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New Cryptosystems From CSP-Based Self-Distributive Systems.

Licheng Wang, Lihua Wang, Zhenfu Cao, Eiji Okamoto, Jun Shao

Published Jan 1, 2009• 2 citations
OpenAlex

Abstract

Abstract. We propose new cryptosystems based on self-distributive systems that are defined by conjugator searching problems (CSP) in noncommutative groups. Under certain assumptions, the ciphertexts of our basic construction are proven indistinguishable against chosen plaintext attacks (IND-CPA) in the standard model, and two extended schemes achieve the IND-CCA security in the random oracle model. Then, our proposal is instantiated with braid groups, and leads to a new braid-based encryption scheme that is directly based on the intractability assumption of CSP in braid groups. Furthermore, we quote an analysis to manifest that our newly derived braid-based cryptosystem has the potential to resist currently known quantum attacks. Keywords: Self-distributive systems, conjugator searching problem, braid groups, resistance to quantum attacks 1

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Functional encryption (FE) can implement fine-grained control to encrypted plaintext via permitting users to compute only some specified functions on the encrypted plaintext using private keys with respect to those functions. Recently, many FEs were put forward; nonetheless, most of them cannot resist chosen-ciphertext attacks (CCAs), especially for those in the secret-key settings. This changed with the work, i.e., a generic transformation of public-key functional encryption (PK-FE) from chosen-plaintext (CPA) to chosen-ciphertext (CCA), where the underlying schemes are required to have some special properties such as restricted delegation or verifiability features. However, examples for such underlying schemes with these features have not been found so far. Later, a CCA-secure functional encryption from projective hash functions was proposed, but their scheme only applies to inner product functions. To construct such a scheme, some nontrivial techniques will be needed. Our key contribution in this work is to propose CCA-secure functional encryptions in the PKE and SK environment, respectively. In the existing generic transformation from (adaptively) simulation-based CPA- (SIM-CPA-) secure ones for deterministic functions to (adaptively) simulation-based CCA- (SIM-CCA-) secure ones for randomized functions, whether the schemes were directly applied to CCA settings for deterministic functions is not implied. We give an affirmative answer and derive a SIM-CCA-secure scheme for deterministic functions by making some modifications on it. Again, based on this derived scheme, we also propose an (adaptively) indistinguishable CCA- (IND-CCA-) secure SK-FE for deterministic functions. The final results show that our scheme can be instantiated under both nonstandard assumptions (e.g., hard problems on multilinear maps and indistinguishability obfuscation (IO)) and under standard assumptions (e.g., DDH, RSA, LWE, and LPN).

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•Nov 20, 2015•0 citations
Abstract. We propose new cryptosystems based on self-distributive systems that are defined by conjugator searching problems (CSP) in noncommutative groups. Under certain assumptions, the ciphertexts of our basic construction are proven indistinguishable against chosen plaintext attacks (IND-CPA) in the standard model, and two extended schemes achieve the IND-CCA security in the random oracle model. Then, our proposal is instantiated with braid groups, and leads to a new braid-based encryption scheme that is directly based on the intractability assumption of CSP in braid groups. Furthermore, we quote an analysis to manifest that our newly derived braid-based cryptosystem has the potential to resist currently known quantum attacks. Keywords: Self-distributive systems, conjugator searching problem, braid groups, resistance to quantum attacks 1
Abstract We propose BRCE (Braid-Ring Convolutional Encryption), a novel quantum-resilient group ring-based encryption scheme built over the non-abelian structure of braid groups and their integral group rings. The encryption mechanism applies convolution-based masking with randomized braid elements to achieve semantic obfuscation without relying on periodic structures. Our design embeds high-entropy messages into non-commutative algebraic carriers , resulting in ciphertexts that resist both classical and quantum algebraic attacks. We provide a provable security reduction from the Conjugacy Search Problem (CSP) in braid groups and show that the scheme satisfies IND-CPA and IND-CCA security notions under reasonable pseudorandomness assumptions. We anchor security in a new hardness assump-tion—the Group Ring Convolution Inversion Problem (GRCIP)—tailored to non-abelian group rings. Further, we demonstrate that the structure resists reductions to the Hidden Subgroup Problem (HSP), positioning BRCE as a competitive post-quantum candidate rooted in topological and algebraic hardness. MSC 2020: 94A60, 20F36, 68Q12, 11T71
The rapid development of quantum computing brings great challenges to public key cryptosystems.The braid group,which is non-commutative,provides a new platform of constructing cryptographic protocols.A convertible authenticated encryption scheme over braid group is proposed on the difficulty of conjugacy search problem and multiple conjugacy problem,in which only the designated receiver can recover and authenticate the message,when the sender repudiates the signature,the receiver can prove the dishonesty of the sender by converting the signature to an ordinary one without the cooperating of the sender.As for the resistance against quantum attacks,the proposed scheme has advantage over the schemes based on commutative algebraic structures.
Chosen-ciphertext security, which guarantees confidentiality of encrypted messages even in the presence of a decryption oracle, has become the defacto notion of security for public-key encryption under active attack. In this manuscript, for the first time, we propose a new approach for constructing post-quantum cryptosystems secure against adaptive chosen ciphertext attack (CCA2-secure) in the standard model using the knapsack problem. The computational version of the knapsack problem is NP-hard. Thus, this problem is expected to be difficult to solve using quantum computers. Our construction is a precoding-based encryption algorithm and uses the knapsack problem to perform a permutation and pad some random fogged data to the message bits. Compared to other approaches were introduced today, our approach is very simple and more efficient.
The development of increasingly sophisticated quantum computers poses a long-term threat to current cryptographic infrastructure. This has spurred research into both quantum-resistant algorithms and how to safely transition real-world implementations and protocols to quantum-resistant replacements. This transition is likely to be a gradual process due to both the complexity and cost associated with transitioning. One method to ease the transition is the use of classical–quantum hybrid schemes, which provide security against both classical and quantum adversaries. We present a new combiner for creating hybrid encryption schemes directly from traditional encryption schemes. Our construction is the only existing proposal in the literature with IND-CCA-security in the classical and quantum random oracle models, respectively.
Functional encryption (FE) can implement fine-grained control to encrypted plaintext via permitting users to compute only some specified functions on the encrypted plaintext using private keys with respect to those functions. Recently, many FEs were put forward; nonetheless, most of them cannot resist chosen-ciphertext attacks (CCAs), especially for those in the secret-key settings. This changed with the work, i.e., a generic transformation of public-key functional encryption (PK-FE) from chosen-plaintext (CPA) to chosen-ciphertext (CCA), where the underlying schemes are required to have some special properties such as restricted delegation or verifiability features. However, examples for such underlying schemes with these features have not been found so far. Later, a CCA-secure functional encryption from projective hash functions was proposed, but their scheme only applies to inner product functions. To construct such a scheme, some nontrivial techniques will be needed. Our key contribution in this work is to propose CCA-secure functional encryptions in the PKE and SK environment, respectively. In the existing generic transformation from (adaptively) simulation-based CPA- (SIM-CPA-) secure ones for deterministic functions to (adaptively) simulation-based CCA- (SIM-CCA-) secure ones for randomized functions, whether the schemes were directly applied to CCA settings for deterministic functions is not implied. We give an affirmative answer and derive a SIM-CCA-secure scheme for deterministic functions by making some modifications on it. Again, based on this derived scheme, we also propose an (adaptively) indistinguishable CCA- (IND-CCA-) secure SK-FE for deterministic functions. The final results show that our scheme can be instantiated under both nonstandard assumptions (e.g., hard problems on multilinear maps and indistinguishability obfuscation (IO)) and under standard assumptions (e.g., DDH, RSA, LWE, and LPN).