How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
An efficient probabilistic public key encryption scheme which hides all partial information
Proceedings of CRYPTO 84 on Advances in cryptology
On using RSA with low exponent in a public key network
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
On hiding information from an oracle
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
RSA and Rabin functions: certain parts are as hard as the whole
SIAM Journal on Computing - Special issue on cryptography
On the generation of cryptographically strong pseudorandom sequences
ACM Transactions on Computer Systems (TOCS)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Efficient, Perfect Random Number Generators
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Batch exponentiation: a fast DLP-based signature generation strategy
CCS '96 Proceedings of the 3rd ACM conference on Computer and communications security
Improved Digital Signature Suitable for Batch Verification
IEEE Transactions on Computers
Performance study of online batch-based digital signature schemes
Journal of Network and Computer Applications
Efficient query integrity for outsourced dynamic databases
Proceedings of the 2012 ACM Workshop on Cloud computing security workshop
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Number theoretic cryptographic algorithms are all based upon modular multiplication modulo some composite or prime. Some security parameter n is set (the length of the composite or prime). Cryptographic functions such as digital signature or key exchange require O(n) or O(驴n) modular multiplications ([DH, RSA, R, E, GMR, FS], etc.).This paper proposes a variant of the RSA scheme which requires only polylog(n) (O(log2 n)) modular multiplications per RSA operation. Inherent to the scheme is the idea of batching, i.e., performing several encryption or signature operations simultaneously. In practice, the new variant effectively performs several modular exponentiations at the cost of a single modular exponentiation. This leads to a very fast RSA-like scheme whenever RSA is to be performed at some central site or when pure-RSA encryption (vs. hybrid encryption) is to be performed.An important feature of the new scheme is a practical scheme that isolates the private key from the system, irrespective of the size of the system, the number of sites, or the number of private operations that need be performed.