Prime or not prime?

Do you think this number is a prime number? ETH Prof. Kenny Paterson reveals the secret behind numbers like this and why they are important in everyday life.

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Video: ETH Zurich

Here is the answer to the question in the video:

79018773324211176042772335560019945481740317280584
85631926375876865078028180049751981627864304181541
06118359049820167300903932953917153923065177695072
7307

This number is not a prime number. It is a composite number that is the product of three primes:

73938149834061418521192073314311208786743496108043 * 8355010931248940292894704284517166592902015060208747 * 12791299921292625404166228683375839120106624826691267

It was specially constructed to fool the primality test used in Apple’s CommonCrypto library, and was always declared as being prime by that library. This issue affected versions of Apple software prior to iOS 12.1, macOS Mojave 10.14.1, tvOS 12.1, watchOS 5.1, iTunes 12.9.1, and iCloud for Windows 7.8.

Apple updated their library in response to our research in late 2018. See external pagehttps://nvd.nist.gov/vuln/detail/CVE-2018-4398 for further details. To read more about our research on primality testing, please see: external pagehttps://eprint.iacr.org/2018/749.pdf  

Contact / Links:

Prof. Kenny Paterson, Applied Cryptography Group

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