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### Constant-Size Group Signatures from Lattices [chapter]

San Ling, Khoa Nguyen, Huaxiong Wang, Yanhong Xu
2018 Lecture Notes in Computer Science
In this work, we introduce the first constant-size group signature from lattices, which means that the size of signatures produced by the scheme is independent of N and only depends on the security parameter  ...  Lattice-based group signature is an active research topic in recent years.  ...  We introduce the first constant-size group signature scheme from lattices.  ...

### A New Constant-Size Group Signature Scheme from Lattices

Qin Luo, Chun-yang Jiang
2020 IEEE Access
At PKC 2018, Ling, Nguyen, Wang and Xu presented the first constant-size group signature scheme under lattice assumptions.  ...  In each LGSS, the size of the group signature usually depends on the number of group members and the security parameter. Thus, designing a constant-size LGSS is an interesting problem.  ...  [9] constructed the first constant-size group signature scheme from lattices.  ...

### Simpler Efficient Group Signatures from Lattices [chapter]

Phong Q. Nguyen, Jiang Zhang, Zhenfeng Zhang
2015 Lecture Notes in Computer Science
paradigm: KeyGen(κ, N): 1 2 Jiang Zhang (TCA) Simpler Efficient Group Signatures from Lattices March 31, 2015 6 / 22 Jiang Zhang (TCA) Simpler Efficient Group Signatures from Lattices  ...  March 31, 2015 8 / 22 Jiang Zhang (TCA) Simpler Efficient Group Signatures from Lattices March 31, 2015 9 / 22 Jiang Zhang (TCA) Simpler Efficient Group Signatures from Lattices March 31, 2015  ...  gpk, j) = (A1 A2,1 + G(j)A2,2) KeyGen(κ, N): 1 Generate gpk = (A1, A2,1, A2,2) with a trapdoor of A1; 2 Define Aj := H(gpk, j) = (A1 A2,1 + G(j)A2,2); 3 Sample a short vector gskj = xj = (xj,1, xj,2) from  ...

### Message Integration Authentication in the Internet-of-Things via Lattice-Based Batch Signatures

Xiuhua Lu, Wei Yin, Qiaoyan Wen, Kaitai Liang, Liqun Chen, Jiageng Chen
2018 Sensors
In this paper, we make use of the intersection method from lattice to propose a novel generic method for batch signature.  ...  However, this structure requires a batch residue, making the size of a batch signature (for a group of messages) even longer than the sum of single signatures.  ...  Generally speaking, our signature size will be larger than the ones constructed in the group where DLP or ECDLP problem is hard.  ...

### Simpler Efficient Group Signature Scheme with Verifier-Local Revocation from Lattices

2016 KSII Transactions on Internet and Information Systems
(PKC 2014) proposed the first VLR group signature based on lattice assumptions in the random oracle model. Their scheme has at least 2 O N factor in both the group public key and the signature size.  ...  The security of our VLR group signature can be reduced to the hardness of learning with errors (LWE) and small integer solution (SIS) in the random oracle model.  ...  Putting the above all together, we obtain a simpler efficient VLR group signature scheme from lattices saving a (log ) O N factor in both sizes of the group public key and the signature.  ...

### A Lattice-Based Threshold Ring Signature Scheme [chapter]

Pierre-Louis Cayrel, Richard Lindner, Markus Rückert, Rosemberg Silva
2010 Lecture Notes in Computer Science
Such gain is also maintained through the application of the Fiat-Shamir heuristics to derive signatures from our identification scheme.  ...  From security perspective we also have improvements, because our scheme exhibits a worst-case to average-case reduction typical of lattice-based cryptosystems.  ...  Differently from its numbertheoretic predecessors, which exhibited a complexity of O(t.N ) (where N is the size the group of users, and t is the size of the sub-group willing to sign a message), TRSS-C  ...

### Lattice-based linearly homomorphic signature scheme over binary field

FengHe Wang, YuPu Hu, BaoCang Wang
2012 Science China Information Sciences
To design an efficient lattice-based linearly homomorphic signature scheme with a short public key size and signature length, this paper proposes an efficient linearly homomorphic signature scheme over  ...  Considering communication efficiency, the large public key size and signature size of the linearly homomorphic signature do increase processing overhead.  ...  Currently, most of the lattice-based signature schemes use PSF as their basic tool, for example, the lattice-based signature in the standard model [2] , the lattice-based group signature [7] and the  ...

### CacheQuote: Efficiently Recovering Long-term Secrets of SGX EPID via Cache Attacks

Fergus Dall, Gabrielle De Micheli, Thomas Eisenbarth, Daniel Genkin, Nadia Heninger, Ahmad Moghimi, Yuval Yarom
2018 Transactions on Cryptographic Hardware and Embedded Systems
We analyze the leaked information using a lattice-based approach for solving the hidden number problem, which we adapt to the zero-knowledge proof in the EPID scheme, extending prior attacks on signature  ...  n signature measurements in our data, and then added 50-loop (corresponding to 2 bits known) samples from the first n signatures to the lattice until key recovery succeeded.  ...  i | 2 ≤ iγ [Sch92] , where γ k is the Hermite constant.  ...

### Remote Timing Attacks Are Still Practical [chapter]

Billy Bob Brumley, Nicola Tuveri
2011 Lecture Notes in Computer Science
Using the timing of the exchanged messages, the messages themselves, and the signatures, we mount a lattice attack that recovers the private key.  ...  These attacks exploit cryptosystem or protocol implementations that do not run in constant time.  ...  Heap h=Heap.new(s); //fixed size=s from 1 to t: Result res=sign_rtn(dgst, privk); if ( !  ...

### Anti-Quantum Lattice-Based Ring Signature Scheme and Applications in VANETs

Chunhong Jiao, Xinyin Xiang
2021 Entropy
In this paper, we propose an anti-quantum ring signature scheme based on lattice, functionality analysis, and performance evaluation to demonstrate that this scheme supports unconditional anonymity and  ...  After efficiency analysis, our scheme proved more effective than the existing ring signature schemes in processing signature generation and verification.  ...  A ring signature can hide the signer's identity from a group, which can better solve these issues.  ...

### NTRU modular lattice signature scheme on CUDA GPUs

Wei Dai, Berk Sunar, John Schanck, William Whyte, Zhenfei Zhang
2016 2016 International Conference on High Performance Computing & Simulation (HPCS)
In this work we show how to use Graphics Processing Units (GPUs) with Compute Unified Device Architecture (CUDA) to accelerate a lattice based signature scheme, namely, the NTRU modular lattice signature  ...  In addition, similar to most lattice based signature schemes, NTRU-MLS provides transcript security with a rejection sampling technique.  ...  However, lattice based signature schemes naturally have large signature sizes compared to RSA and ECC based solutions.  ...

### Lattice-Based Group Signature Scheme with Verifier-Local Revocation [chapter]

Adeline Langlois, San Ling, Khoa Nguyen, Huaxiong Wang
2014 Lecture Notes in Computer Science
In this work, we introduce the first lattice-based VLR group signature, and thus, the first such scheme that is believed to be quantum-resistant.  ...  In comparison with existing lattice-based group signatures, our scheme has several noticeable advantages: support of membership revocation, logarithmicsize signatures, and weaker security assumption.  ...  [23] designed a scheme featuring signature size O(log N ), which is the first lattice-based group signature that overcomes the linear-size barrier.  ...

### The Singular Theta Correspondence, Lorentzian Lattices and Borcherds-Kac-Moody Algebras [article]

Alex Barnard
2003 arXiv   pre-print
In the case of elementary lattices, we show that these vector-valued forms can be obtained by inducing scalar-valued forms.  ...  This allows us to explain the critical signatures which occur in Borcherds' work.  ...  = 1; \\ Matrix to hold genus information genus=matrix(100,3); genus[size,1] = 7; genus[size,2] = 1; genus[size,3] = +5; size++; \\ Matrix to hold vector in L*/L vec=matrix(100,2); vec[1,1] = 1/3; vec[  ...

### Size effects in the electronic properties of finite arrays of exchange coupled quantum dots: A renormalization group approach [article]

Jiaxiang Wang, Sabre Kais, F. Remacle, R. D. Levine
2004 arXiv   pre-print
A first order phase transition occurs upon compression of the lattice and the size dependence is qualitatively different for the two phases.  ...  The discussion uses a multi-stage block renormalization group approach applied to the Hubbard Hamiltonian.  ...  In the (albeit, approximate) real space group renormalization procedure that we use the only way that the size of the original array comes in is in the value of the renormalized coupling constants.  ...

### Better Zero-Knowledge Proofs for Lattice Encryption and Their Application to Group Signatures [chapter]

Fabrice Benhamouda, Jan Camenisch, Stephan Krenn, Vadim Lyubashevsky, Gregory Neven
2014 Lecture Notes in Computer Science
However, the constructions known for more sophisticated schemes such as group signatures are still far from being practical.  ...  Finally, we make use of this to construct a new group signature scheme that is a "hybrid" in the sense that privacy holds under a lattice-based assumption while security is discrete-logarithm-based.  ...  This is in contrast to classical number-theoretic solutions, where both the key and the signature size are constant for arbitrarily many group members.  ...
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