Abstract
This paper proposes a novel public-key cryptosystem, which is practical, provably secure and has some other interesting properties as follows:
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1.
Its trapdoor technique is essentially different from any other previous schemes including RSA-Rabin and Diffie-Hellman.
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2.
It is a probabilistic encryption scheme.
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3.
It can be proven to be as secure as the intractability of factoring n = p2q (in the sense of the security of the whole plaintext) against passive adversaries.
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4.
It is semantically secure under the p-subgroup assumption, which is comparable to the quadratic residue and higher degree residue assumptions.
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5.
Under the most practical environment, the encryption and decryption speeds of our scheme are comparable to (around twice slower than) those of elliptic curve cryptosystems.
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6.
It has a homomorphic property: E(m0, r0)E(m1, r1) mod n = E(@#@ m0 + m1, r2), where E(m, r) means a ciphertext of plaintext m as randomized by r and m0+ m1 < p.
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7.
Anyone can change a ciphertext, C = E(m, r), into another ciphertext, C′ = Chr' mod n, while preserving plaintext of C (i.e., C′ = E(m,r″)), and the relationship between C and C′ can be concealed.
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Okamoto, T., Uchiyama, S. (1998). A new public-key cryptosystem as secure as factoring. In: Nyberg, K. (eds) Advances in Cryptology — EUROCRYPT'98. EUROCRYPT 1998. Lecture Notes in Computer Science, vol 1403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054135
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