Yet law enforcement and intelligence agency leaders argue that such efforts thwart their ability to monitor kidnappers, terrorists and other adversaries. In Britain, Prime Minister David Cameron threatened to ban encrypted messages altogether. In the United States, Michael S. Rogers, the director of the N.S.A., proposed that technology companies be required to create a digital key to unlock encrypted data, but to divide the key into pieces and secure it so that no one person or government agency could use it alone.The encryption debate has left both sides bitterly divided and in fighting mode. The group of cryptographers deliberately issued its report a day before James B. Comey Jr., the director of the Federal Bureau of Investigation, and Sally Quillian Yates, the deputy attorney general at the Justice Department, are scheduled to testify before the Senate Judiciary Committee on the concerns that they and other government agencies have that encryption technologies will prevent them from effectively doing their jobs.