Efficient Pseudorandom Generators Based on the DDH Assumption

“…Farashahi, Schoenmakers and Sidorenko [12] recently constructed pseudorandom number generators following a modified version of the ECRNG, which are secure as DDH over certain groups. This paper does not attempt to analyze the various issues surrounding entropy of the secret state of the RNG.…”

Section: Introductionmentioning

confidence: 99%

A Security Analysis of the NIST SP 800-90 Elliptic Curve Random Number Generator

Brown¹,

Gjøsteen

2007

Advances in Cryptology - CRYPTO 2007

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Abstract. An elliptic curve random number generator (ECRNG) has been approved in a NIST standard and proposed for ANSI and SECG draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional Diffie-Hellman problem and the hardness of two newer problems, the x-logarithm problem and the truncated point problem. The x-logarithm problem is shown to be hard if the decisional DiffieHellman problem is hard, although the reduction is not tight. The truncated point problem is shown to be solvable when the minimum amount of bits allowed in NIST standards are truncated, thereby making it insecure for applications such as stream ciphers. Nevertheless, it is argued that for nonce and key generation this distinguishability is harmless.

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“…Specify a cryptographically secure pseudorandom number generator (PRNG) [32,26,11] H : G T → Z * p . Generators u, v ∈ G 2 and a strongly unforgeable one-time signature scheme sig = (G, S, V).…”

Section: Our Schemementioning

confidence: 99%

Public key encryption with keyword search secure against keyword guessing attacks without random oracle

Fang

Susilo

et al. 2013

Information Sciences

195

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. Public key encryption with keyword search secure against keyword guessing attacks without random oracle. Information Sciences, 238 221-241.Public key encryption with keyword search secure against keyword guessing attacks without random oracle AbstractThe notion of public key encryption with keyword search (PEKS) was put forth by Boneh et al. to enable a server to search from a collection of encrypted emails given a "trapdoor" (i.e., an encrypted keyword) provided by the receiver. The nice property in this scheme allows the server to search for a keyword, given the trapdoor. Hence, the verifier can merely use an untrusted server, which makes this notion very practical. Following Boneh et al. 's work, there have been subsequent works that have been proposed to enhance this notion. Two important notions include the so-called keyword guessing attack and secure channel free, proposed by Byun et al. and Baek et al., respectively. The former realizes the fact that in practice, the space of the keywords used is very limited, while the latter considers the removal of secure channel between the receiver and the server to make PEKS practical. Unfortunately, the existing construction of PEKS secure against keyword guessing attack is only secure under the random oracle model, which does not reflect its security in the real world. Furthermore, there is no complete definition that captures secure channel free PEKS schemes that are secure against chosen keyword attack, chosen ciphertext attack, and against keyword guessing attacks, even though these notions seem to be the most practical application of PEKS primitives. In this paper, we make the following contributions. First, we define the strongest model of PEKS which is secure channel free and secure against chosen keyword attack, chosen ciphertext attack, and keyword guessing attack. In particular, we present two important security notions namely IND-SCF-CKCA and IND-KGA. The former is to capture an inside adversary, while the latter is to capture an outside adversary. Intuitively, it should be clear that IND-SCF-CKCA captures a more stringent attack compared to IND-KGA. Second, we present a secure channel free PEKS scheme secure without random oracle under the well known assumptions, namely DLP, DBDH, SXDH and truncated q-ABDHE assumption. Our contributions fill the gap in the literature and hence, making the notion of PEKS Keywords without, against, random, oracle, secure, encryption, key, public, guessing, search, keyword, attacks AbstractThe notion of public key encryption with keyword search (PEKS) was put forth by Boneh et al. to enable a server to search from a collection of encrypted emails given a "trapdoor" (i.e., an encrypted keyword) provided by the receiver. The nice property in this scheme allows the server to search for a keyword, given the trapdoor. Hence, the verifier can merely use an untrusted server, which makes this notion very practical. Following Boneh et al.'s work, there have been subsequent works that have been proposed to enhance this notion. T...

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Efficient Pseudorandom Generators Based on the DDH Assumption

Cited by 36 publications

References 25 publications

Indistinguishable of AES-Based PRNG against Modification Attack Based on Statistical Distance Tests and Entropy Measures

Indistinguishable of AES-Based PRNG against Modification Attack Based on Statistical Distance Tests and Entropy Measures

A Security Analysis of the NIST SP 800-90 Elliptic Curve Random Number Generator

Public key encryption with keyword search secure against keyword guessing attacks without random oracle

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