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Number-cracking factory gets to work
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Numbercracking factory gets to work
“As well as repairing knees, cartilage tissue made from nose cells might be used for facial reconstruction”
BSIP/Getty Images/Universal Images Group
THE first tests of a “factorisation factory” have beaten the record for breaking gigantic numbers down into their prime-number building blocks. It might one day force firms to strengthen their online encryption. All non-prime numbers can be made by multiplying prime numbers together. Cryptographic algorithms use the fact that reversingengineering this multiplication, or factorising, is very difficult for large numbers. New factorising methods are tested on huge “RSA numbers”, each of which is the product of multiplying two prime numbers, known only to encryption firm RSA Security. Factoring a single RSA number is a massive effort, says Arjen Lenstra of the Swiss Federal Institute of Technology in Lausanne, so he and his colleagues have developed a factorisation factory that can tackle multiple target numbers at once. The technique, proposed in the 1990s, saves effort by pre-computing a massive table of equations that apply to all the target numbers, then doing additional computation for each one. Testing the technique on RSA numbers is currently too hard, so Lenstra turned to Mersenne numbers, which are somewhat easier to factor. The team started attacking 17 of these numbers in 2010. Now they have factored 10, after the equivalent of 2000 years’ computation on a highend PC – about 50 per cent faster than doing them one at a time. The highest number factored was 21193-1, which is a record (Cryptology ePrint Archive, eprint.iacr.org/2014/653). This is roughly the same size as the 1024-bit RSA numbers used in today’s encryption – 1024 being their length in binary – which are very hard to crack. Much smaller 512-bit numbers were standard but in 1999 Lenstra cracked one, which contributed to the industry upgrading to 1024-bit. This latest work could push things again, Lenstra says, but there’s no need to worry about your online security yet. Jacob Aron n
tissue onto the goats’ knees. The cartilage not only settled comfortably into its new home, but also restored the knee joints to good health. It even started to look like knee tissue genetically. After bedding down, the cartilage cells began expressing the genes that you would expect to see in native knee cartilage. This was unexpected. “It shows that the nose cells had
the plasticity to transform and be fully compatible with their new environment,” says Martin (Science Translational Medicine, doi.org/vf8). The success of the experiment led the team to start a preliminary trial in people. A year and a half ago, nine people with acute cartilage damage in their knee, thanks to a sports injury or other accident, had a transplant. It took –Torn cartilage: every runner’s fear– two weeks for researchers to grow enough nose cells from each volunteer, and a further two weeks to form a 3 by 4 centimetre piece of tissue, which was grafted into the recipient’s knee. “So far, all nine have shown with an alternative source of the improvements in the use of their fibrous tissue – with a little help knee and in amount of pain,” says from the nose. Martin, who is continuing the trial Cartilage cells from the nasal in more volunteers to track the septum (the part of your nose long-term success of the which separates the nostrils) are treatment. He says he sees no known to have a great capacity to reason why the therapy couldn’t grow and form new cartilage. also be given to the millions of What was not clear was whether people who have lost knee novel tissue derived from the cartilage because of osteoarthritis. nose would be compatible with a Using cells from the nose joint in another part of the body. to replace damaged cartilage To find out, Martin and his elsewhere in the body is colleagues started by taking nasal exciting both biologically septum cells from goats with and from a wider transplant cartilage damage to their knees: perspective, says Anthony the animals have a similar joint Hollander at the University of anatomy to humans. The team Liverpool, UK. “The same cells added growth factors to increase might also be used for facial the number of cells and coax reconstruction, for example, after them into becoming a new piece road traffic accidents,” he adds. of cartilage. They then grafted this Helen Thomson n
Knackered knees? Nose cartilage can fix them IF YOU need a new knee, look no further than the end of your nose. It turns out that nasal cartilage is a good substitute for the knee’s natural shock-absorbing tissue – so much so that nine people have undergone the first nose-to-knee cartilage transplant. Unlike many tissues in the body, cartilage, which covers and cushions the surface of joints, has little capacity to regenerate once damaged. Sports injuries or falls can lead to loss of cartilage, but it also degenerates in diseases like osteoarthritis. Treatment options are limited and people often need to have the entire joint replaced with an artificial one. Now, Ivan Martin, a tissue engineer at University Hospital Basel in Switzerland, has come up
6 September 2014 | NewScientist | 9
Numbercracking factory gets to work
“As well as repairing knees, cartilage tissue made from nose cells might be used for facial reconstruction”
BSIP/Getty Images/Universal Images Group
THE first tests of a “factorisation factory” have beaten the record for breaking gigantic numbers down into their prime-number building blocks. It might one day force firms to strengthen their online encryption. All non-prime numbers can be made by multiplying prime numbers together. Cryptographic algorithms use the fact that reversingengineering this multiplication, or factorising, is very difficult for large numbers. New factorising methods are tested on huge “RSA numbers”, each of which is the product of multiplying two prime numbers, known only to encryption firm RSA Security. Factoring a single RSA number is a massive effort, says Arjen Lenstra of the Swiss Federal Institute of Technology in Lausanne, so he and his colleagues have developed a factorisation factory that can tackle multiple target numbers at once. The technique, proposed in the 1990s, saves effort by pre-computing a massive table of equations that apply to all the target numbers, then doing additional computation for each one. Testing the technique on RSA numbers is currently too hard, so Lenstra turned to Mersenne numbers, which are somewhat easier to factor. The team started attacking 17 of these numbers in 2010. Now they have factored 10, after the equivalent of 2000 years’ computation on a highend PC – about 50 per cent faster than doing them one at a time. The highest number factored was 21193-1, which is a record (Cryptology ePrint Archive, eprint.iacr.org/2014/653). This is roughly the same size as the 1024-bit RSA numbers used in today’s encryption – 1024 being their length in binary – which are very hard to crack. Much smaller 512-bit numbers were standard but in 1999 Lenstra cracked one, which contributed to the industry upgrading to 1024-bit. This latest work could push things again, Lenstra says, but there’s no need to worry about your online security yet. Jacob Aron n
tissue onto the goats’ knees. The cartilage not only settled comfortably into its new home, but also restored the knee joints to good health. It even started to look like knee tissue genetically. After bedding down, the cartilage cells began expressing the genes that you would expect to see in native knee cartilage. This was unexpected. “It shows that the nose cells had
the plasticity to transform and be fully compatible with their new environment,” says Martin (Science Translational Medicine, doi.org/vf8). The success of the experiment led the team to start a preliminary trial in people. A year and a half ago, nine people with acute cartilage damage in their knee, thanks to a sports injury or other accident, had a transplant. It took –Torn cartilage: every runner’s fear– two weeks for researchers to grow enough nose cells from each volunteer, and a further two weeks to form a 3 by 4 centimetre piece of tissue, which was grafted into the recipient’s knee. “So far, all nine have shown with an alternative source of the improvements in the use of their fibrous tissue – with a little help knee and in amount of pain,” says from the nose. Martin, who is continuing the trial Cartilage cells from the nasal in more volunteers to track the septum (the part of your nose long-term success of the which separates the nostrils) are treatment. He says he sees no known to have a great capacity to reason why the therapy couldn’t grow and form new cartilage. also be given to the millions of What was not clear was whether people who have lost knee novel tissue derived from the cartilage because of osteoarthritis. nose would be compatible with a Using cells from the nose joint in another part of the body. to replace damaged cartilage To find out, Martin and his elsewhere in the body is colleagues started by taking nasal exciting both biologically septum cells from goats with and from a wider transplant cartilage damage to their knees: perspective, says Anthony the animals have a similar joint Hollander at the University of anatomy to humans. The team Liverpool, UK. “The same cells added growth factors to increase might also be used for facial the number of cells and coax reconstruction, for example, after them into becoming a new piece road traffic accidents,” he adds. of cartilage. They then grafted this Helen Thomson n
Knackered knees? Nose cartilage can fix them IF YOU need a new knee, look no further than the end of your nose. It turns out that nasal cartilage is a good substitute for the knee’s natural shock-absorbing tissue – so much so that nine people have undergone the first nose-to-knee cartilage transplant. Unlike many tissues in the body, cartilage, which covers and cushions the surface of joints, has little capacity to regenerate once damaged. Sports injuries or falls can lead to loss of cartilage, but it also degenerates in diseases like osteoarthritis. Treatment options are limited and people often need to have the entire joint replaced with an artificial one. Now, Ivan Martin, a tissue engineer at University Hospital Basel in Switzerland, has come up
6 September 2014 | NewScientist | 9