S. Aaronson and A. Wigderson, Algebrization: A new barrier in complexity theory, ACM Trans. Comput. Theory, vol.12, issue.1, pp.1-2, 2009.

E. Ábrahám, J. Abbott, B. Becker, A. M. Bigatti, M. Brain et al., SC 2 : Satisfiability checking meets symbolic computation, Michael Kohlhase

. Tompa, URL: https://members, Intelligent Computer Mathematics (CICM) Lecture Notes in Computer Science, vol.9791, pp.28-43, 2016.

S. Arora and S. Safra, Probabilistic checking of proofs; A new characterization of NP, 33rd Annual Symposium on Foundations of Computer Science, pp.2-13, 1992.

, Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018.

L. Babai, Trading group theory for randomness, Proceedings of the seventeenth annual ACM symposium on Theory of computing , STOC '85, pp.421-429
DOI : 10.1145/22145.22192

L. Babai, L. Fortnow, and C. Lund, Nondeterministic exponential time has two-prover interactive protocols, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, pp.16-25, 1990.
DOI : 10.1109/FSCS.1990.89520

E. Bangerter, J. Camenisch, and U. M. Maurer, Efficient Proofs of Knowledge of Discrete Logarithms and Representations in Groups with Hidden Order, Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography, PKC'05, pp.154-171, 2005.
DOI : 10.1007/978-3-540-30580-4_11

W. Paul, S. A. Beame, H. J. Cook, and . Hoover, Log depth circuits for division and related problems, SIAM J. Comput, vol.15, pp.994-1003, 1986.

M. Bellare and P. Rogaway, Random oracles are practical, Proceedings of the 1st ACM conference on Computer and communications security , CCS '93, pp.62-73, 1993.
DOI : 10.1145/168588.168596

E. Ben-sasson, I. Bentov, A. Chiesa, A. Gabizon, D. Genkin et al., Computational Integrity with a Public Random String from Quasi-Linear PCPs, Advances in Cryptology -EUROCRYPT 2017 -36th Annual International Conference on the Theory and Applications of Cryptographic Techniques Proceedings , Part III, pp.551-579978, 2017.
DOI : 10.1145/2641562

E. Ben-sasson, I. Bentov, Y. Horesh, and M. Riabzev, Scalable, transparent, and post-quantum secure computational integrity, Cryptology ePrint Archive, p.46, 2018.

M. Blum and S. Kannan, Designing programs that check their work, Journal of the ACM, vol.42, issue.1, pp.269-291, 1995.
DOI : 10.1145/200836.200880

J. Bootle, A. Cerulli, P. Chaidos, J. Groth, and C. Petit, Efficient Zero-Knowledge Arguments for Arithmetic Circuits in the Discrete Log Setting, Advances in Cryptology -EUROCRYPT 2016 -35th Annual International Conference on the Theory and Applications of Cryptographic Techniques Proceedings, Part II, pp.327-357, 2016.
DOI : 10.1007/978-3-662-49896-5_12

. Springer, URL: https, pp.978-981, 2016.

B. Bünz, J. Bootle, D. Boneh, A. Poelstra, P. Wuille et al., Bulletproofs: Short proofs for confidential transactions and more, IEEE Symposium on Security and Privacy (SP), pp.319-338, 2018.

S. Cristian, D. Calude, and . Thompson, Incompleteness, undecidability and automated proofs

E. V. Seiler and . Vorozhtsov, Computer Algebra in Scientific Computing, pp.134-155

F. Chyzak, A. Mahboubi, T. Sibut-pinote, and E. Tassi, A Computer-Algebra-Based Formal Proof of the Irrationality of ?(3), ITP -5th International Conference on Interactive Theorem Proving
URL : https://hal.archives-ouvertes.fr/hal-00984057

R. Cramer, I. Damgård, and J. B. Nielsen, Multiparty computation from threshold homomorphic encryption, Advances in Cryptology ? EUROCRYPT 2001: International Conference on the Theory and Application of Cryptographic Techniques Innsbruck, Austria Proceedings, pp.280-30010, 2001.

A. Richard, R. J. Demillo, and . Lipton, A probabilistic remark on algebraic program testing, Inf. Process. Letters, vol.7, issue.478, pp.193-19590067, 1978.

J. Dumas, P. Giorgi, P. Elbaz-vincent, and A. Urba?ska, Parallel computation of the rank of large sparse matrices from algebraic K-theory, Proceedings of the 2007 international workshop on Parallel symbolic computation, PASCO '07, pp.43-52, 2007.
DOI : 10.1145/1278177.1278186
URL : https://hal.archives-ouvertes.fr/hal-00142141

J. Dumas and E. Kaltofen, Essentially optimal interactive certificates in linear algebra, Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ISSAC '14, pp.146-153
DOI : 10.1145/2608628.2608644
URL : https://hal.archives-ouvertes.fr/hal-00932846

J. Dumas, E. Kaltofen, and E. Thomé, Interactive certificate for the verification of Wiedemann's Krylov sequence: application to the certification of the determinant, the minimal and the characteristic polynomials of sparse matrices, 2016.

J. Dumas, E. Kaltofen, E. Thomé, and G. Villard, Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16, pp.199-206
DOI : 10.1007/3-540-09519-5_73
URL : https://hal.archives-ouvertes.fr/hal-01266041

J. Dumas, E. Kaltofen, G. Villard, and L. Zhi, Polynomial time interactive proofs for linear algebra with exponential matrix dimensions and scalars given by polynomial time circuits URL: http://ljk.imag, In Safey El Din, vol.52, pp.125-132

J. Dumas, D. Lucas, and C. Pernet, Certificates for Triangular Equivalence and Rank Profiles, Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation , ISSAC '17, pp.133-140
DOI : 10.1145/2755996.2756672
URL : https://hal.archives-ouvertes.fr/hal-01466093

J. Dumas and V. Zucca, Prover Efficient Public Verification of Dense or Sparse/Structured Matrix-Vector Multiplication, ACISP 2017, 22nd Australasian Conference on Information Security and Privacy, pp.115-134, 2017.
DOI : 10.1007/978-3-319-13257-0_10
URL : https://hal.archives-ouvertes.fr/hal-01503870

W. Eberly, A new interactive certificate for matrix rank URL: http:// prism.ucalgary.ca/bitstream, pp.2015-1078, 1880.

W. Eberly, Selecting Algorithms for Black Box Matrices, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16
DOI : 10.1007/978-3-642-57201-2_30

K. Elkhiyaoui, M. Önen, M. Azraoui, and R. Molva, Efficient Techniques for Publicly Verifiable Delegation of Computation, Proceedings of the 11th ACM on Asia Conference on Computer and Communications Security, ASIA CCS '16, pp.119-128
DOI : 10.1109/SP.2013.47

A. Fiat and A. Shamir, How To Prove Yourself: Practical Solutions to Identification and Signature Problems, Lecture Notes in Computer Science, vol.263, pp.186-194, 1986.
DOI : 10.1007/3-540-47721-7_12

D. Fiore, C. Fournet, E. Ghosh, M. Kohlweiss, O. Ohrimenko et al., Hash First, Argue Later, Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, CCS'16, pp.1304-1316, 2016.
DOI : 10.14722/ndss.2015.23097

D. Fiore and R. Gennaro, Publicly verifiable delegation of large polynomials and matrix computations, with applications, Proceedings of the 2012 ACM conference on Computer and communications security, CCS '12, pp.501-512
DOI : 10.1145/2382196.2382250

R. Freivalds, Fast probabilistic algorithms, Mathematical Foundations of Computer Science, pp.57-69, 1979.
DOI : 10.1007/3-540-09526-8_5

M. Furer, O. Goldreich, Y. Mansour, M. Sipser, and S. Zachos, On completeness and soundness in interactive proof systems Advances in Computing Research, pp.429-442, 1989.

X. Gao, Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation, 2016.

L. G?sieniec, C. Levcopoulos, A. Lingas, R. Pagh, and T. Tokuyama, Efficiently correcting matrix products. Algorithmica, pp.1-1610, 2016.

C. Gentry, J. Groth, Y. Ishai, C. Peikert, A. Sahai et al., Using Fully Homomorphic Hybrid Encryption to Minimize Non-interative Zero-Knowledge Proofs, Journal of Cryptology, vol.28, issue.4, pp.1-24, 2014.
DOI : 10.1145/100216.100269

P. Giorgi and V. Neiger, Certification of Minimal Approximant Bases, Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation , ISSAC '18
DOI : 10.1007/3-540-09519-5_73
URL : https://hal.archives-ouvertes.fr/hal-01701861

S. Goldwasser, Y. T. Kalai, and G. N. Rothblum, Delegating computation: interactive proofs for muggles, Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp.113-122, 2008.

S. Goldwasser, S. Micali, and C. Rackoff, The knowledge complexity of interactive proof-systems, Sedgewick [54], pp.291-304

E. Kaltofen and B. Trager, Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, pp.301-320, 1990.
DOI : 10.1109/SFCS.1988.21946

E. Kaltofen, Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems, Mathematics of Computation, vol.64, issue.210, pp.777-80610, 1995.

E. Kaltofen and C. Pernet, Sparse polynomial interpolation codes and their decoding beyond half the minimum distance, Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ISSAC '14
DOI : 10.1145/2608628.2608660

E. L. Kaltofen, M. Nehring, and B. Saunders, Quadratictime certificates in linear algebra, Proceedings of the 2011 ACM International Symposium on Symbolic and Algebraic Computation, pp.171-176, 2011.

T. Kimbrel and R. Sinha, A probabilistic algorithm for verifying matrix products using O(n 2 ) time and log 2 n + O(1) random bits, Information Processing Letters, vol.4508, issue.2, pp.107-110, 1991.

C. Lund, L. Fortnow, H. Karloff, and N. Nisan, Algebraic methods for interactive proof systems, Journal of the ACM, vol.39, issue.4, pp.859-868, 1992.
DOI : 10.1145/146585.146605

, Proceedings of the 2014 ACM International Symposium on Symbolic and Algebraic Computation, 2014.

E. W. Ng, International Symposium on Symbolic and Algebraic Computation Proceedings, 1979.

B. Parno, J. Howell, C. Gentry, and M. Raykova, Pinocchio, Proceedings of the 2013 IEEE Symposium on Security and Privacy, SP '13, pp.238-252
DOI : 10.1007/978-1-4614-1460-5

B. Parno, M. Raykova, and V. Vaikuntanathan, How to Delegate and Verify in Public: Verifiable Computation from Attribute-Based Encryption, Theory of Cryptography: 9th Theory of Cryptography Conference, pp.422-43910, 2012.
DOI : 10.1007/978-3-642-28914-9_24

O. Reingold, G. N. Rothblum, and R. D. Rothblum, Constantround interactive proofs for delegating computation, Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, pp.49-62, 2016.
DOI : 10.1145/2897518.2897652

D. Roche, Error Correction in Fast Matrix Multiplication and Inverse, Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation , ISSAC '18
DOI : 10.1145/1077464.1077466

, Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, 2017.

J. T. Schwartz, Probabilistic algorithms for verification of polynomial identities, pp.200-215
DOI : 10.1007/3-540-09519-5_72

, STOC '85, ACM Symposium on Theory of Computing, 1985.

A. Shamir, . Ip, and . Pspace, IP = PSPACE, Journal of the ACM, vol.39, issue.4, pp.869-877, 1992.
DOI : 10.1145/146585.146609

A. Storjohann, Integer matrix rank certification URL: https, Proceedings of the 2009 ACM International Symposium on Symbolic and Algebraic Computation, pp.333-340, 2009.
DOI : 10.1145/1576702.1576748

J. Thaler, Time-Optimal Interactive Proofs for Circuit Evaluation, Lecture Notes in Computer Science, vol.8043, pp.71-89, 2013.
DOI : 10.1007/978-3-642-40084-1_5
URL : https://link.springer.com/content/pdf/10.1007%2F978-3-642-40084-1_5.pdf

M. Walfish and A. J. Blumberg, Verifying computations without reexecuting them, Communications of the ACM, vol.58, issue.2, pp.74-8410, 2015.
DOI : 10.14722/ndss.2015.23097
URL : http://dl.acm.org/ft_gateway.cfm?id=2641562&type=pdf

H. Douglas and . Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, vol.32, issue.1, pp.54-62, 1986.

Y. Zhang and M. Blanton-camenisch, Efficient Secure and Verifiable Outsourcing of Matrix Multiplications, Information Security, pp.158-178, 2014.
DOI : 10.1007/978-3-319-13257-0_10

R. Zippel, Probabilistic algorithms for sparse polynomials, Ng [47], pp.216-226
DOI : 10.1007/3-540-09519-5_73