Using the Chinese remainder theorem, we can prove that implementing as
•
By an ingenious use of Chinese remainder theorem, we can define constructively such a recursive function (using simple number-theoretical functions, all of which can be defined in a total recursive way) fulfilling the "specifications" given above.
•
Using the fundamental theorem of arithmetic is a straightforward way, but there are also more economic approaches, e.g. using pairing function combined with Chinese remainder theorem in a sophisticated way.
Then, for any sets U and V, by the Chinese remainder theorem, the numbers that are quadratic resides modulo every prime in U and nonresidues modulo every prime in V form a periodic sequence, so by Dirichlet's theorem on primes in arithmetic progressions this number-theoretic graph has the extension property.
Chinese | Chinese language | Han Chinese | Chinese people | Mandarin Chinese | Chinese cuisine | Chinese: | Chinese New Year | Chinese Academy of Sciences | Chinese dragon | Chinese Civil War | Chinese Taipei | Chinese People's Political Consultative Conference | Chinese American | Chinese University of Hong Kong | Traditional Chinese characters | Chinese Academy of Social Sciences | Chinese yuan | Standard Chinese | Chinese poetry | Chinese characters | Chinese zodiac | Chinese painting | Chinese culture | Yue Chinese | traditional Chinese medicine | Simplified Chinese characters | Overseas Chinese | Chinese literature | Chinese guardian lions |
In 2003, Boneh and Brumley demonstrated a practical network-based timing attack on SSL-enabled web servers, based on a different vulnerability having to do with the use of RSA with Chinese remainder theorem optimizations.