updated references

README.md

@@ -159,41 +159,13 @@ If you want to contribute to Lattigo, have a feature proposal or request, to rep
 Please use the following BibTex entry for citing Lattigo:
 
     @misc{lattigo,
-	    title = {Lattigo v4},
+	    title = {Lattigo v5},
 	    howpublished = {Online: \url{https://github.com/tuneinsight/lattigo}},
-	    month = Aug,
-	    year = 2022,
+	    month = Nov,
+	    year = 2023,
 	    note = {EPFL-LDS, Tune Insight SA}
     }
     
-## References
-
-1. Efficient Bootstrapping for Approximate Homomorphic Encryption with Non-Sparse Keys
-   (<https://eprint.iacr.org/2020/1203>)
-1. Bootstrapping for Approximate Homomorphic Encryption with Negligible Failure-Probability by Using Sparse-Secret Encapsulation
-   (<https://eprint.iacr.org/2022/024>)
-1. Somewhat Practical Fully Homomorphic Encryption (<https://eprint.iacr.org/2012/144>)
-1. Multiparty Homomorphic Encryption from Ring-Learning-With-Errors (<https://eprint.iacr.org/2020/304>)
-2. An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption (<https://eprint.iacr.org/2022/780>)
-3. A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes
-   (<https://eprint.iacr.org/2016/510>)
-4. An Improved RNS Variant of the BFV Homomorphic Encryption Scheme
-   (<https://eprint.iacr.org/2018/117>)
-5. Homomorphic Encryption for Arithmetic of Approximate Numbers (<https://eprint.iacr.org/2016/421>)
-6. A Full RNS Variant of Approximate Homomorphic Encryption (<https://eprint.iacr.org/2018/931>)
-7. Improved Bootstrapping for Approximate Homomorphic Encryption
-1. Fully Homomorphic Encryption without Bootstrapping (<https://eprint.iacr.org/2011/277>)     
-1. Homomorphic Encryption for Arithmetic of Approximate Numbers (<https://eprint.iacr.org/2016/421>)
-1. A Full RNS Variant of Approximate Homomorphic Encryption (<https://eprint.iacr.org/2018/931>)
-1. Improved Bootstrapping for Approximate Homomorphic Encryption
-   (<https://eprint.iacr.org/2018/1043>)
-8. Better Bootstrapping for Approximate Homomorphic Encryption (<https://eprint.iacr.org/2019/688>)
-9.  Post-quantum key exchange - a new hope (<https://eprint.iacr.org/2015/1092>)
-10. Faster arithmetic for number-theoretic transforms (<https://arxiv.org/abs/1205.2926>)
-11. Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography
-   (<https://eprint.iacr.org/2016/504>)
-12. Gaussian sampling in lattice-based cryptography
-   (<https://tel.archives-ouvertes.fr/tel-01245066v2>)
 
 The Lattigo logo is a lattice-based version of the original Golang mascot by [Renee
 French](http://reneefrench.blogspot.com/).

core/rlwe/README.md

@@ -0,0 +1,6 @@
+## References
+
+1. Somewhat Practical Fully Homomorphic Encryption (<https://eprint.iacr.org/2012/144>)
+2. Fully Homomorphic Encryption without Bootstrapping (<https://eprint.iacr.org/2011/277>)
+3. Efficient Homomorphic Conversion Between (Ring) LWE Ciphertexts (<https://eprint.iacr.org/2020/015>)
+4. HERMES: Efficient Ring Packing using MLWE Ciphertexts and Application to Transciphering (<https://eprint.iacr.org/2023/1244>)

he/hebin/README.md

@@ -0,0 +1,3 @@
+## References
+
+1. Efficient FHEW Bootstrapping with Small Evaluation Keys, and Applications to Threshold Homomorphic Encryption (<https://eprint.iacr.org/2022/198>)

he/hefloat/README.md

@@ -0,0 +1,3 @@
+## References
+
+1. Minimax Approximation of Sign Function by Composite Polynomial for Homomorphic Comparison (<https://ieeexplore.ieee.org/abstract/document/9517029>)

he/hefloat/bootstrapping/README.md

@@ -0,0 +1,11 @@
+## References
+
+1. Bootstrapping for Approximate Homomorphic Encryption (<https://eprint.iacr.org/2018/153>)
+2. Improved Bootstrapping for Approximate Homomorphic Encryption (<https://eprint.iacr.org/2018/1043>)
+3. Better Bootstrapping for Approximate Homomorphic Encryption (<https://eprint.iacr.org/2019/688>)
+4. Faster Homomorphic Discrete Fourier Transforms and Improved FHE Bootstrapping (<https://eprint.iacr.org/2018/1073>)
+5. Efficient Bootstrapping for Approximate Homomorphic Encryption with Non-Sparse Keys (<https://eprint.iacr.org/2020/1203>)
+6. High-Precision Bootstrapping for Approximate Homomorphic Encryption by Error Variance Minimization (<https://eprint.iacr.org/2020/1549>)
+7. High-Precision Bootstrapping of RNS-CKKS Homomorphic Encryption Using Optimal Minimax Polynomial Approximation and Inverse Sine Function (<https://eprint.iacr.org/2020/552>)
+8. Bootstrapping for Approximate Homomorphic Encryption with Negligible Failure-Probability by Using Sparse-Secret Encapsulation (<https://eprint.iacr.org/2022/024>)
+9. META-BTS: Bootstrapping Precision Beyond the Limit (<https://eprint.iacr.org/2022/1167>)

mhe/README.md

@@ -165,3 +165,7 @@ While both protocol variants have slightly different local operations, their ste
 ##### 2.iii.b Decryption
 Once the receivers have obtained the ciphertext re-encrypted under their respective keys, they can use the usual decryption algorithm of the single-party scheme to obtain the plaintext result (see [rlwe.Decryptor](../rlwe/decryptor.go).
 
+## References
+
+1. Multiparty Homomorphic Encryption from Ring-Learning-With-Errors (<https://eprint.iacr.org/2020/304>)
+2. An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption (<https://eprint.iacr.org/2022/780>)

ring/README.md

@@ -0,0 +1,6 @@
+## References
+
+1. Faster arithmetic for number-theoretic transforms (<https://arxiv.org/abs/1205.2926>)
+2. Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography (<https://eprint.iacr.org/2016/504>)
+3. Gaussian sampling in lattice-based cryptography (<https://tel.archives-ouvertes.fr/tel-01245066v2>)
+4. Post-quantum key exchange - a new hope (<https://eprint.iacr.org/2015/1092>)

schemes/bgv/README.md

@@ -53,3 +53,9 @@ The above change enables an implementation of the BGV scheme with an MSB encodin
 This unified scheme can also be seen as a variant of the BGV scheme with two tensoring operations:
 - The BGV-style tensoring with a noise growth proportional to the current noise
 - The BFV-style tensoring with a noise growth invariant to the current noise
+
+## References
+
+1. Practical Bootstrapping in Quasilinear Time (<https://eprint.iacr.org/2013/372>)
+2. A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes (<https://eprint.iacr.org/2016/510>)
+3. An Improved RNS Variant of the BFV Homomorphic Encryption Scheme (<https://eprint.iacr.org/2018/117>)

schemes/ckks/README.md

@@ -167,3 +167,11 @@ entropy, by modifying their distribution to {(1-p)/2, p, (1-p)/2}, for any p bet
 for p>>1/3 can result in low Hamming weight keys (*sparse* keys). *We recall that it has been shown
 that the security of sparse keys can be considerably lower than that of fully entropic keys, and the
 CKKS security parameters should be re-evaluated if sparse keys are used*.
+
+## References
+
+1. Homomorphic Encryption for Arithmetic of Approximate Numbers (<https://eprint.iacr.org/2016/421>)
+2. A Full RNS Variant of Approximate Homomorphic Encryption (<https://eprint.iacr.org/2018/931>)
+3. Approximate Homomorphic Encryption over the Conjugate-invariant Ring (<https://eprint.iacr.org/2018/952>)
+4. Approximate Homomorphic Encryption with Reduced Approximation Error (<https://eprint.iacr.org/2020/1118>)
+5. On the precision loss in approximate homomorphic encryption (<https://eprint.iacr.org/2022/162>)