The Federal Reserve Board is testing what computer scientist believe is the world's first unbreakable code system to maintain secrecy of the funds the Fed transfer from bank to bank and the projections it makes of foreign currency exchange rates.

The computerized code is being plugged into the Federal Reserve's telephone lines to garble phone messages so completely that it would be impossible to ge useful information from a tap on the lines. One estimate of the time needed to "break" the code being tested is 17,000 years.

Another estimate is 15 years but only by using an enormous machine whose cost might be $200 million and whose sole purpose would be to perform an exhaustive search for the key. The machine would try every possible key, one at a time, until it stumbled on the right one.

"Even then you would have only customer's key," said Walter Tuchman of the International Business Machines Corp. in Kingston, N.Y., where the first computerized code was developed. "It would be a ridiculous undertaking."

The system being tested by the Federal Reserve is the first of what is expected to be nomerous uses for the unbreakable code keys. Several European governments are considering the system to guard telephone links to far flung embassies. At least two European banks have ordered the system and a Japanese bank is understood to have a ordered it.

So have half a dozen U.S. banks and multinational corporations whose telephone lines are crowded with confidential traffic.The Social Security Administration is looking at it as a way of protecting the privacy of the estimated 140 million Americans it has on file.

The computerized code in all this goes under the more formal name of Data Encryption Standard (DES), given it by the National Bureau of Standards which adopted it two years ago as a model to safeguard government information stored and transmitted by computers.

First developed by IBM, DES involves the use of what mathematicians call an encryption algorithm. In the black art of cryptology, an algorithm transforms intelligible text into coded gibberish by procedures so complicated that decyrption depends on firsthand knowledge of the procedures.

Also essential is a "key," that mysterious third port in a cryptographic machine that controls the transformation of text into gibberish and back to text again. Without the key, even knowing the procedures is useless.

The key is a lt like the combination numbers on a lock. Not the kind of lock that gets picked in Hollywood movies by a thief listening with a stethoscope as the tumblers fall, but a lock that has no tumblers, a high quality lock.

In the DES, the key is 56 digits long. That means the key is any combination of those 56 digits. The key is usually punched into the DES machine when information is ready to be coded, stored and transmitted.

Inside the DES machine is the algorithm, [WORD ILLEGIBLE] stored [WORDS ILLEGIBLE] smaller than a postage stamp that carries the equivalent of 3,500 electrical circuits. Also stored on the chip is the key so that when th right combination of digits is punched in the algorithm is ready to start coding information.

The algorithm took five years to develop but it can code and decode information at a speed of 250,000 letters a second. Its speed help give it what computer people call "random access," meaning it can retrieve information to be coded without disturbing other information in the same computer file.

For instance, it can reach into a file and withdraw a patient's name, age, occupation and physical condition, without retrieving the patient's psychiatric condition, which is very important if privacy is to be protected.

The steps from research and development to testing by the Federal Reserve Board have not been easy. Ther have been charges by computer scientist that DES has been tampered with by the National Security Agency, the supersecret cryptographic arm of the Pentagon whose job is codes, code breaking and eavesdropping. So serious were the charges that the Senate Select Committee on Interligence conducted classified hearing last spring. tr fora dd five.

Stanford University scientist Martin Hellman charged that the NSA ordered IBM to limit the length of the key to 56 digits. Hellman said a 56 digit key was small enough to be broken by NSA's own secret machines. Hellman suggested NSA did not want any encryption machines on the market that it couldn't break.

Hellman suggested there may have been collusion between IBM and NSA, claiming the two might have conspired to place a "Trojan Horse" concept of mathematics into the algorithm so that NSA could shortcut its solution and break the code. Hellman suggested the reason it took so long to develop the algorithm was to devise its Trojan Horse.

The Intelligence Committee cleared NSA of tampering in the selection of the 56-digit key. The committee also found no evidence of any Trojan Horse. The comittee did say that the NSA "indirectly assisted" IBM in development of the algorithm and selection of its key.

But testimony revealed that NSA did ask IBM to keep one thing a secret: "why" the algorithm and its key are designed the way they are. The reason given the committee was that IBM "had inadvertently reinvented some of the secret techniques" already in use at NSA to encode and decode messages.

The controversy over the 5-6-digit key still smolders in some academic circles, but eh Senate committee is convinced the key is not only adequate but is also unbreakble. If a technological breakthrough threatens in the next 10 years to change that. IBM claims all it has to do is double the size of the key to make it permanently unbreakable.