There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on the Weil pairing. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.

/pdf/identity-based-encryption-from-the-weil-pairing-sfqdyadlbb.pdf

Identity-Based Encryption from the Weil Pairing

This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to public-key cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.

/pdf/public-key-cryptosystems-based-on-composite-degree-1zopwb21ba.pdf

Public-key cryptosystems based on composite degree residuosity classes

We propose a fully functional identity-based encryption (IBE) scheme. The scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational Diffie--Hellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure IBE schemes and give several applications for such systems.

/pdf/identity-based-encryption-from-the-weil-pairing-1x4254f2zc.pdf

We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.

/pdf/short-signatures-from-the-weil-pairing-5ajupg0cpi.pdf

Short Signatures from the Weil Pairing

We show that the decisional version of the Ko-Lee assumption for braid groups put forward by Lee, Lee and Hahn at Crypto 2001 is false, by giving an efficient algorithm that solves (with high probability) the corresponding decisional problem. Our attack immediately applies to the pseudo-random generator and synthesizer proposed by the same authors based on the decisional Ko-Lee assumption, and shows that neither of them is cryptographically secure.

/pdf/cryptanalysis-of-a-pseudorandom-generator-based-on-braid-118h82ynw5.pdf

Cryptanalysis of a Pseudorandom Generator Based on Braid Groups

This paper initiates a study of Fine Grained Secure Computation: i.e. the construction of secure computation primitives against “moderately complex” adversaries. We present definitions and constructions for compact Fully Homomorphic Encryption and Verifiable Computation secure against (non-uniform) \(\mathsf {NC}^1\) adversaries. Our results do not require the existence of one-way functions and hold under a widely believed separation assumption, namely \(\mathsf {NC}^{1}\subsetneq \oplus \mathsf {L}/ {\mathsf {poly}}\). We also present two application scenarios for our model: (i) hardware chips that prove their own correctness, and (ii) protocols against rational adversaries potentially relevant to the Verifier’s Dilemma in smart-contracts transactions such as Ethereum.

Fine-Grained Secure Computation

In this paper we explore pseudo-random number generation on the IBM 4758 Secure Crypto Coprocessor. In particular we compare several variants of Gennaro's provably secure generator, proposed at Crypto 2000, with more standard techniques based on the SHA-1 compression function. Our results show how the presence of hardware support for modular multiplication and exponentiation affects these algorithms.

/pdf/pseudo-random-number-generation-on-the-ibm-4758-secure-527j55zmqa.pdf

Pseudo-random Number Generation on the IBM 4758 Secure Crypto Coprocessor

Fine-Grained Secure Computation.

This paper presents the Generalized Randomized Iterate of a (regular) one-way function f and show that it can be used to build Universal One-Way Hash Function (UOWHF) families with O(n2) key length.

We then show that Shoup's technique for UOWHF domain extension can be used to improve the efficiency of the previous construction. We present the Reusable Generalized Randomized Iterate which consists of k≥n+1 iterations of a regular one-way function composed at each iteration with a pairwise independent hash function, where we only use logk such hash functions, and we "schedule" them according to the same scheduling of Shoup's domain extension technique. The end result is a UOWHF construction from regular one-way functions with an O(n logn) key. These are the first such efficient constructions of UOWHF from regular one-way functions of unknown regularity.

Finally we show that the Shoup's domain extension technique can also be used in lieu of derandomization techniques to improve the efficiency of PRGs and of hardness amplification constructions for regular one-way functions.

/pdf/the-generalized-randomized-iterate-and-its-application-to-5afdkl9cf6.pdf

Rosario Gennaro

Papers

Cryptanalysis of a Pseudorandom Generator Based on Braid Groups

Fine-Grained Secure Computation

Pseudo-random Number Generation on the IBM 4758 Secure Crypto Coprocessor

Fine-Grained Secure Computation.

the generalized randomized iterate and its application to new efficient constructions of UOWHFs from regular one-way functions