Have a look at http://www.nsa.gov/publications/publi00039.cfm . The
one-time pad was used to superencrypt a codebook; two different
codebooks were used. Most of the successful decryptions were done by
1952; there was some additional help from a partial codebook recovered
in 1953. Here's the key section of that monograph:
The Translations and KGB Cryptographic Systems
The VENONA translations from 1942 to 1943 messages occasionally
are fragmentary and difficult to understand. The code itself
was complex and difficult to exploit using pure analytic
techniques. Moreover, the broad contextual sweep of the
content of these messages vastly complicated the difficulty
of reading these KGB systems.
The cryptographic systems used by the KGBís First Chief
Directorate involved a codebook in which words and phrases
were represented by numbers. These numbers were then further
enciphered by the addition of random number groups, additives
taken from a so-called one-time pad. A one-time pad comprised
pages of random numbers, copies of which were used by the
sender and receiver of a message to add and remove an extra
layer of encipherment. One-time pads used properly only
once are unbreakable; however, the KGB?s cryptographic
material manufacturing center in the Soviet Union apparently
reused some of the pages from one-time pads. This provided
Arlington Hall with an opening. Very few of the 1942 KGB
messages could be solved because there was very little
duplication of one-time pad pages in those messages. The
situation was more favorable in 1943, even more so in 1944,
and the success rate improved accordingly. In order to
break into the system successfully, Arlington Hall analysts
had to first identify strip off the layer of additive in
order to attack the underlying code. These two levels of
encryption caused immense difficulty in exploiting the
codebook, and many code groups were, therefore, never
recovered. The KGB messages from 1942 through 1943 and into
1944, as well as from earlier years, were based on one
codebook version. The 1944 to 1945 messages were based on
a new codebook.
Given that intelligence scrutiny of the intercepts continued until 1980,
I doubt there's any more to recover. That said, the NSA admits of the
possibility:
There are still gaps of two different types in the translated
messages, as indicated by the words "unrecovered" or
"unrecoverable." The phrase "unrecovered" meant that the
underlying Russian text in theory could be obtained, but the
cryptanalysts did not have sufficient text to do so.
"Unrecoverable," on the other hand, indicates passages
unaffected by the Soviet misuse of their own system which
therefore could never be solved by cryptanalysts
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