#Apollo45

July 20, 1969.

I’ve blogged about it before.

There are people who can write eloquently about events of such significance.  I am not one of them.  I hope that doesn’t stand in the way of folks remembering the amazing accomplishment that the Apollo program was.

 

P0wned! Don’t make the same mistake I did

I fell victim to an interesting attack, which I am recounting here so that others may avoid it.

In a nutshell, I fell victim to a trojan, which the malefactor was able to place in a trusted location in my search path. A wrapper obscured the malicious payload. Additionally, a second line of defense did not catch the substitution. I believe the attackers were not out to harm me, but that this trojan was put in place partially for lulz, and partially to allow a more-important attack on the systems RBAC mechanisms to succeed.

Attack Details

I was attempting to purchase a six pack of New Belgium Rampant IPA, shown immediately below.

IMG_2242.JPG

I obtained the six pack from the canonical location in the system – a reach-in refrigerator in the supermarket’s liquor aisle. I proceeded to the cashier, who rang up my purchase, bagged it, and accepted payment.

I realized upon arrival home, that this was a trojan six pack, as seen below:

IMG_2243.JPG

Clearly, the attacker to care to make his payload look legitimate. What I noticed later, was the subtle difference I zoom in on below

IMG_2245.JPG

:

IMG_2244.JPG

Yes, the attacker had substituted root beer for real beer.

Needless to say, this was a devious denial of service, which the perpetrators undoubtedly laughed about. However, this was likely not just “for the lulz”. I think this was the work of juvenile attackers, whose motives were to defeat the RBAC (real beer access control) system. Knowing that a purchase of real beer would be scrutinized closely, I believe they exfiltrated the target beer by hiding it in a root beer package.

Mitigations put in place by the system did not catch this error – the cashier/reference monitor allowed the purchase (and likely, the offsetting real beer as root beer purchase).

Possible Countermeasures

The keys to this attack were that the trojan was in the right place in the search path, and that it appeared legitimate. Obviously, this location must be readable by all, since items need to be fetched from it. However, allowing items to be placed in it by untrusted users is a definite risk. Technical constraints make the obvious countermeasure — allowing only privileged stocking, while permitting “world” fetching — presents serious usability concerns, and increases system cost, since the privileged stocker must be paid.

Nonetheless, such countermeasures are in place for certain other items, notably where the cost to the system — as opposed to the user — of an illicit item substitution is quite high.

Lessons learned

Ultimately, system usability and cost tradeoffs put the onus on the end-user. Before taking a non-idempotent step, inspect the objects closely!

Neil Armstrong, RIP

Neil Armstrong in Eagle, photographed by Buzz Aldrin

Neil Armstrong died August 25, aged 82.

It’s difficult to properly memorialize this man, because, to a degree almost unheard of in our media-saturated times, he avoided the limelight. A statement by his family notes:

As much as Neil cherished his privacy, he always appreciated the expressions of good will from people around the world and from all walks of life.

EC has a certain fondness for privacy and for Apollo. If you do, too, please consider this suggestion made by Armstrong’s family:

For those who may ask what they can do to honor Neil, we have a simple request. Honor his example of service, accomplishment and modesty, and the next time you walk outside on a clear night and see the moon smiling down at you, think of Neil Armstrong and give him a wink.

Image source: NASA

we mutually pledge to each other our Lives, our Fortunes and our sacred Honor

declaration-of-independence.jpg

In CONGRESS, July 4, 1776

The unanimous Declaration of the thirteen united States of America,

When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature’s God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. –That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, –That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security. —Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain [George III] is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.

He has refused his Assent to Laws, the most wholesome and necessary for the public good.

He has forbidden his Governors to pass Laws of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them.

He has refused to pass other Laws for the accommodation of large districts of people, unless those people would relinquish the right of Representation in the Legislature, a right inestimable to them and formidable to tyrants only.

He has called together legislative bodies at places unusual, uncomfortable, and distant from the depository of their public Records, for the sole purpose of fatiguing them into compliance with his measures.

He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.

He has refused for a long time, after such dissolutions, to cause others to be elected; whereby the Legislative powers, incapable of Annihilation, have returned to the People at large for their exercise; the State remaining in the mean time exposed to all the dangers of invasion from without, and convulsions within.

He has endeavoured to prevent the population of these States; for that purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their migrations hither, and raising the conditions of new Appropriations of Lands.

He has obstructed the Administration of Justice, by refusing his Assent to Laws for establishing Judiciary powers.

He has made Judges dependent on his Will alone, for the tenure of their offices, and the amount and payment of their salaries.

He has erected a multitude of New Offices, and sent hither swarms of Officers to harass our people, and eat out their substance.

He has kept among us, in times of peace, Standing Armies without the consent of our legislatures.

He has affected to render the Military independent of and superior to the Civil power.

He has combined with others to subject us to a jurisdiction foreign to our constitution and unacknowledged by our laws; giving his Assent to their Acts of pretended Legislation:

For Quartering large bodies of armed troops among us:

For protecting them, by a mock Trial, from punishment for any Murders which they should commit on the Inhabitants of these States:

For cutting off our Trade with all parts of the world:

For imposing Taxes on us without our Consent:

For depriving us, in many cases, of the benefits of Trial by Jury:

For transporting us beyond Seas to be tried for pretended offences:

For abolishing the free System of English Laws in a neighbouring Province, establishing therein an Arbitrary government, and enlarging its Boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule into these Colonies:

For taking away our Charters, abolishing our most valuable Laws, and altering fundamentally the Forms of our Governments:

For suspending our own Legislatures, and declaring themselves invested with power to legislate for us in all cases whatsoever.

He has abdicated Government here, by declaring us out of his Protection and waging War against us.

He has plundered our seas, ravaged our Coasts, burnt our towns, and destroyed the lives of our people.

He is at this time transporting large Armies of foreign Mercenaries to compleat the works of death, desolation and tyranny, already begun with circumstances of Cruelty and perfidy scarcely paralleled in the most barbarous ages, and totally unworthy the Head of a civilized nation.

He has constrained our fellow Citizens taken Captive on the high Seas to bear Arms against their Country, to become the executioners of their friends and Brethren, or to fall themselves by their Hands.

He has excited domestic insurrections amongst us, and has endeavoured to bring on the inhabitants of our frontiers, the merciless Indian Savages, whose known rule of warfare, is an undistinguished destruction of all ages, sexes and conditions.

In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury. A Prince whose character is thus marked by every act which may define a Tyrant, is unfit to be the ruler of a free people.

Nor have We been wanting in attentions to our British brethren. We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. We have reminded them of the circumstances of our emigration and settlement here. We have appealed to their native justice and magnanimity, and we have conjured them by the ties of our common kindred to disavow these usurpations, which, would inevitably interrupt our connections and correspondence. They too have been deaf to the voice of justice and of consanguinity. We must, therefore, acquiesce in the necessity, which denounces our Separation, and hold them, as we hold the rest of mankind, Enemies in War, in Peace Friends.

We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by the Authority of the good People of these Colonies, solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do. And for the support of this Declaration, with a firm reliance on the protection of divine Providence, we mutually pledge to each other our Lives, our Fortunes and our sacred Honor.

The signers of the Declaration represented the new states as follows:

New Hampshire

Josiah Bartlett, William Whipple, Matthew Thornton

Massachusetts

John Hancock, Samual Adams, John Adams, Robert Treat Paine, Elbridge Gerry

Rhode Island

Stephen Hopkins, William Ellery

Connecticut

Roger Sherman, Samuel Huntington, William Williams, Oliver Wolcott

New York

William Floyd, Philip Livingston, Francis Lewis, Lewis Morris

New Jersey

Richard Stockton, John Witherspoon, Francis Hopkinson, John Hart, Abraham Clark

Pennsylvania

Robert Morris, Benjamin Rush, Benjamin Franklin, John Morton, George Clymer, James Smith, George Taylor, James Wilson, George Ross

Delaware

Caesar Rodney, George Read, Thomas McKean

Maryland

Samuel Chase, William Paca, Thomas Stone, Charles Carroll of Carrollton

Virginia

George Wythe, Richard Henry Lee, Thomas Jefferson, Benjamin Harrison, Thomas Nelson, Jr., Francis Lightfoot Lee, Carter Braxton

North Carolina

William Hooper, Joseph Hewes, John Penn

South Carolina

Edward Rutledge, Thomas Heyward, Jr., Thomas Lynch, Jr., Arthur Middleton

Georgia

Button Gwinnett, Lyman Hall, George Walton

Image: Washington’s copy of the Declaration of Independence, from the Library of Congress.

Niels Bohr was right about predictions

There’s been much talk of predictions lately, for some reason. Since I don’t sell anything, I almost never make them, but I did offer two predictions early in 2010, during the germination phase of a project a colleague was working on. Since these sort of meet Adam’s criteria by having both numbers and dates, I figured I’d share.

With minor formatting changes, the following is from my email of April, 2010.

Prediction 1

Regulation E style accountholder liability limitation will be extended
to commercial accountholders with assets below some reasonably large
value by 12/31/2010.

Why:  ACH and wire fraud are an increasingly large, and increasingly
public, problem.  Financial institutions will accept regulation in order
to preserve confidence in on-line channel.

WRONG!

Prediction 2

An episode of "state-sponsored SSL certificate fraud/forgery" will make
the public press.

Why: There is insufficient audit of the root certs that browser vendors
innately trust, making it sufficiently easy for a motivated attacker to
"build insecurity in" by getting his untrustworthy root cert trusted by
default.  The recent Mozilla kerfuffle over CNNIC is an harbinger of
this[1].  Similarly, Chris Soghoian's recent work[2] will increase
awareness of this issue enough to result in a governmental actor who has
done it being exposed.

Right!

But only because for this one I forgot to put in a date (I meant to also say “by 12/31/2010”, which makes this one WRONG! too.

I was motivated to make this post because I once again came across Soghoian’s paper just the other day (I think he cited it in a blog post I was reading). He really nailed it. I predict he’ll do so again in 2012.

Sleepless in Seattle?

Reportedly, Seattle police have begun issuing tickets to drivers who honk their horns after 10 PM in support of the Occupy protest there.

To the extent that the police are only doing this to those expressing a specific point of view, there seems to be a legitimate issue. I am certain that the police would say they’d enforce the law equally, but it’s just that all the honking is for Occupy support.

If I were a Seattle prankster, I’d have a “Honk if you support law enforcement” sign made, and test that claim in whatever passes for a conservative ‘hood out there.

California gets a strengthened Breach Notification Law

Governor Brown of California has signed a strengthened breach notification bill, which amends Sections 1798.29 and 1798.82 of the California Civil Code in important ways. Previous versions had been repeatedly vetoed by Arnold Schwarzenegger.

As described[.DOC] by its sponsor’s office, this law:

  • Establishes standard, core content — such as the type of information breached, time of breach, and toll-free telephone numbers and addresses of the major credit reporting agencies — for security breach notices in California;
  • Requires public agencies, businesses, and persons subject to California’s security breach notification law, if more than 500 California residents are affected by a single breach, to send an electronic copy of the breach notification to the Attorney General; and,
  • Requires public agencies, businesses and persons subject to California’s security breach notification law, if they are utilizing the substitute notice provisions in current law, to also provide that notification to the Office of Information Security or the Office of Privacy Protection, as applicable.
  • senatorsimitian.com

    This makes California the fifteenth (!) state with a central notification provision on the books, the others being: Hawaii, Iowa, Maryland, Massachusetts, Minnesota, New Hampshire, New York, North Carolina, Oregon, Vermont, Virginia, West Virginia, Wisconsin, and Wyoming. Puerto Rico also has such a requirement. Ibid.

    I’m looking forward to the resulting information, and I hope California’s Attorney General has the good sense to post all received notification letters. This will undoubtedly be easier for the state than dealing with the inevitable FOIA requests, and serves the public interest by increasing transparency.

    In Congress Assembled, July 4, 1776

    declaration-of-independence.jpg

    In CONGRESS, July 4, 1776

    The unanimous Declaration of the thirteen united States of America,

    When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature’s God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

    We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. –That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, –That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security. —Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain [George III] is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.

    Continue reading

    Welcome to the club!

    As EC readers may know, I’ve been sort of a collector of breach notices, and an enthusiastic supporter of the Open Security Foundation’s DataLossDB project. Recently, I had an opportunity to further support DataLossDB, by making an additional contribution to their Primary Sources archive – a resource I find particularly valuable.

    Unfortunately, that contribution was a breach notification letter[pdf] addressed to me! Since I now have some skin in the game, I figured I’d use the opportunity to take a close look at this incident and see what can be learned from it.

    Who sent the letter, and how do I reach them?

    Let’s start with the letter itself. While it identifies the data owner (“EHP”, an emergency room practice I had patronized), it provides no return address, and the letter is unsigned. Unsurprisingly given this opacity, the envelope return address is a post office box. While a toll-free number is provided, this is a requirement of many state breach laws, and repeated calls to the number resulted in my being placed in an ACD queue, rather than being routed to a human being. So far, it looks to me like they’re trying to ensure that all communication regarding this issue is either squelched by the magic of painful on-hold music, or diverted into a call center. In particular, there seems to be no enthusiasm for written correspondence.

    What was exposed, and how?

    Now let’s consider the nature of the exposed data. According to the notification letter, a hard drive was stolen from a 3rd party service provider (Millennium Medical Management Resources). That hard drive contained “unencrypted copies of records with health and financial information about [me]”. Furthermore, the service provider

    …believes the hard drive contained personally identifiable information about EHP patients, including name, address, phone number, date of birth, and Social Security Number and, in some cases, other information such as diagnosis and/or diagnosis code, types of procedure and/or procedure code, medical record number, account number, driver’s license number, and health insurance information.

    Surprisingly, the letter does not say that “the exposure appears to be the work of criminals interested in the hardware” or other such language often used to suggest that crooks don’t go after data. This even though the police report notes that the “suite [was] in disarray”. Kudos to EHP for this. And kudos to the Westmont, IL PD for handling my FOIA request same day. I understand they received literally hundreds of requests for this report. Anyone who handles a dramatic, unexpected increase in work so cheerfully deserves praise.

    As to what was stolen, the notification letter — seemingly drafted by an attorney — states what the service provider believes, not what the service provider knows. This suggests there is some question as to what precisely was on the unencrypted drive. Clearly, though, health and financial information are involved, suggesting that this breach is subject to HITECH and HIPAA provisions, as well as to myriad state breach laws. Reading on, this is further reinforced, when EHP says they “…will report this security breach to the Office of Civil Rights of the U.S. Department of Health and Human Services.” Such a report is required by HITECH when more than 499 persons have been affected by a breach, which establishes a lower bound for the likely number of affected individuals in this incident. (In the few days I have been composing this blog post, the report has appeared on HHS’s web site. 180,111 folks impacted by this one. Ouch. Why not put this in the letter to me, if it will be one mouse-click away anyhow?)

    How long did notification take?

    HITECH requires that notification occur within sixty days of the discovery of the breach. This breach was discovered March 1st. The letter is dated April 30. I wonder if the delay would have been longer, were it legally permissible?

    How will future incidents be prevented?

    According to the letter,the service provider has

    …implemented new and improved technical, physical, and administrative security measures to prevent future thefts and security breaches, including encryption of electronic personally identifiable information stored on portable storage devices. Millennium will also take additional steps to further secure patient information.

    Meanwhile,

    EHP is carefully monitoring these security measures to ensure that they meet regulatory requirements and appropriately secure information about its patients.

    With a letter such as this, which undoubtedly was closely crafted by people who pay attention to word choice, it seems fair to read it as attentively as it was written. An admittedly cynical interpretation is that this “careful monitoring” is a new thing for EHP. After all, they didn’t say they would “continue to carefully monitor” or would “more carefully monitor”. As to what “technical, physical, and administrative” measures Millennium might be adding, who knows? It’s hard enough to audit ones own service provider. Knowing what somebody else’s is doing is harder still.

    So what can I do?

    The letter concludes with sections which roughly follow the guidelines provided by various sample breach notification letters. This is impressive. After reading many notification letters, I’ve come to expect some soft-pedaling of the risk of identity theft. This one does not do that. Again, kudos.

    Closing Thoughts

    So this has been a long blog post about one incident and one letter, and not exactly a man bites dog situation either. Apologies. I think two things are interesting about this particular letter:

    1. For matters that pertain to breaches generally rather than to this one specifically, it was straightforward, clear, and reasonably complete. The advice about what to do, how to interact with credit bureaus, when to notify law enforcement, etc., was all sound, with little or no “spin”.
    2. With respect to the details of this specific incident, the letter was more circumspect, with — to my eyes — more parsing of words.

    Unsurprising, perhaps, but (I have not done a content analysis to verify this) I wonder how typical the openness would have been three or four years ago. Perhaps, if California’s SB 1166 is signed by the Governor (rather than vetoed, as was a previous version), this greater transparency will extend to incident-specific details as well. I don’t see the harm in it. I’ve already filled in the blanks with what I think really happened to my information. There isn’t too much EHP could say that would make me feel much different about their vendor management program, or about the degree of care Millennium evinced here, so they should just say it.

    Logging practices

    Via a tweet from @WeldPond, I was led to a Daily Mail article which discusses allegations that Facebook founder Mark Zuckerberg “hacked into the accounts of [Harvard] Crimson staff”. Now, I have no idea what happened or didn’t, and I will never have a FB account thanks to my concerns about their approach to privacy, but I was curious about the form of this alleged hacking.

    My curiosity was rewarded:

    “he allegedly examined a report of failed logins to see if any of the Crimson members had ever entered an incorrect password into TheFacebook.com.

    In the instances where they had, Business Insider claimed that Zuckerberg said he tried using those incorrect passwords to access the Crimson members’ Harvard email accounts.”

    dailymail.co.uk, 2010-03-06

    So, it looks like the allegation is that actual passwords entered for failed logins were routinely logged.

    Yuck.

    Another Week, Another GSM Cipher Bites the Dust

    Bag Contents

    Orr Dunkelman, Nathan Keller, and Adi Shamir have released a paper showing that they’ve broken KASUMI, the cipher used in encrypting 3G GSM communications. KASUMI is also known as A5/3, which is confusing because it’s only been a week since breaks on A5/1, a completely different cipher, were publicized. So if you’re wondering if this is last week’s news, it isn’t. It’s next week’s news.

    The paper isn’t up on IACR’s Eprint archive yet, but copies of it are circulating around privately. I’m writing about it with Adi Shamir’s permission.

    KASUMI is a modified version of the MISTY cipher. The KASUMI designers made MISTY faster and more hardware friendly by changing the key schedule and modifying some internal parameters. However, they also made it vulnerable to related key attacks.

    Of all the weaknesses that a cipher can have, related key attacks are the ones to worry about least. Operationally, crypto engineers know that they should never reuse keys and when in doubt just pull another one off of the random number generator. Consequently, this doesn’t mean that the guys at Weizmann Institute of Science are listening to 3G calls.

    Nonetheless, related key attacks are bad to have because implementers do screw up, and related key attacks indicate that the cipher designers didn’t have as tight a handle on things as they thought they did. It is no cause for panic, but it is no cause for either warmness or fuzziness (particularly since the DKS team point out that the KASUMI designers wrote that they’d taken care of related-key issues when they simplified MISTY into KASUMI).

    Moreover, the attack here is completely practical. Here is a quote from the abstract:

    In this paper we describe a new type of attack called a sandwich attack, and use it to construct a simple distinguisher for 7 of the 8 rounds of KASUMI with an amazingly high probability of 2?14. By using this distinguisher and analyzing the single remaining round, we can derive the complete 128 bit key of the full KASUMI by using only 4 related keys, 226 data, 230 bytes of memory, and 232 time. These complexities are so small that we have actually simulated the attack in less than two hours on a single PC, and experimentally verified its correctness and complexity. Interestingly, neither our technique nor any other published attack can break MISTY in less than the 2128 complexity of exhaustive search, which indicates that the changes made by the GSM Association in moving from MISTY to KASUMI resulted in a much weaker cryptosystem.

    It will be interesting to see the response from the GSM Association. They have the opportunity to show leadership. If they recognize that this is a real problem, reassure us that it’s not a catastrophe, and show that they’re taking it seriously, then this can be an all-around good thing for them and us.

    We’re all adults (well, okay, most of us are adults and act like adults some of the time), and if we know that there will be an upgrade in a few years, then that’s great. We lived through the WEP issues. We are living through the SSL evil proxy issues. This is less acute than either of those. But we need to have some assurance that in a few years, we’ll just get wireless devices with a safety net. Their challenge is to have a response before this news metastasizes into a common perception that 3G crypto is worthless.

    Photo “bag_contents” courtesy of openfly. Selected because it looked good and it was the only photo that came back on a search of “3g crypto.”

    768-bit RSA key factored

    The paper is here.

    The very sane opening paragraph is:

    On December 12, 2009, we factored the 768-bit, 232-digit number RSA-768 by the number field sieve (NFS, [19]). The number RSA-768 was taken from the now obsolete RSA Challenge list [37] as a representative 768-bit RSA modulus (cf. [36]). This result is a record for factoring general integers. Factoring a 1024-bit RSA modulus would be about a thousand times harder, and a 768-bit RSA modulus is several thousands times harder to factor than a 512-bit one. Because the first factorization of a 512-bit RSA modulus was reported only a decade ago (cf. [7]) it is not unreasonable to expect that 1024-bit RSA moduli can be factored well within the next decade by an academic effort such as ours or the one in [7]. Thus, it would be prudent to phase out usage of 1024-bit RSA within the next three to four years.

    It’s an interesting read if factoring fascinates you.