Avigdor Lieberman, Israeli Foreign Minister, Resigns

JERUSALEM — Facing indictment for breach of trust and fraud, Israel’s foreign minister, Avigdor Lieberman, resigned his post Friday afternoon amid mounting political pressure, upending the campaign landscape five weeks before national elections.

Mr. Lieberman, a powerful but polarizing figure, wrote on his Facebook page, “I know that I committed no crime,” but said he was stepping down so “I will be able to put an end to this matter swiftly and without delay and to clear my name completely.”

Mr. Lieberman, who is also a member of Parliament, indicated that he still hoped to compete in the Jan. 22 balloting, suggesting a possible plea bargain. The expected indictment, which prosecutors announced on Thursday, concerns a relatively minor offense compared with a broader case of money laundering and fraud that was dropped after an investigation stretching for more than 12 years.

“I believe that the citizens of the State of Israel are entitled to go to the polling stations after this matter has already been resolved,” Mr. Lieberman’s statement said. If a legal ruling could be made before the elections, “I might continue to serve the State of Israel and the citizens of Israel as part of a strong and united leadership that will cope with the security, political and economic challenges facing the State of Israel.”

Mr. Lieberman, 54, leads the secular, ultranationalist Yisrael Beiteinu party, which joined forces in October with Prime Minister Benjamin Netanyahu’s Likud Party. A populist immigrant from the former Soviet Union, he was widely considered as a potential successor to Mr. Netanyahu as leader of Israel’s right wing, though his hard line on the Palestinian question, among other issues, alienated many Western allies.

After the charges were announced, Mr. Lieberman told supporters that he had been hounded by corruption accusations since July 1996, when he served as a top aide to Mr. Netanyahu during his first term as prime minister. “Since then till today, not a day has passed without me being referred to as ‘a suspect,’ ‘being under investigation,’ ‘being an intelligence target,’ ” Mr. Lieberman said. “This has been one long and rolling case, receiving a different title every now and then.”

The conduct for which Mr. Lieberman will face indictment stems from an investigation into other allegations. He is accused of promoting Israel’s former ambassador to Belarus for another post after the ambassador gave him confidential information regarding an Israeli police investigation into Mr. Lieberman’s activities.

But Mr. Lieberman will not face charges on the underlying, more serious case, in which he was suspected of receiving millions of dollars from international tycoons with business interests in Israel through companies formally led by family members or associates.

Israel’s attorney general, Yehuda Weinstein, said Thursday in a report announcing his decision that he could not adequately prove a link between Mr. Lieberman and the money, though he said, “The suspicions against Lieberman’s series of intricate and intertwined, underhanded actions cannot be ruled out.”

Born in Moldova, Mr. Lieberman enjoys wide support among Israel’s one million immigrants from the former Soviet Union. He lives in a West Bank settlement considered illegal under international law, and he is perhaps the government’s harshest critic of President Mahmoud Abbas of the Palestinian Authority, having called for his ouster and denounced as “diplomatic terrorism” his recent bid for upgraded Palestinian status at the United Nations.

Polls have consistently shown that Mr. Lieberman’s joint ticket with Mr. Netanyahu, known here as Likud Beiteinu, is expected to receive up to 40 of the 120 seats in Israel’s next Parliament, by far the largest bloc. The merger was seen as crowning him a top contender to eventually follow Mr. Netanyahu as prime minister.

Opposition leaders, who on Thursday had called for Mr. Lieberman’s resignation, were swift to embrace it on Friday, but not without adding jabs.

Zahava Gal-On, chairwoman of the left-wing Meretz party, said Mr. Lieberman had “spared himself ignobility and disgrace” by stepping down, according to the Web site of Channel 2 News. Shelly Yacimovich, chairwoman of the Labor Party, said he had “severely undermined the rule of law and damaged the public’s faith in its elected officials and democracy.”

Tzipi Livni, a former foreign minister who now heads the new Hatnua Party, issued a more moderate statement, saying: “Avigdor Lieberman performed the right and necessary action. We hope he will receive a swift legal proceeding.”

Mr. Netanyahu had no immediate comment on Mr. Lieberman’s resignation Friday, but on Thursday had offered only support. “I believe in Israel’s legal system and respect it,” the prime minister said in a statement. “The right that it grants any Israeli citizen to defend himself also extends to Minister Lieberman, and I hope for him that he’ll be able to prove that he’s also innocent regarding the only case that remains.”

Under Israeli law, when a cabinet minister resigns, the prime minister becomes “custodian” of his portfolio, and Mr. Netanyahu is expected to handle foreign affairs himself at least until after the elections.

Jonathan Rosen contributed reporting.

This article has been revised to reflect the following correction:

Correction: December 14, 2012

An earlier version of this article misstated the timing of the forming of a coalition between Yisrael Beiteinu and Likud. It took place in October, not last month.

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Shares Continue to Slide, Awaiting a Budget Accord

Stocks fell on Friday as another decline in Apple took a toll and investors unloaded some shares because of the uncertainty surrounding the budget negotiations in Washington.

All three major stock indexes ended the week slightly lower, the Nasdaq for the second consecutive week.

Apple’s stock slid 3.76 percent, to $509.79, after the iPhone 5 received a tepid reception in China.

UBS maintained its buy rating on Apple, but cut its price target to $700 from $780 and expressed concerns that iPhone production may be dropping.

Shares of Apple have fallen 27.4 percent since their closing high of $702.10 on Sept. 19.

The S.& P. Information Technology Index lost 1 percent as Apple fell and Jabil Circuit fell 5.5 percent, to $17.51, after UBS cut its price target.

Stocks have been treading water as the possibility of not reaching a deal to settle the budget impasse until early next year is rising.

“We’re faced with uncertainty,” said Larry Peruzzi, senior equity trader at Cabrera Capital Markets in Boston. “And that’s going to continue now into January. It basically puts everybody on hold and just have the markets kind of thrash around.”

President Obama and the House speaker, John A. Boehner, held a “frank” meeting on Thursday at the White House to discuss how to avoid the tax increases and spending cuts set to kick in early in 2013.

The Dow Jones industrial average slipped 35.71 points, or 0.27 percent, to 13,135.01. The Standard & Poor’s 500-stock index fell 5.87 points, or 0.41 percent, to 1,413.58. The Nasdaq composite index lost 20.83 points, or 0.70 percent, to 2,971.33.

For the week, the Dow slipped 0.15 percent, while the S.& P. 500 fell 0.3 percent and the Nasdaq declined 0.2 percent.

Among other Nasdaq decliners, shares of the chip maker Qualcomm slid 4.7 percent, to $59.83.

Best Buy slid 14.7 percent, to $12.05, after the electronics retailer agreed to extend the deadline for the company’s founder to make a bid.

Among the day’s economic data, consumer prices fell in November for the first time in six months, indicating inflation pressures were muted.

A separate report showed manufacturing grew at its swiftest rate in eight months in December.

Chinese data was encouraging, as Chinese manufacturing grew at its fastest rate in 14 months in December. The news was deemed as helpful for materials companies in the United States, including United States Steel, which rose 6.8 percent, to $23.85.

Interest rates were lower. The Treasury’s benchmark 10-year note rose 8/32, to 99 9/32, and the yield fell to 1.70 percent from 1.73 percent late Thursday.

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My Story: Taking on Cancer Again, This Time With the Wisdom of Age

After I finished eight months of treatment for testicular cancer in my mid-20s, my psychologist said, “Well, that was like having five years of therapy all at once.” What he meant was that you learn a lot about yourself in weekly talk sessions, but during a life-threatening illness, the “issues” come at you nonstop. I relished the slow unfolding of myself in the first, but I resented — no, hated — every step of the second. Nearly two decades later, when confronted with the same diagnosis, I finally understood the benefits of that earlier trial by fire, much as I did the wisdom of Ralph Waldo Emerson when he wrote, “The years teach much which the days never knew.”

To be sure, there were benefits to being young — I was 26 — when I was first diagnosed, not the least of which was my competitive swimmer’s body. After almost dying in the I.C.U. and becoming a “patient-in-residence,” I plunged back into the pool (and my day job) just a fortnight after my release.

Ah, the determination — and denial — of youth.

But facing cancer at that young age had more drawbacks than benefits, not the least of which was losing my sense of invulnerability when confronted with the prospect of disfigurement and disability, even death.

Less obvious, but still unsettling, was the loss of my laissez-faire attitude toward life itself. I had always been the kind of guy who focused on the journey (the experience) more than the destination (winning). During backstroke events prior to falling ill I was more interested in watching the clouds race overhead than the swimmer racing in the next lane. This mindset didn’t do much for my success in the pool, but it helped define who I was.

To make matters worse, conventional wisdom says only one thing matters when it comes to cancer: Beating the hell out of it. Suddenly I had to find an emotional depth I hadn’t sought before, a passion for a fight that I didn’t want.

Am I the kind of person who can win this battle? I asked myself early on.

To ensure that I was, I did a complete about-face, saying “No way” to the journey and “Hell, yes” to the destination. Every decision began to turn on life and longevity, and for that I tolerated side effects like hair loss, neuropathy and “dry ejaculation” — because I simply had to win.

I re-read Dylan Thomas, who told me to “rage, rage against the dying of the light,” and I did. I became a rager. And it almost ruined my life.

Not in terms of my health, because in fact my treatment was effective. I was “clinically cured” and chalked up that achievement to my new “Top Gun” mentality. Then I jumped back into daily life — and managed to mess everything up. I applied my new approach to relationships (“My way or the highway”), and got dumped by my boyfriend. In graduate school, I aced my studies but lost friends.

Fortunately, my best friends didn’t hold back on telling me I had become a jerk, and that got my attention. I had upshifted at the start of my treatment, but now I needed to downshift. I struggled to find my pace, but eventually found a middle gear, more vulnerable than I cared to be but also more human.

The second time I was diagnosed, the oncologist sat me down to give me the new installment of the old bad news. I surprised myself and my friends with a very different approach.

I did not rage, which isn’t to say I was happy about this predicament. And I had moved on from my original question to a new one: How can I go through this and still be the kind of person I want to be?

In the intervening years, I had come to realize that cancer victories are not won by personality types, but by a combination of doggedness (choosing the best physician, getting the right diagnosis and treatment), responsibility (doing your own research and taking care of your overall health), and plain old luck.

From that very first day of my second time around, I challenged myself not to shift into that “win at any cost” mentality. That’s where the gift of age and experience came to my aid, even if my older body did not. Over the years I had learned that life was not a series of choices between winners and losers — I knew that way of seeing things to be oversimplified, if not dead wrong. You can be stronger than an ox, never miss a day of work, or swim your lungs out and, damn it, still die.

I could become a jerk again and focus on the end point, or I could accept that the journey is the destination – which I did.

Two months after I had been diagnosed and two days before the surgeon was scheduled to excise my remaining testicle, I had a dream so vivid — “I am cancer-free!” — that I demanded to go on a “surveillance” protocol. Reluctantly my doctor agreed, but by year’s end I had “won” the debate when my so-called tumor was reclassified as a benign nodule.

The years had taught me much — both to listen to my body and to trust in its wisdom. And, most importantly, to find the courage to speak its truth — whether in the doctor’s office or out in the world.

Steven Petrow writes the Civil Behavior column for Booming, addressing questions about gay and straight etiquette for a boomer-age audience. You can find him on Facebook and Twitter.

You can follow Booming via RSS here or visit nytimes.com/booming.

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My Story: Taking on Cancer Again, This Time With the Wisdom of Age

After I finished eight months of treatment for testicular cancer in my mid-20s, my psychologist said, “Well, that was like having five years of therapy all at once.” What he meant was that you learn a lot about yourself in weekly talk sessions, but during a life-threatening illness, the “issues” come at you nonstop. I relished the slow unfolding of myself in the first, but I resented — no, hated — every step of the second. Nearly two decades later, when confronted with the same diagnosis, I finally understood the benefits of that earlier trial by fire, much as I did the wisdom of Ralph Waldo Emerson when he wrote, “The years teach much which the days never knew.”

To be sure, there were benefits to being young — I was 26 — when I was first diagnosed, not the least of which was my competitive swimmer’s body. After almost dying in the I.C.U. and becoming a “patient-in-residence,” I plunged back into the pool (and my day job) just a fortnight after my release.

Ah, the determination — and denial — of youth.

But facing cancer at that young age had more drawbacks than benefits, not the least of which was losing my sense of invulnerability when confronted with the prospect of disfigurement and disability, even death.

Less obvious, but still unsettling, was the loss of my laissez-faire attitude toward life itself. I had always been the kind of guy who focused on the journey (the experience) more than the destination (winning). During backstroke events prior to falling ill I was more interested in watching the clouds race overhead than the swimmer racing in the next lane. This mindset didn’t do much for my success in the pool, but it helped define who I was.

To make matters worse, conventional wisdom says only one thing matters when it comes to cancer: Beating the hell out of it. Suddenly I had to find an emotional depth I hadn’t sought before, a passion for a fight that I didn’t want.

Am I the kind of person who can win this battle? I asked myself early on.

To ensure that I was, I did a complete about-face, saying “No way” to the journey and “Hell, yes” to the destination. Every decision began to turn on life and longevity, and for that I tolerated side effects like hair loss, neuropathy and “dry ejaculation” — because I simply had to win.

I re-read Dylan Thomas, who told me to “rage, rage against the dying of the light,” and I did. I became a rager. And it almost ruined my life.

Not in terms of my health, because in fact my treatment was effective. I was “clinically cured” and chalked up that achievement to my new “Top Gun” mentality. Then I jumped back into daily life — and managed to mess everything up. I applied my new approach to relationships (“My way or the highway”), and got dumped by my boyfriend. In graduate school, I aced my studies but lost friends.

Fortunately, my best friends didn’t hold back on telling me I had become a jerk, and that got my attention. I had upshifted at the start of my treatment, but now I needed to downshift. I struggled to find my pace, but eventually found a middle gear, more vulnerable than I cared to be but also more human.

The second time I was diagnosed, the oncologist sat me down to give me the new installment of the old bad news. I surprised myself and my friends with a very different approach.

I did not rage, which isn’t to say I was happy about this predicament. And I had moved on from my original question to a new one: How can I go through this and still be the kind of person I want to be?

In the intervening years, I had come to realize that cancer victories are not won by personality types, but by a combination of doggedness (choosing the best physician, getting the right diagnosis and treatment), responsibility (doing your own research and taking care of your overall health), and plain old luck.

From that very first day of my second time around, I challenged myself not to shift into that “win at any cost” mentality. That’s where the gift of age and experience came to my aid, even if my older body did not. Over the years I had learned that life was not a series of choices between winners and losers — I knew that way of seeing things to be oversimplified, if not dead wrong. You can be stronger than an ox, never miss a day of work, or swim your lungs out and, damn it, still die.

I could become a jerk again and focus on the end point, or I could accept that the journey is the destination – which I did.

Two months after I had been diagnosed and two days before the surgeon was scheduled to excise my remaining testicle, I had a dream so vivid — “I am cancer-free!” — that I demanded to go on a “surveillance” protocol. Reluctantly my doctor agreed, but by year’s end I had “won” the debate when my so-called tumor was reclassified as a benign nodule.

The years had taught me much — both to listen to my body and to trust in its wisdom. And, most importantly, to find the courage to speak its truth — whether in the doctor’s office or out in the world.

Steven Petrow writes the Civil Behavior column for Booming, addressing questions about gay and straight etiquette for a boomer-age audience. You can find him on Facebook and Twitter.

You can follow Booming via RSS here or visit nytimes.com/booming.

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Citing Internet Standoff, U.S. Rejects International Telecommunications Treaty

DUBAI — Talks on a proposed treaty governing international telecommunications collapsed in acrimony on Thursday when the United States rejected the agreement on the eve of its scheduled signing, citing an inability to resolve an impasse over the Internet.

“It is with a heavy heart that I have to announce that the United States must communicate that it is unable to sign the agreement in its current form,” Terry Kramer, head of the American delegation, announced moments after a final draft appeared to have been approved by a majority of nations.

The United States announcement was seconded by Canada and several European countries after nearly two weeks of talks that had often pitted Western governments against Russia, China and developing countries. The East-West and North-South divisions harked back to the cold war, even though that conflict did not stop previous agreements to connect telephone calls across the Iron Curtain.

While the proposed agreement was not set to take effect until 2015 and was not legally binding, Mr. Kramer insisted that the United States and its supporters had headed off a significant threat to the “open Internet.”

The messy end to the proceedings highlighted intractable differences of opinion over the ever-growing importance of digital communications networks as tools for personal communications, global commerce, political proselytization and even unconventional warfare.

“The word ‘Internet’ was repeated throughout this conference and I believe this is simply a recognition of the current reality — the two worlds of telecommunications and Internet are inextricably linked,” said Hamadoun Touré, secretary general of the International Telecommunication Union.

The United States has consistently maintained that the Internet should not have been mentioned in the proposed treaty, which dealt with technical matters like connecting international telephone calls, because doing so could lead to curbs on free speech and replace the existing, bottom-up form of Internet oversight with a government-led model.

“We cannot support a treaty that is not supportive of the multistakeholder model of Internet governance,” Mr. Kramer said. His announcement came moments after the telecommunication union, the United Nations agency that convened the talks here, announced that a final version of the text had been formulated.

A bloc of countries led by Russia that included China and the host nation, the United Arab Emirates, argued throughout the negotiations that the Internet was within the scope of the talks because Internet traffic traveled through telecommunications networks.

The goal of the talks, which were led by Mohamed Nasser al-Ghanim, director general of the Telecommunications Regulatory Authority of the United Arab Emirates, was to revise a document that was last updated in 1988, when the Internet was in its early stages of development.

Agreement was never going to be easy. Like most U.N. agencies, the International Telecommunication Union tries to operate by consensus, resorting to majority vote only when this fails.

The United States delegation was apparently angered by developments early Wednesday, when Russia and its allies succeeded in winning, by a mere show of hands, approval of a resolution that mentioned the Internet. The informal vote followed an attempt by Mr. Ghanim to gauge, as he put it, “the temperature of the room.”

The United States and its supporters interpreted the wording of the resolution as supporting a shift in the governance of the Internet to bring it under the regulatory framework of the telecommunication union.

The Internet is currently overseen by a loose grouping of organizations, mostly in the private sector, rather than by governments. But at least one, the Internet Corporation for Assigned Names and Numbers, operates under a contract from the United States government.

Resolutions are not officially part of the treaty wording, and Russia and its allies previously tried to include a similar clause in the actual treaty. But under a compromise, it agreed this week to withdraw that proposal and settle for the lesser measure. Even that, however, was insufficient to address the concerns of the United States and its supporters.

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S.&P. Streak Comes to an End on Fiscal Worries

The Standard & Poor’s 500-stock index ended its six-day winning streak Thursday, retreating as worries intensified that Washington’s fiscal negotiations were dragging on with little progress.

Anxiety about the talks between Democrats and Republicans was enough to offset encouraging data on retail sales and jobless claims.

Investors are concerned that tax increases and spending cuts, set to begin in 2013 if a deal is not reached in Washington, will hurt growth. The stock market had taken the heated talk in stride lately, but downbeat remarks from the House speaker, John A. Boehner of Ohio, prompted some selling Thursday.

Mr. Boehner accused President Obama of “slow walking” the economy toward the automatic tax increases and spending cuts that will occur on Jan. 1, 2013, if no deal is reached. He was scheduled to meet with Mr. Obama later on Thursday.

“There is no conviction here and Boehner’s comments — as harsh as they were — were realistic,” said Jason Weisberg, managing director at the Seaport Securities Corporation in New York.

“The fiscal cliff is already built in,” Mr. Weisberg said. “That being said, people don’t like to be told the apocalypse is coming over and over and over again. The real players in this market have already closed their books.”

After nearing a 1 percent decline for the day, the S.& P. 500 pared losses late in the session. The index had posted six consecutive sessions of gains through Wednesday, and at one point Wednesday, the S.& P. 500 touched its highest intraday level since Oct. 22.

While the Federal Reserve’s announcement on Wednesday of a new round of economic stimulus bolstered stocks, Chairman Ben Bernanke’s comments that monetary policy would not be sufficient to offset the impact of the fiscal crisis weighed on sentiment.

The Dow Jones industrial average tumbled 74.73 points, or 0.56 percent, to 13,170.72 at the close. The S.& P. 500-stock index fell 9.03 points, or 0.63 percent, to 1,419.45. The Nasdaq composite index slid 21.65 points, or 0.72 percent, to end at 2,992.16.

Apple’s stock, down 1.7 percent at $529.69, was among the biggest drags on the Nasdaq, while I.B.M., down 0.5 percent at $191.99, was among the biggest weights on the Dow. A federal jury in Delaware Thursday found that Apple’s iPhone infringed on three patents owned by MobileMedia Ideas.

Among the day’s biggest gainers, Best Buy shares shot up 15.9 percent to $14.12 after a report that the company’s founder, Richard M. Schulze, was expected to offer to buy the consumer electronics retailer this week.

The energy and information technology sectors were the S.& P.’s weakest performers, with the S.& P. energy index declining 0.9 percent. Shares of the American refining company Phillips 66 lost 1.6 percent to $52.21.

The day’s data sent some positive signals on the economy, with weekly claims for jobless benefits dropping to nearly the lowest level since February 2008, and retail sales rising in November after an October decline, improving the picture for consumer spending.

In Europe, European Union finance ministers reached agreement to make the European Central Bank the bloc’s top banking supervisor, which could increase confidence in the ability of European Union leaders to confront the euro zone’s sovereign debt crisis.

The Treasury’s 10 year note fell 9/32 to 99 1/32, with the yield rising to 1.73 from 1.70 on Wednesday.

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Eli Lilly to Conduct Additional Study of Alzheimer’s Drug

The drug maker Eli Lilly & Company said on Wednesday that it planned an additional study of an experimental Alzheimer’s drug that failed to improve the condition of people with the disease, saying that it remained hopeful about the drug’s prospects.

The newest study is expected to get under way in the third quarter of 2013 and will focus on patients with mild Alzheimer’s disease. Lilly released results of two clinical trials in August that showed the drug, called solanezumab, did not significantly improve either the cognition or the daily functioning of people with mild and moderate forms of the disease. But despite that failure, the results also gave some reason for hope: when patients with mild Alzheimer’s were separated out, the drug was shown to significantly slow their decline in cognition.

In a statement on Wednesday, the company said it decided not to pursue approval of the drug based on existing study results after it met with officials from the Food and Drug Administration. A Lilly executive said, however, that the company was still optimistic.

“We remain encouraged and excited by the solanezumab data,” David Ricks, a senior vice president at Lilly and president of Lilly Bio-Medicines, said in the statement. “We are committed to working with the F.D.A. and other regulatory authorities to bring solanezumab to the millions of patients and caregivers suffering from this devastating disease who urgently need this potential treatment.”

The Lilly drug is the second Alzheimer’s treatment to fail in clinical trials this year. Pfizer and Johnson & Johnson stopped development of a similar treatment, bapineuzumab, after it, too, was not shown to work. Both drugs target beta amyloid, a protein in the brain that is found in people with Alzheimer’s disease.

Lilly shares closed at $49, down 3.2 percent.

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Eli Lilly to Conduct Additional Study of Alzheimer’s Drug

The drug maker Eli Lilly & Company said on Wednesday that it planned an additional study of an experimental Alzheimer’s drug that failed to improve the condition of people with the disease, saying that it remained hopeful about the drug’s prospects.

The newest study is expected to get under way in the third quarter of 2013 and will focus on patients with mild Alzheimer’s disease. Lilly released results of two clinical trials in August that showed the drug, called solanezumab, did not significantly improve either the cognition or the daily functioning of people with mild and moderate forms of the disease. But despite that failure, the results also gave some reason for hope: when patients with mild Alzheimer’s were separated out, the drug was shown to significantly slow their decline in cognition.

In a statement on Wednesday, the company said it decided not to pursue approval of the drug based on existing study results after it met with officials from the Food and Drug Administration. A Lilly executive said, however, that the company was still optimistic.

“We remain encouraged and excited by the solanezumab data,” David Ricks, a senior vice president at Lilly and president of Lilly Bio-Medicines, said in the statement. “We are committed to working with the F.D.A. and other regulatory authorities to bring solanezumab to the millions of patients and caregivers suffering from this devastating disease who urgently need this potential treatment.”

The Lilly drug is the second Alzheimer’s treatment to fail in clinical trials this year. Pfizer and Johnson & Johnson stopped development of a similar treatment, bapineuzumab, after it, too, was not shown to work. Both drugs target beta amyloid, a protein in the brain that is found in people with Alzheimer’s disease.

Lilly shares closed at $49, down 3.2 percent.

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10 Arrested in Theft of Personal Data

International authorities, with some help from Facebook, have arrested 10 people accused of operating a network of infected computers that stole personal information from millions of victims.

The Justice Department said Tuesday night that the F.B.I. and international agencies were helped in their investigations by Facebook, whose users were among those targeted by the malware, or malicious software, over the last several years.

The agencies arrested people from Bosnia and Herzegovina, Britain, Croatia, Macedonia, New Zealand, Peru and the United States, the F.B.I. said.

The suspects used a chain of infected computers to form what was known as the Butterfly botnet, which spread a piece of malicious software called Yahos, officials said. Versions of the software have long been trafficked among criminals who spread it over social networks and by other means, compromising the security of infected PCs and letting criminals steal personal data, including credit card numbers.

In a statement, the Justice Department said variants of this kind of software had infected about 11 million computers and caused more than $850 million in losses. A Justice Department official said those figures referred to the cumulative damage from the long-running problem, not a measure of the damage done by the people who were arrested.

Mark Hammell, Facebook’s Internet threat researcher, said the company had begun investigating suspicious behavior on its service two years ago. The malware had hijacked some users’ accounts and posted links on their friends’ Facebook pages. A person who clicked on those links could download the software and infect his computer.

Facebook’s researchers reverse-engineered the software to understand how it worked, and eventually traced some of its activities to computer servers controlled by the suspects. That helped Facebook determine the identities of some of the people involved in the crime ring, Mr. Hammell said.

“We realized we didn’t have the ability to stop it completely, and at that point, we decided the best response was to escalate this to law enforcement,” he said in an interview. Two of the people who were arrested were the original authors of the malware, he noted. Facebook said its users made up only a small percentage of those who were infected.

Security firms and social networks are generally on the lookout for this particular form of malware, and software to detect and eliminate it has been available for years. The Justice Department urged computer users to take common-sense measures, like antivirus scanning, to guard against the risk of infections, and said people who suspect they have been victimized should file a complaint with the F.B.I.’s Internet crime complaint center at ic3.gov.

Facebook said users who were concerned about being infected could check their computers at on.fb.me/infectedMSE. The malware does not infect Apple computers, Facebook said.

Manos Antonakakis, director of academic research at Damballa, a company that specializes in fighting botnets, said the size of the Butterfly botnet was significant. It was more than double the size of the last major botnet that authorities took down last November, one that used a piece of malware called DNSChanger that had infected an estimated four million computers.

“This is a major achievement for law enforcement,” he said, “and we look forward to many things like this, so we can effectively tackle emerging botnets out there.”

But Dr. Antonakakis said the estimate of 11 million infected machines was probably high, because a computer could be counted as a new device each time it connected to a different network, like the Wi-Fi at a Starbucks or a home router.

The $850 million figure may also be high given that credit card companies typically wipe out fraudulent charges.

Peter G. Neumann, principal scientist at SRI International, an engineering research laboratory, was less excited about the arrests. He said that defeating this particular botnet did not solve the fundamental problem of computer security being too weak. Anybody could easily take the same software and create the botnet again, he said.

“You’re solving a problem that wouldn’t exist if the systems were designed properly,” he said.

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Kidnappings Fuel Extremists in Western Africa

Issouf Sanogo/Agence France-Presse — Getty Images

Fighters with the Movement for Oneness and Jihad in West Africa in northern Mali in July. Extremist groups’ control of the area has complicated military plans to take back the territory.

BAMAKO, Mali — Oumar Ould Hamaha, a notorious Islamist commander in the deserts of western Africa, has nothing but disdain for the international powers he opposes or the hapless Westerners he and other militants subject to extreme deprivation, hunger, thirst and proselytizing for months on end.

But he openly appreciates them for helping Islamists acquire the one thing they cannot do without.

“Lots of Western countries are paying enormous sums to the jihadists,” he said in a telephone interview from northern Mali, crowing about the hefty ransoms militants have collected in the region. “The source of our financing is the Western countries. They are paying for jihad.”

Kidnapping is such a lucrative industry for extremists in western Africa, netting them tens of millions of dollars in recent years, that it has reinforced their control over northern Mali and greatly complicated plans for an African-led military campaign to take back Islamist-held territory.

Beyond the immediate risk to the 10 Europeans and 3 Algerians still being held — “At the first strike, the hostages will have their throats cut like chickens, one after the other,” Mr. Hamaha threatened — an intervention could face formidable opponents. Al Qaeda in the Islamic Maghreb, one of the factions that have seized northern Mali, is estimated to have amassed as much as $90 million or more in ransoms over the past decade, turning it into one of the region’s wealthiest, best-armed militant groups.

But Mali and its neighbors are still scrambling to cobble together soldiers, money and a workable plan to recapture lost ground. In fact, Mali, which is supposed to lead the international offensive against the Islamists, does not even have a stable government. On Tuesday, the nation’s prime minister resigned after being arrested by soldiers the night before, part of the continuing political disarray that allowed the Islamists to take the north in the first place.

As the United Nations debates plans for a military intervention in northern Mali, Islamists in the region appear to be on the hunt for more hostages. Three weeks ago, a French tourist was abducted in Mali and five humanitarian workers were seized in Niger in October, after a lull in kidnappings that lasted for months.

The abductions often follow the same frightening script: a sudden burst of movement, usually in the dark; guttural orders and shoves at gunpoint; then days of harsh driving deep into the desert.

The days stretch into weeks, months and even years in a sea of sand, waiting for deliverance or death. A gaunt acacia thorn-tree might be the only shade, the desert ground the only bed, and water — when it is given — often comes from a gasoline jerrycan.

“I lived through an experience that is absolutely unimaginable,” said Françoise Larribe, a Frenchwoman kidnapped in 2010 in northern Niger, where her husband was working at a uranium mine operated by the French company Areva. Her husband, Daniel, is still a captive; she was released unexpectedly after five and a half months that were “extremely tough.”

“The separation from my husband was rapid and painful,” she added.

Mr. Hamaha was with Al Qaeda in the Islamic Maghreb when he helped kidnap a Canadian diplomat, Robert Fowler, late one December afternoon in 2008 outside the capital of Niger, Niamey. Now the jihadist says he is “in charge of security” for the Malian offshoot of Al Qaeda in the Islamic Maghreb, Mujao, the Movement for Oneness and Jihad in West Africa, another of the three radical groups that control northern Mali.

The brigade commanded by Mr. Hamaha zoomed ahead of the diplomat’s car in “a slick, violent, well-coordinated and impeccably executed grab,” Mr. Fowler wrote in a new memoir, “A Season in Hell: My 130 Days in the Sahara with Al Qaeda.” He and an aide were on their way to dinner in the capital.

He lived through weeks of fear, sleeping on the sand, exposed to the brutal Sahara sun, to snakes and scorpions, fed meager bowls of rice, bounced from barren desert outpost to outpost.

“I spent nearly five months terrified,” Mr. Fowler said in a recent interview. “I was terrified that it would end in a tent with a knife at my throat, and my family would see it on YouTube.”

Mr. Hamaha, his captor, who takes calls from reporters, said: “Ah yes, the Canadian that we kidnapped. I don’t regret it at all. He was in a state of being lost,” referring to what he considered the Westerner’s perilous spiritual condition. The Canadian, Mr. Hamaha said, “learned many things from us.”

During his captivity Mr. Fowler, who was the United Nations special envoy to Niger, gained perhaps the sharpest insight yet into the mentality of some of the men who now hold northern Mali. “There’s no doubt of their faith: they would sit chanting in the full Sahara sun for hour after hour.”

Maïa de la Baume contributed reporting from Paris.

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