram-0312.html#9 http://www.schneier.com/crypto-gram-0411.html#1 http://www.schneier.com/crypto-gram-0411.html#2 There are some very ingenious proposals to use encryption in ways that permit a voter to be assured that their vote was counted as intended without allowing that voter to prove to anyone else how they voted. Some of these schemes promise paperless elections. Other schemes give the voter a printed copy of their encrypted ballot, proving to the voter that this ballot really does indeed include their selections in the voting booth, and then destroying the proof before the voter walks away.
