The most efficient collision attacks on members of the SHA family presented so far all use complex characteristics which were manually constructed by Wang et al. In this report, we describe a method to search for characteristics in an automatic way. This is particularly useful for multi-block attacks, and as a proof of concept, we give a two-block collision for 64-step SHA-1 based on a new characteristic. The highest number of steps for which a SHA-1 collision was published so far was 58. We also give a unified view on the expected work factor of a collision search and the needed degrees of freedom for the search, which facilitates optimization.

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Finding SHA-1 characteristics: general results and applications

SHA-1 is a widely used 1995 NIST cryptographic hash function standard that was officially deprecated by NIST in 2011 due to fundamental security weaknesses demonstrated in various analyses and theoretical attacks.

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The first collision for full SHA-1

This book constitutes the refereed proceedings of the 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2011, held in Tallinn, Estonia, in May 2011. The 31 papers, presented together with 2 invited talks, were carefully reviewed and selected from 167 submissions. The papers are organized in topical sections on lattice-base cryptography, implementation and side channels, homomorphic cryptography, signature schemes, information-theoretic cryptography, symmetric key cryptography, attacks and algorithms, secure computation, composability, key dependent message security, and public key encryption.

Advances in cryptology : Eurocrypt 2011 : 30th annual international conference on the theory and applications of cryptographic techniques, Tallinn, Estonia, May 15-19, 2011 : proceedings

Low Cost Cryptography.- Quark: A Lightweight Hash.- PRINTcipher: A Block Cipher for IC-Printing.- Sponge-Based Pseudo-Random Number Generators.- Efficient Implementations I.- A High Speed Coprocessor for Elliptic Curve Scalar Multiplications over .- Co-Z Addition Formulae and Binary Ladders on Elliptic Curves.- Efficient Techniques for High-Speed Elliptic Curve Cryptography.- Side-Channel Attacks and Countermeasures I.- Analysis and Improvement of the Random Delay Countermeasure of CHES 2009.- New Results on Instruction Cache Attacks.- Correlation-Enhanced Power Analysis Collision Attack.- Side-Channel Analysis of Six SHA-3 Candidates.- Tamper Resistance and Hardware Trojans.- Flash Memory 'Bumping' Attacks.- Self-referencing: A Scalable Side-Channel Approach for Hardware Trojan Detection.- When Failure Analysis Meets Side-Channel Attacks.- Efficient Implementations II.- Fast Exhaustive Search for Polynomial Systems in .- 256 Bit Standardized Crypto for 650 GE - GOST Revisited.- Mixed Bases for Efficient Inversion in and Conversion Matrices of SubBytes of AES.- SHA-3.- Developing a Hardware Evaluation Method for SHA-3 Candidates.- Fair and Comprehensive Methodology for Comparing Hardware Performance of Fourteen Round Two SHA-3 Candidates Using FPGAs.- Performance Analysis of the SHA-3 Candidates on Exotic Multi-core Architectures.- XBX: eXternal Benchmarking eXtension for the SUPERCOP Crypto Benchmarking Framework.- Fault Attacks and Countermeasures.- Public Key Perturbation of Randomized RSA Implementations.- Fault Sensitivity Analysis.- PUFs and RNGs.- An Alternative to Error Correction for SRAM-Like PUFs.- New High Entropy Element for FPGA Based True Random Number Generators.- The Glitch PUF: A New Delay-PUF Architecture Exploiting Glitch Shapes.- New Designs.- Garbled Circuits for Leakage-Resilience: Hardware Implementation and Evaluation of One-Time Programs.- ARMADILLO: A Multi-purpose Cryptographic Primitive Dedicated to Hardware.- Side-Channel Attacks and Countermeasures II.- Provably Secure Higher-Order Masking of AES.- Algebraic Side-Channel Analysis in the Presence of Errors.- Coordinate Blinding over Large Prime Fields.

Cryptographic hardware and embedded systems : CHES 2010 : 12th international workshop, Santa Barbara, USA, August 17-20, 2010 : proceedings

The first collision for full SHA-1.

At CRYPTO2005, Xiaoyun Wang, Hongbo Yu and Yiqun Lisa Yin proposed a collision attack on SHA-0 that could generate a collision with complexity 239 SHA-0 hash operations. Although the method of Wang et al. can find messages that satisfy the sufficient conditions in steps 1 to 20 by using message modification, it makes no mention of the message modifications needed to yield satisfaction of the sufficient conditions in steps 21 and onwards.

In this paper, first, we give sufficient conditions for the steps from step 21, and propose submarine modification as the message modification technique that will ensure satisfaction of the sufficient conditions from steps 21 to 24. Submarine modification is an extension of the multi-message modification used in collision attacks on the MD-family. Next, we point out that the sufficient conditions given by Wang et al. are not enough to generate a collision with high probability; we rectify this shortfall by introducing two new sufficient conditions. The combination of our newly found sufficient conditions and submarine modification allows us to generate a collision with complexity 236 SHA-0 hash operations. At the end of this paper, we show the example of a collision generated by applying our proposals.

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Improved collision search for SHA-0

We present blockcipher-based MACs (Message Authentication Codes) that have beyond the birthday bound security without message length in the sense of PRF (Pseudo-Random Function) security. Achieving such security is important in constructing MACs using blockciphers with short block sizes (e.g., 64 bit).

Blockcipher-Based MACs: Beyond the Birthday Bound Without Message Length

In EUROCRYPT2005, a collision attack on MD5 was proposed by Wang et al. In this attack, conditions which are sufficient to generate collisions (called “sufficient condition”) are introduced. This attack raises the success probability by modifing messages to satisfy these conditions. In this attack, 37 conditions cannot be satisfied even messages are modified. Therefore, the complexity is 2. After that, Klima improved this result. Since 33 conditions cannot be satisfied in his method, the complexity is 2. In this paper, we propose new message modification techniques which are more efficient than attacks proposed so far. In this method, 29 conditions cannot be satisfied. However, this method is probabilistic, and the probability that this method work correctly is roughly 1/2. Therefore, the complexity of this attack is 2. Furthermore, we propose a more efficient collision search algorithm than that of Wang et al. By using this algorithm, the total complexity is reduced into roughly 5/8. keywords: MD5, collision attack, message modification, sufficient condition

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Improved Collision Attack on MD5.

In EUROCRYPT2005, a collision attack on MD4 was proposed by Wang, Lai, Chen, and Yu. They claimed that collision messages were found with probability 2 -6 to 2 -2 , and the complexity was less than 2 8 MD4 hash operations. However, there were some tyops and oversights in their paper. In this paper, first, we reevaluate the exact success probability. Second, we point out the typos and oversights in the paper of Wang et al, and we show how to improve them. Third, we propose a new message modification method for the third round of MD4. From the first result, we reevaluate that the method of Wang et al. can find collision messages with success probability 2 -5.61 . From the second result, we can find collision messages with success probability 2 -2 . Also by combining the second result and the third result, our improved method is able to find collision messages with probability almost 1. This complexity is less than 3 repetitions of MD4 hash operations. Our improved method is about 85 times as fast as the method of Wang et al.

Improved Collision Attack on MD4 with Probability Almost 1

This paper proposes tweakable block cipher (TBC) based modes \(\mathsf {PFB\_Plus}\) and \(\mathsf {PFB}\omega \) that are efficient in threshold implementations (TI). Let t be an algebraic degree of a target function, e.g. \(t=1\) (resp. \(t>1\)) for linear (resp. non-linear) function. The d-th order TI encodes the internal state into \(d t + 1\) shares. Hence, the area size increases proportionally to the number of shares. This implies that TBC based modes can be smaller than block cipher (BC) based modes in TI because TBC requires s-bit block to ensure s-bit security, e.g. PFB and Romulus, while BC requires 2s-bit block. However, even with those TBC based modes, the minimum we can reach is 3 shares of s-bit state with \(t=2\) and the first-order TI (\(d=1\)).

Yusuke Naito

Papers

Improved collision search for SHA-0

Blockcipher-Based MACs: Beyond the Birthday Bound Without Message Length

Improved Collision Attack on MD5.

Improved Collision Attack on MD4 with Probability Almost 1

Lightweight Authenticated Encryption Mode Suitable for Threshold Implementation.