IGE mode used in Telegram's customized protocol has not been fully investigated in terms of post-quantum security. In this letter, we show that IGE mode is IND-qCPA insecure by Simon's algorithm, assuming that the underlying block cipher is a standard-secure pseudorandom function (sPRF). Under a stronger assumption that the block cipher is a quantum-secure pseudorandom function (qPRF), IND-qCPA security of IGE mode is proved using one-way to hiding lemma.
IGE mode used in Telegram's customized protocol has not been fully investigated in terms of post-quantum security. In this letter, we show that IGE mode is IND-qCPA insecure by Simon's algorithm, assuming that the underlying block cipher is a standard-secure pseudorandom function (sPRF). Under a stronger assumption that the block cipher is a quantum-secure pseudorandom function (qPRF), IND-qCPA security of IGE mode is proved using one-way to hiding lemma.
The OCB mode of operation for block ciphers has three variants, OCB1, OCB2 and OCB3. OCB1 and OCB3 can be used as secure authenticated encryption schemes whereas OCB2 has been shown to be classically insecure (Inoue et al., Crypto 2019). Even further, in the presence of quantum queries to the encryption functionality, a series of works by Kaplan et al. (Crypto 2016), Bhaumik et al. (Asiacrypt 2021) and Bonnetain et al. (Asiacrypt 2021) have shown how to break the unforgeability of the OCB modes. However, these works did not consider the confidentiality of OCB in the presence of quantum queries.We fill this gap by presenting the first formal analysis of the IND-qCPA security of OCB. In particular, we show the first attacks breaking the IND-qCPA security of the OCB modes. Surprisingly, we are able to prove that OCB2 is IND-qCPA secure when used without associated data, while relying on the assumption that the underlying block cipher is a quantum-secure pseudorandom permutation. Additionally, we present new quantum attacks breaking the universal unforgeability of OCB. Our analysis of OCB has implications for the post-quantum security of XTS, a well-known disk encryption standard, that was considered but mostly left open by Anand et al. (PQCrypto 2016).
We investigate the quantum security of nonce-based encryption under the indistinguishability against quantum chosen-plaintext attacks (IND-qCPA). While classical results establish that IV-based modes such as CBC, CFB, OFB, and CTR achieve IND-qCPA security, we demonstrate that simply replacing the random IV with a nonce undermines both classical and quantum security. To address this, we propose a general transformation from R-IND-qCPA security to N-IND-qCPA security and introduce enhanced variants, namely, CBC2, CFB2, OFB2, and CTR2, that are provably secure in the nonce-based quantum setting. We further show that nonce-based stream cipher encryption inherently satisfies N-IND-qCPA security. These results provide a systematic framework for upgrading IV-based constructions to secure nonce-based counterparts, thereby strengthening practical symmetric encryption against quantum adversaries.
COPA is a notable authenticated online cipher and was one of the winning proposals for the CAESAR competition. Current works describe how to break the existentially unforgeable under quantum chosen message attack (EUF-qCMA) of COPA. However, these works do not demonstrate the confidentiality of COPA in the quantum setting. This paper fills this gap, considers the indistinguishable under quantum chosen-plaintext attack (IND-qCPA) security for privacy, and presents the first IND-qCPA security analysis of COPA. In addition, in order to effectively avoid the problems of quantum existential forgery attack and quantum distinguishing attack, we introduce an intermediate state doubling-point technology into COPA, restrict the associated data non-emptiness, and present an enhanced variant, called COPA-ISDP, to support the IND-qCPA and EUF-qCMA security. Our work is of great significance, as it provides a simple and effective post-quantum secure design idea to resist Simon's attack.
Pseudorandom permutations are ubiquitous in theoretical and applied cryptography. PRPs that offer security even against adversaries making quantum queries are of increasing interest, and used in applications ranging from constructing pseudorandom unitaries to separating SZK from BQP.
A successful framework for constructing classically-secure PRPs is the key-alternating Even-Mansour approach, which interleaves applications of public permutations with additions of round keys. The single-round construction is already classically secure in the ideal permutation model (IPM), with added rounds offering improved concrete security. However, in the quantum-query setting, the status of this framework is presently unclear. A simple quantum-query attack based on Simon's algorithm breaks the one-round cipher. For two or more rounds, security is only known against non-adaptive adversaries who must prepare all queries in advance.
In this work, we show that the two-round Even-Mansour cipher is information theoretically secure in the IPM against adversaries making polynomially-many adaptive forward and inverse quantum queries to all available oracles. Our proof uses compressed permutation oracles and a specially crafted isometry relating the ideal and real experiments. We also show that this construction is minimal, in the sense that essentially any cipher constructed via a single call to a public permutation is quantumly insecure.
Authenticated encryption with associated data (AEAD) play a critical role in secure communication protocols, by offering confidentiality, integrity, and authenticity. However, the advent of quantum computing poses a significant threat to the security of AEAD schemes, including ISO/IEC standards such as OCB (offset codebook) and GCM (Galois/counter mode), highlighting the need for a thorough evaluation of their quantum resistance. Combined feedback mode (COFB) is a lightweight AEAD mode proposed at CHES'17, gaining significant attention due to its excellent performance in both software and hardware implementations. In this paper, we study the post-quantum security of COFB. First, we show COFB is insecure under the security notion of quantum-secure pseudo-random funtion (qPRF) by presenting an attack with a single encryption query. Next, we investigate the IND-qCPA (indistinguishability under quantum chosen-plaintext attack) security of COFB. Specifically, we show that if instantiated with a qPRF-securen-bit block cipher, the IND-qCPA security bound of COFB is roughly(Q7/4⋅ℓ11/4)/2n/2+Qℓ/2n/4, whereQdenotes the number of encryption queries andℓrepresents the maximum length (in blocks) of messages in each query. Furthermore, we extend this result to GIFT-COFB, a finalist in the NIST Lightweight Cryptography competition, and establish its security bound as(Q7/4⋅ℓ11/4)/2n/2.
Tweakable block ciphers are more flexible than traditional block ciphers and widely used in modes of operation such as MAC and authenticated encryption. With the development of quantum computing, the threat of quantum algorithms to the security of cryptosystems is increasing. Research shows that some classical secure symmetric cryptographic constructions or schemes become vulnerable to the quantum attacks based on Simon's algorithm. This paper studies the security of tweakable block cipher constructions under quantum attacks based on Simon's algorithm, summarizes the quantum attack methods of Simon's algorithm and quantum-resistant constructions, and provides methods to enhance the quantum security of tweakable block ciphers.