How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
The notion of security for probabilistic cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Inferring sequences produced by pseudo-random number generators
Journal of the ACM (JACM)
Public-key cryptosystems provably secure against chosen ciphertext attacks
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
SIAM Journal on Computing
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
"Pseudo-Random" Number Generation Within Cryptographic Algorithms: The DDS Case
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Relations Among Notions of Security for Public-Key Encryption Schemes
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
On the Security of ElGamal Based Encryption
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
A New Aspect for Security Notions: Secure Randomness in Public-Key Encryption Schemes
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Secret linear congruential generators are not cryptographically secure
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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In this paper, we consider what condition is sufficient for random inputs to secure probabilistic public-key encryption schemes. Although a framework given in [16] enables us to discuss uniformly and comprehensively security notions of public-key encryption schemes even for the case where cryptographically weak pseudorandom generator is used as random nonce generator to encrypt single plaintext messages, the results are rather theoretical. Here we naturally generalize the framework in order to handle security for the situation where we want to encrypt many messages with the same key. We extend some results w.r.t. single message security in [16] - separation results between security notions and a non-trivial sufficient condition for the equivalence between security notions - to multiple messages security. Besides the generalization, we show another separation between security notions for k-tuple messages and for (k+1)-tuple messages. The natural generalization, obtained here, rather improves to understand the security of public-key encryption schemes and eases the discussion of the security of practical public-key encryption schemes. In other words, the framework contributes to elucidating the role of randomness in public-key encryption scheme. As application of results in the generalized framework, we consider compatibility between the ElGamal encryption scheme and some sequence generators. Especially, we consider the applicability of the linear congruential generator (LCG) to the ElGamal encryption scheme.