New Directions of Modern Cryptography by Cao Zhenfu

Author:Cao, Zhenfu [Cao, Zhenfu]
Language: eng
Format: epub
ISBN: 978-1-4665-9761-7
Publisher: CRC Press
Published: 2012-03-24T16:00:00+00:00

We get the plaintext from Equation (4.25).

We can find that m’1 = m1, which shows the correctness of our implementation. Note that m2, m3, …, m7 can be computed in the same way from Equation (4.25) and Equation (4.26). In fact, we compute m2, m3, …, m7 first and then compute m1 as Remark 4.4.1, we can finish the split (decryption) efficiently.

4.4.3 Implementation Based on Minus-Type Equations

We find that the solutions of the following Diophantine Equation

can also be used to implement batch RSA so that αi, which satisfies Equation (4.22), can be constructed directly and the whole decryption only uses modular N. We call Equation (4.33) the Minus-Type Diophantine Equation or Minus-Type Equation. For convenience, throughout this book, Equation (4.33) with n unknown variables is denoted as Equation (4.33)n.

Our new implementation of batch RSA also contains three algorithms: KeyGen, Encrypt, and Decrypt. The essence of the implementation is in the decryption algorithm. Algorithm KeyGen and Encrypt are the same as our implementation based on the Plus-Type Equations.

Decrypt: This algorithm takes a public key (N, b, e1, e2, …, eb, x = 1≤i≤nxi), a private key d, and ciphertexts c1, c2, …, cb as input. It evaluates A0 1≤i≤bcie/ei (mod N) by the methods proposed by Fiat, and A Ad0 (mod N). Obviously

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