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- Charanjit S. Jutla, Anindya C. Patthak
- IACR Cryptology ePrint Archive
- 2005

We develop a new computer assisted technique for lower bounding the minimum distance of linear codes similar to those used in SHA-1 message expansion. Using this technique, we prove that a modified SHA-1 like code has minimum distance at least 82, and that too in just the last 64 of the 80 expanded words. Further the minimum weight in the last 60 words… (More)

- Charanjit S. Jutla, Anindya C. Patthak, Atri Rudra, David Zuckerman
- 45th Annual IEEE Symposium on Foundations of…
- 2004

We present an efficient randomized algorithm to test if a given function f : F/sub p/ /sup n/ /spl rarr/ F/sub p/ (where p is a prime) is a low-degree polynomial. This gives a local test for generalized Reed-Muller codes over prime fields. For a given integer t and a given real /spl epsiv/ > 0, the algorithm queries f at 1//spl epsiv/ + t/spl middot/p/sup… (More)

- Venkatesan Guruswami, Anindya C. Patthak
- 2006 47th Annual IEEE Symposium on Foundations of…
- 2006

We define a new family of error-correcting codes based on algebraic curves over finite fields, and develop efficient list decoding algorithms for them. Our codes extend the class of algebraic-geometric (AG) codes via a (non-obvious) generalization of the approach in the recent breakthrough work of F. Parvaresh and A. Vardy (2005). Our work shows that the PV… (More)

- Charanjit S. Jutla, Anindya C. Patthak
- IACR Cryptology ePrint Archive
- 2005

Recently, Wang, Yin, and Yu ([WYY05b]) have used a low weight codeword in the SHA-1 message expansion to show a better than brute force method to find collisions in SHA-1. The smallest minimum weight codeword they report has a (bit) weight of 25 in the last 60 of the 80 expanded words. In this paper we show, using a computer assisted method, that this is… (More)

- Charanjit S. Jutla, Anindya C. Patthak
- IACR Cryptology ePrint Archive
- 2005

We argue that if the message expansion code of SHA-1 is replaced by a linear code with a better minimum distance, then the resulting hash function is collision resistant. To support this argument, we characterize the disturbance vectors which are used to build local collision attacks as a linear code. This linear code is the xor-sum of two codes, the… (More)

- Anindya C. Patthak, Indrajit Bhattacharya, Anirban Dasgupta, Pallab Dasgupta, P. P. Chakrabarti
- Inf. Process. Lett.
- 2002

Computation Tree Logic (CTL) is one of the most syntactically elegant and computationally attractive temporal logics for branching time model checking. In this paper, we observe that while CTL can be verified in time polynomial in the size of the state space times the length of the formula, there is a large set of reachability properties which cannot be… (More)

- Charanjit S. Jutla, Anindya C. Patthak
- IEEE Transactions on Information Theory
- 2006

A new technique to lower-bound the minimum distance of certain types of quasi-cyclic codes with large dimension by reducing the problem to lower-bounding the minimum distance of a few significantly smaller codes has been developed. These codes have the property that they have extremely efficient software encoders. Using this technique, it is proved that a… (More)

vii Chapter

In the last lecture we have seen the combinatorial version of list decoding. Recall that we are given a code of distance d and we would like to correct more than d/2 errors. We argued that unique decoding is not possible. Therefore we decided on outputting a small list of codewords that has good agreement with the received word. We established the following… (More)

- Mitul Tiwari, Mike Dahlin, +20 authors Upendra Shevade
- 2007

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