Abraham Sinkov, 90, one of the nation's master cryptanalysts -- a leader among those who labored in secret over the decades to crack the codes of the nation's adversaries -- died Jan. 19 at a hospital in Mesa, Ariz. He had Parkinson's disease and a heart ailment.

Dr. Sinkov, a mathematician, was one of three men hired in the early 1930s by the legendary code-breaker William Friedman to work under him in the Army's new Signal Intelligence Service.

From this small nucleus grew the nation's huge cryptologic apparatus of today, author David Kahn wrote in "The Codebreakers," a comprehensive history of the world of secret communication.

During World War II, Dr. Sinkov headed the communications intelligence organization attached to the headquarters of Gen. Douglas MacArthur in Australia. It was charged with intercepting and decoding Japanese messages from all over the Southwest Pacific theater.

"Sinkov worked wonders," Kahn wrote. When an enemy airplane was shot down, providing keys to secret Japanese air-to-ground communications, it was found that Dr. Sinkov had already broken most of the codes involved, the author wrote.

Even during the 1940s, much of the work involved mathematics. Dr. Sinkov began in code-breaking when one of the main pieces of equipment was the mechanical calculating machine. He was credited with doing much to bring cryptanalysis into the age of the high-speed electronic computer. "He was one of the leading mathematicians in the growth of the cryptologic community in World War II and in the period after the war," said Mike Levin, a retired official of the National Security Agency, the nation's code-breaking organization.

Dr. Sinkov became one of the top officials of the NSA, from which he retired in 1963.

Dr. Sinkov was born in Philadelphia and moved with his family while young to New York. He was a graduate of the City College of New York and received a master's degree in mathematics from Columbia University. He later received a doctorate in mathematics from George Washington University.

Dr. Sinkov began teaching high school in New York during the late 1920s, but a civil service exam helped funnel him into the Army code-breaking unit run by Friedman, who was looking for mathematicians who were also linguists.

Working in a highly sensitive area, Dr. Sinkov developed the habit of not discussing his work, said his son, Michael. "When people asked what he did, he said, I'm a mathematician,' " his son recalled.

In 1941, only months before the United States entered World War II, Dr. Sinkov, then an Army major, led a U.S. group to England aboard a British battleship to exchange secret code-breaking information.

The Americans took with them one of the major cryptological developments of the prewar period, a machine created to break what specialists called the Japanese Purple Code.

The trip, according to intelligence historians, laid the groundwork for a formal cooperation -- which continues to this day -- between U.S. code-breakers and those of the United Kingdom, Canada, Australia and New Zealand.

Although Dr. Sinkov said little at home about what he did, his son said, he was unambiguous about how he felt about it.

He said he loved it so much that he would have done it for nothing. "He considered himself a very, very lucky man," Michael Sinkov said.

During World War II, Dr. Sinkov rose to the rank of colonel, and he was decorated with the Legion of Merit and an Oak Leaf Cluster. In his book, Kahn described him as a "sweet and unmilitary man" who seemed slightly embarrassed by the colonel's eagles on his shoulders and was unable to return a salute "without blurting out a good morning.' " Dr. Sinkov's son said he believed that his father had been "a little nonplused" by the characterization, "but he was certainly an extremely gentle, thoughtful, tolerant man."

After retiring from the NSA, Dr. Sinkov moved to Arizona and taught mathematics for 20 years at Arizona State University.

He was one of the first people inducted into the Army Intelligence Hall of Fame at Fort Huachuca, Ariz., his son said.

Last August, according to Levin, the retired NSA official, Dr. Sinkov received a letter from President Clinton, congratulating him on his 90th birthday and "thanking him for the outstanding contribution to the nation's security that he had made."

Friedman and Solomon Kullback, who was hired along with Dr. Sinkov in the early 1930s for the Army, have died, Levin said. He said the last survivor of their four-member group is Frank Rowlett, who was well known for his work in breaking the Purple Code.

Dr. Sinkov's wife, Delia, died in 1983. Survivors include his son, of Los Angeles.