The experts say this new method may make it possible to read other ancient scrolls, including several Dead Sea scrolls and about 300 carbonized ones from Herculaneum, which were destroyed by the volcanic eruption of Mount Vesuvius in A.D. 79.

The date of the En-Gedi scroll is the subject of conflicting evidence. A carbon-14 measurement indicates that the scroll was copied around A.D. 300. But the style of the ancient script suggests a date nearer to A.D. 100. “We may safely date this scroll” to between A.D. 50 and 100, wrote Ada Yardeni, an expert on Hebrew paleography, in an article in the journal Textus. Dr. Tov said he was “inclined toward a first-century date, based on paleography.”

The feat of recovering the text was made possible by software programs developed by W. Brent Seales, a computer scientist at the University of Kentucky. Inspired by the hope of reading the many charred and unopenable scrolls found at Herculaneum, near Pompeii in Italy, Dr. Seales has been working for the last 13 years on ways to read the text inside an ancient scroll.

Methods like CT scans can pick out blobs of ink inside a charred scroll, but the jumble of letters is unreadable unless each letter can be assigned to the surface on which it is written. Dr. Seales realized that the writing surface of the scroll had first to be reconstructed and the letters then stuck back to it.

He succeeded in 2009 in working out the physical structure of the ruffled layers of papyrus in a Herculaneum scroll.

He has since developed a method, called virtual unwrapping, to model the surface of an ancient scroll in the form of a mesh of tiny triangles. Each triangle can be resized by the computer until the virtual surface makes the best fit to the internal structure of the scroll, as revealed by the scanning method. The blobs of ink are assigned to their right place on the structure, and the computer then unfolds the whole 3-D structure into a 2-D sheet.