Probability Properties of Splitting Procedure

The paper contains a probability analysis of information safety providing with data splitting method that has been proposed before by the present authors. The research was made in analogy to the Claude Shannon’s proof of perfect secrecy of gamming procedure under certain properties of gammas. The present paper shows that the probabilities of values obtained after splitting procedure have the required properties of independence and incompatibility. Due to this fact the paper concludes that our splitting procedure, followed by gamming one, remains absolutely safe. Besides, the paper provides a theorem on asymptotic safety of splitting alone as the splitting depth tends to infinity. Independently the present paper shows that the splitting procedure has certain advantages which differ it from traditional gamming, and which make it especially difficult to perform statistical recovery of the original text on the base of its content even in the case when real randomness is replaced with pseudorandom numbers.