Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

HIBE Scheme Based on Programmable Hash Function on Lattices

YE Qing, WANG Mingming, TANG Yongli, QIN Panke, WANG Yongjun

Published Jan 1, 2020• 0 citations
Publisher

Abstract

To address the computational complexity of trapdoor generation of Hierarchical Identity-Based Encryption(HIBE) scheme on lattices under the standard mode,this paper proposes a HIBE scheme based on programmable hash function.First,the trapdoor is generated by MP12 trapdoor function.Then,the master public key,the master private key and the ciphertext are obtained by programmable hash function.Experimental results show that compared with the HIBE scheme with fixed dimension under the standard mode,the computational complexity of trapdoor generation of this method is significantly diminished,and the length of the main public key is reduced to O(logbn),which can satisfy the INDr-aID-CPA security.

DOI
10.19678/j.issn.1000-3428.0053213

Related papers

Efficient hierarchical identity based encryption scheme in the standard model over lattices

Fenghe Wang, Chunxiao Wang, Zhenhua Liu

Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only ( dm 2 + mn ) log q bits and whose message-ciphertext expansion factor is only log q , where d is the maximum hierarchical depth and ( n , m , q ) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2 d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2 dm 2 + mn + m ) log q . To reduce the message-ciphertext expansion factor of the proposed scheme to log q , the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.

Frontiers of Information Technology & Electronic Engineering•Aug 1, 2016•5 citations

An ideal lattice based IBE scheme in the standard model

Xiaoyuan Yang, Liqiang Wu, Minqing Zhang +2 more

Under the standard model, an IND-sID-CPA secure IBE (Identity Based Encryption) scheme is proposed, which is based on an improved trapdoor generation function over ring and decisional R-LWE (ring-learning with errors) assumption, thus the hardness of recovering system master key can be reduced to solve the Ideal-SIS (small integer solution) problem, and the attack to the ciphertext is equivalent to solving the SVP (the shortest vector problem) in the worst case on ideal lattice to within a fixed poly( n ) factor. Moreover, the proposed scheme has advantages of high encryption and decryption speed and low encryption blowup factor compared with all known IBE scheme from the standard lattice under the standard model.

Wuhan University Journal of Natural Sciences•Sep 3, 2011•2 citations

How to Delegate a Lattice Basis.

David M. Cash, Dennis Hofheinz, Eike Kiltz

We present a technique, which we call basis delegation, that allows one to use a short basis of a given lattice to derive a new short basis of a related lattice in a secure way. And since short bases for lattices essentially function like cryptographic trapdoors, basis delegation turns out to be a very powerful primitive. As the main application of our technique, we show how to construct hierarchical identity-based encryption (HIBE) that is secure, without random oracles, under the assumption that certain standard lattice problems are hard in the worst case. This construction and its variants constitute the first HIBE schemes from lattices, as well as the first lattice-based constructions of stateless signatures and identity-based encryption without random oracles. 1

•Jan 1, 2009•55 citations

Deterministic Identity-Based Encryption from Lattice-Based Programmable Hash Functions with High Min-Entropy.

Daode Zhang, Jie Li, Bao Li +4 more

There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of basic matrices.

•Jan 1, 2019•0 citations

Deterministic Identity-Based Encryption from Lattice-Based Programmable Hash Functions with High Min-Entropy

Daode Zhang, Jie Li, Bao Li +4 more

There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of O(λ) basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of ω(log⁡λ) basic matrices.

Security and Communication Networks•Jan 13, 2019•5 citations

Tightly Secure Hierarchical Identity-Based Encryption

Roman Langrehr, Jiaxin Pan

Abstract We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation.

Journal of Cryptology•Sep 15, 2020•16 citations
To address the computational complexity of trapdoor generation of Hierarchical Identity-Based Encryption(HIBE) scheme on lattices under the standard mode,this paper proposes a HIBE scheme based on programmable hash function.First,the trapdoor is generated by MP12 trapdoor function.Then,the master public key,the master private key and the ciphertext are obtained by programmable hash function.Experimental results show that compared with the HIBE scheme with fixed dimension under the standard mode,the computational complexity of trapdoor generation of this method is significantly diminished,and the length of the main public key is reduced to O(logbn),which can satisfy the INDr-aID-CPA security.
Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only ( dm 2 + mn ) log q bits and whose message-ciphertext expansion factor is only log q , where d is the maximum hierarchical depth and ( n , m , q ) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2 d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2 dm 2 + mn + m ) log q . To reduce the message-ciphertext expansion factor of the proposed scheme to log q , the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.
Under the standard model, an IND-sID-CPA secure IBE (Identity Based Encryption) scheme is proposed, which is based on an improved trapdoor generation function over ring and decisional R-LWE (ring-learning with errors) assumption, thus the hardness of recovering system master key can be reduced to solve the Ideal-SIS (small integer solution) problem, and the attack to the ciphertext is equivalent to solving the SVP (the shortest vector problem) in the worst case on ideal lattice to within a fixed poly( n ) factor. Moreover, the proposed scheme has advantages of high encryption and decryption speed and low encryption blowup factor compared with all known IBE scheme from the standard lattice under the standard model.
We present a technique, which we call basis delegation, that allows one to use a short basis of a given lattice to derive a new short basis of a related lattice in a secure way. And since short bases for lattices essentially function like cryptographic trapdoors, basis delegation turns out to be a very powerful primitive. As the main application of our technique, we show how to construct hierarchical identity-based encryption (HIBE) that is secure, without random oracles, under the assumption that certain standard lattice problems are hard in the worst case. This construction and its variants constitute the first HIBE schemes from lattices, as well as the first lattice-based constructions of stateless signatures and identity-based encryption without random oracles. 1
There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of basic matrices.
There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of O(λ) basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of ω(log⁡λ) basic matrices.
Abstract We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation.