Fast batch verification for modular exponentiation and digital signatures. (English) Zbl 0929.68053

Nyberg, Kaisa (ed.), Advances in Cryptology. International conference on the Theory and application of cryptographic techniques. Espoo, Finland, May 31 - June 4, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1403, 236-250 (1998).
Summary: Many tasks in cryptography (e.g., digital signature verification) call for verification of a basic operation like modular exponentiation in some group: given \((g,x,y)\) check that \(g^x=y\). This is typically done by re-computing \(g^x\) and checking we get \(y\). We would like to do it differently, and faster.
The approach we use is batching. Focusing first on the basic modular exponentiation operation, we provide some probabilistic batch verifiers, or tests, that verify a sequence of modular exponentiations significantly faster than the naive re-computation method. This yields speedups for several verification tasks that involve modular exponentiations.
Focusing specifically on digital signatures, we then suggest a weaker notion of (batch) verification which we call “screening.” It seems useful for many usages of signatures, and has the advantage that it can be done very fast; in particular, we show how to screen a sequence of RSA signatures at the cost of one RSA verification plus hashing.
For the entire collection see [Zbl 0889.00042].


68P25 Data encryption (aspects in computer science)
94A60 Cryptography
11Y16 Number-theoretic algorithms; complexity