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Lecture notes in computer science

Round5: Compact and Fast Post-quantum Public-Key Encryption

Hayo Baan, Sauvik Bhattacharya, Scott R. Fluhrer, Óscar García-Morchón, Thijs Laarhoven, Ronald Rietman, Markku-Juhani Olavi Saarinen, Ludo M. G. M. Tolhuizen, Zhenfei Zhang

Published Jan 1, 2019• 50 citations
Publisher
DOI
10.1007/978-3-030-25510-7_5

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The rapid proliferation of cloud computing enables users to access computing resources and storage space over the internet, but it also presents challenges in terms of security and privacy. Ensuring the security and availability of data has become a focal point of current research when utilizing cloud computing for resource sharing, data storage, and querying. Public key encryption with equality test (PKEET) can perform an equality test on ciphertexts without decrypting them, even when those ciphertexts are encrypted under different public keys. That offers a practical approach to dividing up or searching for encrypted information directly. In order to deal with the threat raised by the rapid development of quantum computing, researchers have proposed post-quantum cryptography to guarantee the security of cloud services. However, it is challenging to implement these techniques efficiently. In this paper, a compact PKEET scheme is pro-posed. The new scheme does not encrypt the plaintext's hash value immediately but embeds it into the test trapdoor. We also demon-strated that our new construction is one-way secure under the quantum security model. With those efforts, our scheme can withstand the chosen ciphertext attacks as long as the learning with errors (LWE) assumption holds. Furthermore, we evaluated the new scheme's performance and found that it only costs approximately half the storage space compared with previous schemes. There is an almost half reduction in the computing cost throughout the encryption and decryption stages. In a nutshell, the new PKEET scheme is less costly, more compact, and applicable to cloud computing scenarios in a post-quantum environment.
Abstract Code-based public key encryption (PKE) is a popular choice to achieve post-quantum security, partly due to its capability to achieve fast encryption/decryption. However, code-based PKE has larger ciphertext and public key sizes in comparison to conventional PKE schemes (e.g., those based on RSA). In 2018, Lau and Tan proposed a new rank metric code-based PKE scheme, which has smaller public key and ciphertext sizes compared to other code-based PKE schemes. They also proved that their scheme achieves IND-CPA security, assuming the intractability of the decisional rank syndrome decoding problem. It is known that IND-CCA2 security is the strongest and most popular security assurance for PKE schemes. Therefore, in this paper, we obtain a new code-based PKE scheme from Lau and Tan’s scheme, in order to inherit the underlying small public key and ciphertext sizes. However, our new scheme is shown to achieve IND-CCA2 security, instead of the weaker IND-CPA security. Specifically, the respective public key size and ciphertext size in our new scheme are 15.06 KB and 1.37 KB under 141-bit security level, and 16.76 KB and 1.76 KB under 154-bit security level. We then present a use case for the proposed scheme, that is for secure cloud storage.
We present BAT – an IND-CCA secure key encapsulation mechanism (KEM) that is based on NTRU but follows an encryption/decryption paradigm distinct from classical NTRU KEMs. It demonstrates a new approach of decrypting NTRU ciphertext since its introduction 25 years ago. Instead of introducing an artificial masking parameter p to decrypt the ciphertext, we use 2 linear equations in 2 unknowns to recover the message and the error. The encryption process is therefore close to the GGH scheme. However, since the secret key is now a short basis (not a vector), we need to modify the decryption algorithm and we present a new NTRU decoder. Thanks to the improved decoder, our scheme works with a smaller modulus and yields shorter ciphertexts, smaller than RSA-4096 for 128-bit classical security with comparable public-key size and much faster than RSA or even ECC. Meanwhile, the encryption and decryption are still simple and fast in spite of the complicated key generation. Overall, our KEM has more compact parameters than all current lattice-based schemes and a practical efficiency. Moreover, due to the similar key pair structure, BAT can be of special interest in some applications using Falcon signature that is also the most compact signature in the round 3 of the NIST post-quantum cryptography standardization. However, different from Falcon, our KEM does not rely on floating-point arithmetic and can be fully implemented over the integers.