WILLIAM F. FRIEDMAN. the greatest cryptographer of all time, was himself indecipherable and may always remain so. In this biography, the first attempted in book length, Ronald Clark pries a few clues free from the almost impenetrable matrix of his personality, but the Solution remains beyond his, or doubtless anyone's grasp.

What was it in a man only indifferently educated in mechanics and science (and most of that in no way germane to his later work) and almost not at all in higher mathematics that led him to a train of statistical and orthographical-numerical insights that utterly revolutionized - indeed created - modern cryptanalysis? As well ask what made Mozart a gifted composer before he grew his 12-year molars. Prudently, Clark does not try to explain but simply states the facts.

What was it that led to repeated mental breakdowns, agonized self-doubts and persecution complexes in a man recognized by his peers - which was all that should have counted - and at last by the public as the Prometheus of his field, under whose examination every cipher conceived by man and engendered by machine up to his time was resolved to a naked clarity? To that question, les prudently, Clark offers some suggestions: the immigrant Russian Jew's ineradicable sense of nonacceptance; the general idiocy of the military puff-balls who surrounded him; the feeling that he was involved in a dirty game. Perhaps, but not entirely convincing.

Where Clark succeeds is in writing a biography that reads like a novel, as it certainly should, for Friedman's life and work were more wonderful than any fiction. It is the stroy of a lad struggling in straitened circustances - angular, nonconformist, a bit head-strong, grasping for an education and grabbing, not very enthusiastically, at the first promising offer. It was as a geneticist (he had studied botany and agriculture for a few years at Cornell and elsewhere) on the Geneva, Illionors, estate of George Fabyan, a wealthy cotton merchant turned eccentric and subsidizer of quasi-scientific experiments for which he was prepared to take exclusive credit from his underlings.

Among other projects that Fabyan bankrolled was that of an earnest and obsessed woman attempting to prove, by supposed ciphers in the First Folio (1622-23), that Francis Bacon wrote the works attributed to Shakespeare Handy with a camera, the 25-year-old Friedman was called on to make some enlargements of the Folio text, and was thus lured into cryptography. Also employed on the project was a certain Elizebeth Smith, a graduate in English literature. They met, worked together, fell in love, married a year before the United States entered World War 1 and, during 42 ensuing years of profound devotion, made themselves into the most famous husband-and-wife team in the history of cyptography.

From the start, both were deeply skeptical of the Baconian theory; decades later, working out of the Folger Library and with a wit and style unsuspected of them, they produced a book so mordantly devastating of the notion of any ciphers in Shakespeare that, in a rational world, it should have forever laid that nuisance to rest.

How Friedman was whisked from Fabyan's experimental flea-circus to Washington during World War I: how he became between the wars the prime mover and creative fountain of American military cyptography; how his earliest writings totally revolutionized the science and how, as the climax of his career, he broke the Japanese diplomatic code, "the Purple," before Pearl Harbor and created by sheer mathematical deduction a replica of the fiendishly ingenious machine that did the enciphering - all that and much more was far more expertly and usefully recounted ten years ago by David Kahn. in his magnificent book. The Codebrakers.

But what Clark does reveal for the first time publicly is a ghastly story of the harassment in postwar years of Friedman by officials of the National Security Administration, the very organization of which his genious was the foundation. The individual incidents, including the classification of documents that had been public for years and the confiscation from Friedman's library of his own writings, add up to an account of such cruelty and lunacy as to demand, eight years after, his death, some sort of investigation and official declaration of contrition. Any thing less would be an improper memorial to a man to whom the nation owes so much.