Greedy distinguishers and nonrandomness detectors
Author
Editor
- Guang Gong
- Kishan Chand Gupta
Summary, in English
We present the concept of greedy distinguishers and show how some simple observations and the well known greedy heuristic can be combined into a very powerful strategy (the Greedy Bit Set Algorithm) for efficient and systematic construction of distinguishers and nonrandomness detectors. We show how this strategy can be applied to a large array of stream and block ciphers, and we show that our method outperforms every other method we have seen so far by presenting new and record-breaking results for Trivium, Grain-$128$ and Grain v1.
We show that the greedy strategy reveals weaknesses in Trivium reduced to $1026$ (out of $1152$) initialization rounds using $2^{45}$ complexity -- a result that significantly improves all previous efforts. This result was further improved using a cluster; $1078$ rounds at $2^{54}$ complexity. We also present an $806$-round distinguisher for Trivium with $2^{44}$ complexity.
Distinguisher and nonrandomness records are also set for Grain-$128$. We show nonrandomness for the full Grain-$128$ with its $256$ (out of $256$) initialization rounds, and present a $246$-round distinguisher with complexity $2^{42}$.
For Grain v1 we show nonrandomness for $96$ (out of $160$) initialization rounds at the very modest complexity of $2^7$, and a $90$-round distinguisher with complexity $2^{39}$.
On the theoretical side we define the Nonrandomness Threshold, which explicitly expresses the nature of the randomness limit that is being explored.
We show that the greedy strategy reveals weaknesses in Trivium reduced to $1026$ (out of $1152$) initialization rounds using $2^{45}$ complexity -- a result that significantly improves all previous efforts. This result was further improved using a cluster; $1078$ rounds at $2^{54}$ complexity. We also present an $806$-round distinguisher for Trivium with $2^{44}$ complexity.
Distinguisher and nonrandomness records are also set for Grain-$128$. We show nonrandomness for the full Grain-$128$ with its $256$ (out of $256$) initialization rounds, and present a $246$-round distinguisher with complexity $2^{42}$.
For Grain v1 we show nonrandomness for $96$ (out of $160$) initialization rounds at the very modest complexity of $2^7$, and a $90$-round distinguisher with complexity $2^{39}$.
On the theoretical side we define the Nonrandomness Threshold, which explicitly expresses the nature of the randomness limit that is being explored.
Department/s
Publishing year
2010
Language
English
Pages
210-226
Publication/Series
Progress in Cryptology - INDOCRYPT 2010 / Lecture Notes in Computer Science
Volume
6498
Full text
- Available as PDF - 205 kB
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Document type
Conference paper
Publisher
Springer
Topic
- Electrical Engineering, Electronic Engineering, Information Engineering
Keywords
- algebraic cryptanalysis
- distinguisher
- nonrandomness detector
- maximum degree monomial
- Trivium
- Grain
- Rabbit
- Edon80
- AES
- DES
- XTEA
- TEA
- SEED
- PRESENT
- SMS4
- Camellia
- RC6
- RC5
- HIGHT
- CLEFIA
- Sosemanuk
- HC
- MICKEY
- Salsa
Conference name
INDOCRYPT 2010, 11th International Conference on Cryptology in India
Conference date
2010-12-12 - 2010-12-15
Conference place
Hyderabad, India
Status
Published
Research group
- Crypto and Security
ISBN/ISSN/Other
- ISSN: 0302-9743
- ISSN: 1611-3349
- ISBN: 978-3-642-17400-1