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METHODS AND SYSTEMS FOR ENCRYPTING RATIONAL NUMBERS AND ADDING RANDOMNESS TO RSA CRYPTOSYSTEMS USING P-ADIC NUMBERS
METHODS AND SYSTEMS FOR ENCRYPTING RATIONAL NUMBERS AND ADDING RANDOMNESS TO RSA CRYPTOSYSTEMS USING P-ADIC NUMBERS
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机译:使用P-ADIC数加密有理数并向RSA密码系统添加随机性的方法和系统
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摘要
Disclosed are methods and systems to use p-adic numbers for an RSA cryptosystem to send rational numbers or to add randomness to the RSA cryptosystem. An embodiment may convert at the source device a rational number to an integer as p-adic based Hensel code representation of the rational number at the source device and then recover the rational number at the destination device by reversing the Hensel code back to the original rational number. Another embodiment may use a ??-adic inverse of a message together with a random number to obtain a different rational number to encrypt for each different random number resulting in different ciphertexts representing the same message while still recovering the original message despite having different ciphertexts for the same message value. The various embodiments further retain the multiplicative homomorphism of the RSA cryptosystem since the p-adic Hensel codes are also multiplicative homomorphic.
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