s1234

binary precedence set_covering invariant_knapsack binpacking knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Siwei Sun	2945	8418	1.80069e-03	hard	SiweiSun	29	s1234.mps.gz

These models come from my cryptographic research and are used to search for the best differential characteristics of the round-reduced versions of the block cipher Serpent with the mixed-integer programming technique. For all the models, including S1234.lp, S56701.lp, S456701.lp, I have found a feasible solution in the corresponding mst file. The challenge is that can we find better solutions or can we find the best solutions.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	2945	2944
Constraints	8418	8337
Binaries	2945	2944
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00180069	0.00180899
Nonzeroes	44641	44400

Constraint Classification Properties
	Original	Presolved
Total	8418	8337
Empty	0	0
Free	0	0
Singleton	1	0
Aggregations	0	0
Precedence	3072	3032
Variable Bound	0	0
Set Partitioning	0	0
Set Packing	0	0
Set Covering	1	1
Cardinality	0	0
Invariant Knapsack	1024	984
Equation Knapsack	0	0
Bin Packing	0	72
Knapsack	0	4248
Integer Knapsack	0	0
Mixed Binary	4320	0
General Linear	0	0
Indicator	0	0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

Nonzero entries of original problem

Nonzero entries after trivial presolving

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

	value	min	median	mean	max
Components	0.7781512
Constraint %		0.0119947	12.0931	15.1134	15.1134
Variable %		4.3478300	18.2609	21.7391	21.7391
Score	0.4732280

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion

ID	Objective	Exact	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
1	29		0	0	0	Ed Klotz	2019-11-15	Found using CPLEX 12.9

Similar instances in collection

The following instances are most similar to s1234 in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance	Status	Variables	Binaries	Constraints	Nonz.	Submitter	Group	Objective	Tags
bnatt400	easy	3600	3600	5614	21698	Tatsuya Akutsu	bnatt	1	benchmark binary benchmark_suitable precedence set_covering invariant_knapsack binpacking knapsack
bnatt500	easy	4500	4500	7029	27203	Tatsuya Akutsu	bnatt	Infeasible	benchmark infeasible binary benchmark_suitable precedence set_covering invariant_knapsack binpacking knapsack
circ10-3	open	2700	2700	42620	307320	M. Winkler	–	258.0*	binary decomposition precedence variable_bound set_partitioning set_packing invariant_knapsack knapsack mixed_binary
supportcase4	easy	3162	3162	9492	38036	Michael Winkler	–	0	binary feasibility benchmark_suitable aggregations precedence variable_bound invariant_knapsack knapsack mixed_binary
neos-2075418-temuka	easy	122304	122304	349602	7610261	Hans Mittelmann	neos-pseudoapplication-62	Infeasible	benchmark infeasible binary benchmark_suitable precedence variable_bound set_covering invariant_knapsack knapsack

Reference

@inproceedings{DBLP:conf/asiacrypt/SunHWQMS14,
  author    = {Siwei Sun and
               Lei Hu and
               Peng Wang and
               Kexin Qiao and
               Xiaoshuang Ma and
               Ling Song},
  title     = {Automatic Security Evaluation and (Related-key) Differential Characteristic
               Search: Application to SIMON, PRESENT, LBlock, {DES(L)} and Other
               Bit-Oriented Block Ciphers},
  booktitle = {Advances in Cryptology - {ASIACRYPT} 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security,
               Kaoshiung, Taiwan, R.O.C., December 7-11, 2014. Proceedings, Part
               {I}},
  pages     = {158--178},
  year      = {2014},
  crossref  = {DBLP:conf/asiacrypt/2014-1},
  url       = {http://dx.doi.org/10.1007/978-3-662-45611-8_9},
  doi       = {10.1007/978-3-662-45611-8_9},
  timestamp = {Mon, 10 Nov 2014 13:41:59 +0100},
  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/asiacrypt/SunHWQMS14},
  bibsource = {dblp computer science bibliography, http://dblp.org}
}

@misc{cryptoeprint:2014:747,
    author = {Siwei Sun, Lei Hu, Meiqin Wang, Peng Wang, Kexin Qiao, Xiaoshuang Ma, Danping Shi, Ling Song, Kai Fu},
    title = {Towards Finding the Best Characteristics of Some Bit-oriented Block Ciphers and Automatic Enumeration of (Related-key) Differential and Linear Characteristics with Predefined Properties},
    howpublished = {Cryptology ePrint Archive, Report 2014/747},
    year = {2014},
    note = {\url{http://eprint.iacr.org/2014/747}},
}