Fast software implementations of bilinear pairings, IEEE Trans. Dependable Sec. Comput, vol.14, issue.6, 2017. ,
Improved proxy re-encryption schemes with applications to secure distributed storage, ACM Trans. Inf. Syst. Secur, vol.9, issue.1, 2006. ,
,
Implementing pairings at the 192-bit security level, Pairing-Based Cryptography -Pairing 2012 -5th International Conference, vol.3152, pp.177-195, 2004. ,
DOI : 10.1007/978-3-642-36334-4_11
URL : https://eprint.iacr.org/2012/232.pdf
Subgroup security in pairing-based cryptography, BD18. Razvan Barbulescu and Sylvain Duquesne, vol.9230, 2015. ,
A variant of Miller's formula and algorithm, Pairing, vol.6487, p.1, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01083368
Identity-based encryption from the Weil pairing, Advances in Cryptology -CRYPTO, vol.2139, 2001. ,
High-speed software implementation of the optimal Ate pairing over Barreto-Naehrig curves, Pairing-Based Cryptography -Pairing, vol.6487, 2010. ,
Improving NFS for the discrete logarithm problem in non-prime finite fields, Advances in CryptologyEurocrypt, vol.9056, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01112879
A heuristic quasipolynomial algorithm for discrete logarithm in finite fields of small characteristic, BGK15. Razvan Barbulescu, Pierrick Gaudry, and Thorsten Kleinjung. The Towed Number Field Sieve, vol.8441, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00835446
Aggregate and verifiably encrypted signatures from bilinear maps, Advances in Cryptology -Eurocrypt, vol.2656, 2003. ,
Collusion resistant broadcast encryption with short ciphertexts and private keys, Advances in Cryptology -CRYPTO 2005, vol.3621, 2005. ,
Multi-core implementation of the Tate pairing over supersingular elliptic curves, Cryptology and Network Security -CANS 2009, vol.5888, 2009. ,
Constructing elliptic curves with prescribed embedding degrees, Security in Communication Networks, 2002. ,
Short signatures from the Weil pairing, J. of Cryptology, vol.17, issue.4, 2004. ,
Pairing-friendly elliptic curves of prime order, Selected Areas in Cryptography -SAC 2005, 1999. ,
BlindIDS: Market-compliant and privacy-friendly intrusion detection system over encrypted traffic, Asia Conference on Computer and Communications Security. ACM, 2017. Cha08. Steve Chang. Trend micro, 2008. ,
Faster hashing to G2, Selected Areas in Cryptography -SAC 2011, vol.2259, 2011. ,
Faster pairing computations on curves with high-degree twists, Public Key Cryptography -PKC 2010, vol.6056, 2010. ,
Special polynomial families for generating more suitable elliptic curves for pairing-based cryptosystems, The 5th WSEAS International Conference on Electronics, Hardware, Wireless and Optimal Communications, 2005. ,
Choosing and generating parameters for low level pairing implementation on BN curves, Appl. Algebra Eng. Commun. Comput, vol.29, issue.2, 2018. ,
Memory-saving computation of the pairing final exponentiation on BN curves, Groups Complexity Cryptology, vol.8, issue.1, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01317398
Estimating size requirements for pairings: Simulating the tower-NFS algorithm in GF, 2017. ,
On constructing families of pairing-friendly elliptic curves with variable discriminant, Progress in cryptology -INDOCRYPT 2011, vol.7107, 2011. ,
Implementing cryptographic pairings over Barreto-Naehrig curves, Pairing-Based Cryptography -Pairing, vol.4575, 2007. ,
European Union Agency of Network and Information Security (ENISA). Algorithms, key sizes and parameters report, Progress in Cryptology -AFRICACRYPT 2011, vol.6737, 2011. ,
2018. FM18. Georgios Fotiadis and Chloe Martindale. Optimal tnfs-secure pairings on elliptic curves with even embedding degree, Journal of Mathematical Cryptology, vol.12, issue.2, 2018. ,
Computing optimal ate pairings on elliptic curves with embedding degree 9, 15 and 27. IACR Cryptology ePrint Archive, p.10, 2016. ,
A taxonomy of pairing-friendly elliptic curves, J. of Cryptology, vol.23, issue.2, 2010. ,
Efficient implementation of bilinear pairings on ARM processors, Selected Areas in Cryptography -SAC 2012, vol.7707, 2012. ,
Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation, Arithmetic of Finite Fields -WAIFI 2016, vol.1, 2016. ,
A comparison of pairing-friendly curves at the 192-bit security level, 2019. ,
Pairing lattices. In Pairing-based cryptography -Pairing, Lecture Notes in Computer Science, vol.5209, 2008. ,
The Eta pairing revisited, IEEE Trans. Information Theory, vol.52, issue.10, 2006. ,
Extended tower number field sieve with application to finite fields of arbitrary composite extension degree, vol.526, 2016. ,
The number field sieve in the medium prime case, Advances in Cryptology -CRYPTO 2006, vol.4117, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-01102034
Identity-Based Cryptography, Cryptology and Information Security Series, vol.2, 2009. ,
A one round protocol for tripartite Diffie-Hellman, Algorithmic Number Theory (ANTS-IV), vol.1838, 2000. ,
The special number field sieve in Fpn -application to pairing-friendly constructions, Pairing-Based Cryptography -Pairing, vol.8365, 2013. ,
On polynomial selection for the general number field sieve, Math. Comp, vol.75, issue.256, 2006. ,
Polynomial selection, CADO workshop on integer factorization, INRIA Nancy, 2008. ,
Pairing-based cryptography at high security levels, IMA Int. Conf., volume, vol.3796, 2005. ,
Efficient optimal ate pairing at 128-bit security level, Progress in Cryptology -INDOCRYPT 2017, vol.10698, p.8, 1997. ,
Constructing Brezing-Weng pairingfriendly elliptic curves using elements in the cyclotomic field, Pairing-Based CryptographyPairing, 2008. ,
On the near prime-order mnt curves. Applicable Algebra in Engineering, vol.30, 2019. ,
DOI : 10.1007/s00200-018-0363-1
URL : http://arxiv.org/pdf/1806.02536
Unbelievable security: Matching AES security using public key systems, Advances in cryptology -ASIACRYPT, vol.2248, 2001. ,
Factoring polynomials with rational coefficients, Mathematische Annalen, vol.261, issue.4, 1982. ,
DOI : 10.1007/bf01457454
Computing the ate pairing on elliptic curves with embedding degree k= 9, IEICE Transactions on Fundamentals of Electronics, vol.91, issue.9, 2008. ,
Effective version of the number field sieve for discrete logarithm in a field GF (p k ), Trudy po Diskretnoi Matematike, issue.9, 2006. ,
, , 2011.
A study of pairing computation for elliptic curves with embedding degree 15, IACR Cryptology ePrint Archive, p.370, 2009. ,
Characterization of elliptic curve traces under FR-reduction, ICISC, vol.17, 2000. ,
Building cyclic elliptic curves modulo large primes, Advances in Cryptology -Eurocrypt 91, vol.547, 1991. ,
DOI : 10.1007/3-540-46416-6_28
URL : https://link.springer.com/content/pdf/10.1007%2F3-540-46416-6_28.pdf
Challenges with assessing the impact of NFS advances on the security of pairing-based cryptography, Paradigms in CryptologyMycrypt, vol.10311, 2016. ,
Compressed pairings, CRYPTO, vol.3152, 2004. ,
DOI : 10.1007/978-3-540-28628-8_9
URL : https://link.springer.com/content/pdf/10.1007%2F978-3-540-28628-8_9.pdf
,
On the final exponentiation for calculating pairings on ordinary elliptic curves, Pairing-Based Cryptography -Pairing, 2009. ,
A new family of pairing-friendly elliptic curves, Finite Fields arithmetic -WAIFI 2018, 2018. ,
DOI : 10.1007/978-3-030-05153-2_2
URL : https://hal.archives-ouvertes.fr/hal-01875361
Privacy Enhancing Protocols using Pairing Based Cryptography, 2010. ,
Blindbox: Deep packet inspection over encrypted traffic, ACM SIGCOMM Computer communication review, vol.45, issue.4, 2015. ,
Fine tuning the function field sieve algorithm for the medium prime case, IEEE Transactions on Information Theory, vol.62, issue.4, 2016. ,
DOI : 10.1109/tit.2016.2528996
A generalisation of the conjugation method for polynomial selection for the extended tower number field sieve algorithm. Cryptology ePrint Archive, SS16c. Palash Sarkar and Shashank Singh, vol.9665, 2016. ,
Practical attack on bilinear pairings to disclose the secrets of embedded devices, 2014 Ninth International Conference on Availability, Reliability and Security, 1962. ,
Optimal pairings, IEEE Trans. Information Theory, vol.56, issue.1 ,
DOI : 10.1109/tit.2009.2034881
Sur les fonctions algebriquesàalgebriquesà corps de constantes fini, Les Comptes rendus de l'Academie des sciences, vol.210, p.1940 ,
DOI : 10.1007/978-1-4757-1705-1_34
Analysis of optimum pairing products at high security levels, Progress in Cryptology -INDOCRYPT 2012, vol.7668, 2012. ,
Generating pairing-friendly elliptic curves using parameterized families, IEICE Transactions on Fundamentals of Electronics, vol.101, issue.1, 2018. ,