A New Secure Quantum Key Expansion Scheme

Fenghe Wang, Chunxiao Wang, Yupu Hu

Abstract: Using the Bonsai trees primitive and Gentry’s CPA-secure (chosen-plaintext attack) public-key encryption (PKE) scheme, we propose an efficient chosen-ciphtertext secure PKE scheme over lattice. If the decision variant of the learning with errors (LWE) problem is hard and the one-time signature used in this scheme is strong unforgeable, the proposed PKE scheme is indistinguishable against the adaptive chosen-ciphtertext attack (IND-CCA2). One of the characters for this scheme is that, before any encryption operation, the encryption algorithm uses a new choice rule to fix the public parameter matrixes used in the encryption operation. With the help of this new choice rule, we can achieve the chosen-ciphtertext security with much shorter the public key size in contrast to the lattice-based encryption scheme proposed in STOC’09 by Peikert. Moreover, as a CCA-secure PKE scheme, the message-tociphtertext expanse factor of this scheme which is controlled efficiently is nearly closed to the message-to-ciphtertext expanse factor of Gentry’s scheme which is CPA secure. Due to the quantum intractability of the LWE problem on which the scheme is based, the proposed PKE scheme is secure even in quantum-era.

Ivan B. Djordjević

Wang Jizhong, Wang Chunxiao

Using a known lattice-based chosen plain-text secure encryption scheme and the Bonsai trees primitive, a identity-based encryption (IBE) scheme is proposed in this paper. A public matrices chosen rule that has been used in a known efficient lattice-based chosen ciphtertext secure encryption scheme is used in this paper to reduce the public key size and the message-to ciphtertext expanse factor. Under the hardness of the decision variant of the learning with errors (LWE) problem, we prove that the proposed IBE scheme is indistinguishable against the adaptive chosen identities and chosen-plaintext attack in the standard model. Since a new public key chosen rule is used in our design scheme, the public key size of the proposed scheme would be short. Moreover, the message-to-ciphtertext expanse factor of this scheme is also controlled efficiently which is nearly closed to that of Gentry's scheme. Due to the quantum intractability of the LWE problem on which the scheme is based, the proposed IBE scheme is secure even in quantum-era.

Georgi Bebrov

雄祐 吉田, Yusuke Yoshida

Public-key encryption is a cryptographic primitive used for establishing a secure channel between two parties.Depending on the situation and purpose, public-key encryption schemes must satisfy appropriate security requirements.Non-committing encryption (NCE) is a public-key encryption scheme that satisfies a security notion essential to establish a secure channel in adaptively secure multi-party computation (MPC) protocols.Informally, NCE can generate a dummy ciphertext.The dummy ciphertext is indistinguishable from the real ciphertext.Moreover, we can explain the dummy ciphertext as encryption of an arbitrary message by producing consistent randomness.It has been a challenge in the theory of adaptively secure MPC to find an NCE scheme with small ciphertext expansion (required ciphertext length per bit of message).This thesis proposes the first NCE schemes with constant ciphertext expansion in the standard model (i.e., without assuming the randomness used in the cryptosystem can be securely erased or use of the random oracle).We show two instantiations of the scheme, one from the Decisional Diffie-Hellman (DDH) problem and another from the Learning with Errors (LWE) problem.Before constructing the constant ciphertext expansion scheme, we demonstrate the new approach to constructing NCE through the construction of a simpler NCE scheme based on obliviously samplable key-encapsulation mechanism (KEM).The ciphertext expansion of this simpler scheme is O(λ) for security parameter λ.In detail, we use KEM to construct a weak NCE scheme with O(λ) ciphertext expansion.Weak NCE is NCE where its correctness and security requirements are weakened.Then weak NCE is amplified to a full-fledged NCE scheme using an information theoretical primitive called wiretap codes.This amplification increases the cipher text expansion only by a constant factor.The constant ciphertext expansion scheme is obtained by using a primitive called obliviously samplable chameleon encryption, instead of KEM in the above construction.We show instantiations of obliviously samplable chameleon encryption based on the DDH and the LWE problems.

Ivan B. Djordjević