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  • hislat
    For restoration of secret message X in this case it is enough to calculate secret key - common divisor on the basis of elements from 480-th and 90-th lines (it
    Message 1 of 1 , Apr 3 8:43 AM
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      For restoration of secret message X in this case it is enough to
      calculate secret key - common divisor on the basis of elements from
      480-th and 90-th lines (it means y=X^480mod481 and y=X^90mod91), for
      P=481 on a line 480 there are numbers 248,417. From these numbers it
      is possible to find (248-1) = 247 and (417-1) =416 which has the
      greatest common divisor 13 with 481, that is the first common divisor
      of the modulo. Further does not represent difficulties of calculation
      of the second common divisor 37 modules that allows to calculate
      function Euler (481) =12*36=432 on the basis of which there is a
      secret key i2 for restoration of message X with use algorithm of
      Euclidean as i2=i1-1 mod 432. Here, i1 an open key with which use
      message X is encrypted.

      Such numbers have the some properties as Carmichael numbers, but
      unique difference of Carmichael numbers consists that Carmichael
      numbers are the product of least three distinct primes and necessary
      what P-1 divides n-1 for every prime divisor P of n, n={P1, P2,
      P3...Pk}. For new kind of numbers it is not necessary.

      If P =P1*P2*P3 (1) or P1*P2 (2) is modulo of function Y = Xi mod P ,
      value of

      function Y = X(P1-1)+(P2-1)+(P3-1) mod P= X(P-1)mod P (1) or

      Y = X (P1-1) +(P2-1)mod P = X(P-1)mod P (2) will true.

      This best regards
      Hislat
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