Batch Verification with Applications to Cryptography and Checking

Let R(·) be a polynomial time-computable boolean relation. Suppose we are given a sequence inst 1,..., inst n of instances and asked whether it is the case that R(inst i )=1 for all i=1,...,n. The naive way to figure out the answer is to compute R(inst i ) for each i and check that we get 1 each time. But this takes n computations of R. Can one do any better?

[1]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[2]  Baruch Awerbuch,et al.  Verifiable secret sharing and achieving simultaneity in the presence of faults , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[3]  Ernest F. Brickell,et al.  Secure Audio Teleconference , 1987, CRYPTO.

[4]  Matthijs J. Coster,et al.  Addition Chain Heuristics , 1989, CRYPTO.

[5]  Manuel Blum,et al.  Designing programs that check their work , 1989, STOC '89.

[6]  Manuel Blum,et al.  Self-testing/correcting with applications to numerical problems , 1990, STOC '90.

[7]  Kireeti Kompella,et al.  Fast Checkers for Cryptography , 1990, CRYPTO.

[8]  Ronitt Rubinfeld,et al.  Self-testing/correcting for polynomials and for approximate functions , 1991, STOC '91.

[9]  Manuel Blum,et al.  Checking the correctness of memories , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[10]  Yacov Yacobi,et al.  Batch Diffie-Hellman Key Agreement Systems and their Application to Portable Communications , 1992, EUROCRYPT.

[11]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[12]  Ronitt Rubinfeld.  Batch Checking with Applications to Linear Functions , 1992, Inf. Process. Lett..

[13]  Ernest F. Brickell,et al.  Fast Exponentiation with Precomputation (Extended Abstract) , 1992, EUROCRYPT.

[14]  Chae Hoon Lim,et al.  More Flexible Exponentiation with Precomputation , 1994, CRYPTO.

[15]  Ronitt Rubinfeld,et al.  On the robustness of functional equations , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[16]  David M'Raïhi,et al.  Can D.S.A. be Improved? Complexity Trade-Offs with the Digital Signature Standard , 1994, EUROCRYPT.

[17]  Mihir Bellare,et al.  Distributed pseudo-random bit generators—a new way to speed-up shared coin tossing , 1996, PODC '96.

[18]  Ronitt Rubinfeld,et al.  Approximate checking of polynomials and functional equations , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[19]  Ronitt Rubinfeld,et al.  Robust Characterizations of Polynomials with Applications to Program Testing , 1996, SIAM J. Comput..