I did another synaptic reload and got the same messages ...

W: There is no public key available for the following key IDs:
7638D0442B90D010
W: There is no public key available for the following key IDs:
9D6D8F6BC857C906
W: There is no public key available for the following key IDs:
9D6D8F6BC857C906
W: There is no public key available for the following key IDs:
7638D0442B90D010
W: There is no public key available for the following key IDs:
7638D0442B90D010
W: There is no public key available for the following key IDs:
7638D0442B90D010
W: There is no public key available for the following key IDs:
7638D0442B90D010

I closed the error window . I then used synaptic package manager to update a couple packages , gawk and grep , and the update was successful.
It appears synaptic is working.
I am running Knoppix 7.4.2 on a flash drive with a persistent memory file.

Larry