# Advances in Cryptology — EUROCRYPT ’99

@inproceedings{Stern1999AdvancesIC, title={Advances in Cryptology — EUROCRYPT ’99}, author={Jacques Stern}, booktitle={Lecture Notes in Computer Science}, year={1999} }

We show that if the private exponent d used in the RSA public-key cryptosystem is less than N then the system is insecure. This is the first improvement over an old result of Wiener showing that when d < N the RSA system is insecure. We hope our approach can be used to eventually improve the bound to d < N.

## 814 Citations

### Provable Security against Impossible Differential Cryptanalysis Application to CS-Cipher

- Computer Science, MathematicsMCO
- 2008

A new way to bound the probability of occurrence of an n-round differential in the context of differential cryptanalysis is presented, to which, assuming some non-trivial hypothesis, provable security against impossible differential crypt analysis is obtained.

### Improved Cryptanalysis of the Multi-Prime φ - Hiding Assumption

- Mathematics, Computer ScienceAFRICACRYPT
- 2011

This paper investigates the Multi-Prime φ-Hiding Problem as introduced in a recent construction by Kiltz et al. from Crypto 2010 and makes use of a recent result from Herrmann and May to solve linear equations modulo divisors.

### RSA Vulnerabilities with Small Prime Difference

- Computer Science, MathematicsWEWoRC
- 2011

It is shown that the bound on small private key with respect to small prime difference can be further improved and the technique of unravelled linearization for constructing lattices is adapted and yield a benefit compared to known bounds.

### Algebraic Attack on the MQQ Public Key Cryptosystem

- Computer Science, MathematicsCANS
- 2009

This cryptanalysis breaks the MQQ cryptosystem by solving a system of multivariate quadratic polynomial equations using both the MutantXL algorithm and the F4 algorithm.

### Impossible Differential Cryptanalysis of ARIA Reduced to 7 Rounds

- Computer Science, MathematicsCANS
- 2010

This paper finds a new impossible differential property of ARIA, and proposes an attack against ARIA-256 reduced to 7 rounds based on this property, while previous attacks can only attack ARIA up to 6 rounds.

### Trapdoor Permutation Polynomials of Z/ n Z and Public Key Cryptosystems

- Computer Science, MathematicsISC
- 2007

It is shown that the ideas developed in this extended abstract can be used to design the most efficient known cryptosystem with semantic security under non-adaptive chosen ciphertext attacks in the standard security model.

### Digital Signatures from Strong RSA without Prime Generation

- Computer Science, MathematicsPublic Key Cryptography
- 2015

A signature scheme that is proved secure, without random oracles, under the strong RSA assumption, and adapts the prefix signing technique of Hohenberger and Waters (CRYPTO 2009) to work without generating primes.

### On the Differential Security of Multivariate Public Key Cryptosystems

- Computer Science, MathematicsPQCrypto
- 2011

This work presents a reasonable measure for security against the common differential attacks and derives this measurement for several modern multivariate public key cryptosystems.

### Partial Key Exposure Attacks on Takagi's Variant of RSA

- Mathematics, Computer ScienceACNS
- 2014

Three cases when the exposed bits are the most significant bits, the least significant bits and the middle bits of the private exponent respectively are considered, based on Coppersmith's method for finding small roots of modular polynomial equations.

### Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and lIC-Derivatives

- Computer Science, MathematicsPQCrypto
- 2008

We present instances of MPKCs (multivariate public key cryptosystems) with design, given the best attacks we know, and implement them on commodity PC hardware. We also show that they can hold their…

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