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{
"estimators": [
{
"estimator_id": "SDEstimator",
"algorithm_id": "SDAlgorithm",
"display_label": "Binary Syndrome Decoding",
"landing_page_content": "# Binary Syndrome Decoding Estimator\n\n\nThis project provides an estimator for the hardness of the binary syndrome decoding problem. This problem is defined as follows:\n\nLet $\\mathbf H\\in\\mathbb{F}_2^{(n-k)\\times n}$ be the parity-check matrix of a code of length $n$ and dimension $k$. Given $\\mathbf H$, a syndrome $\\mathbf{s}\\in\\mathbb{F}_2^{n-k}$ and an integer $\\omega < n$ the syndrome decoding problem asks to find a vector $\\mathbf e \\in \\mathbb{F}_2^n$ satisfying $\\mathbf H \\mathbf e=\\mathbf s$ while $\\mathbf e$ has a Hamming weight smaller or equal to $\\omega$.\n\nThe estimator covers Information Set Decoding (ISD) algorithms to estimate the hardness of given instances. More details on the theoretical foundations of the estimator can be found in the corresponding papers:\n\n*[[EB22]](https://link.springer.com/chapter/10.1007/978-3-030-97121-2_5) Andre Esser and Emanuele Bellini. Syndrome Decoding Estimator. [[eprint]](https://eprint.iacr.org/2021/1243.pdf)*\n\n*[[BM18]](https://link.springer.com/chapter/10.1007/978-3-319-79063-3_2) Leif Both and Alexander May. Decoding Linear Codes with High Error Rate and its Impact for LPN Security. [[eprint]](https://eprint.iacr.org/2017/1139.pdf)*\n\n*[[MO15]](https://link.springer.com/chapter/10.1007/978-3-662-46800-5_9) Alexander May and Ilya Ozerov. On computing nearest neighbors with applications to decoding of binary linear codes [[preprint]](https://www.iacr.org/archive/eurocrypt2015/90560136/90560136.pdf)*\n \n*[[BJMM12]](https://link.springer.com/chapter/10.1007/978-3-642-29011-4_31) Anja Becker, Antoine Joux, Alexander May and Alexander Meurer. Decoding random binary linear codes in 2^(n/20): How 1+ 1= 0 improves information set decoding. [[eprint]](https://eprint.iacr.org/2012/026.pdf)* \n\n*[[MMT11]](https://link.springer.com/chapter/10.1007/978-3-642-25385-0_6) Alexander May, Alexander Meurer and Enrico Thomae. Decoding random linear codes in 2^(0.054n) [[preprint]](https://www.cits.ruhr-uni-bochum.de/imperia/md/content/may/paper/ac11_decoding.pdf)*\n\n*[[FS09]](https://link.springer.com/chapter/10.1007/978-3-642-10366-7_6) Matthieu Finiasz and Nicolas Sendrier. Security Bounds for the Design of Code-based\nCryptosystems. [[eprint]](https://eprint.iacr.org/2009/414.pdf)*\n\n*[[Dum91]](https://doi.org/10.1007/BFb0019850) Ilya Dumer. On minimum distance decoding of linear codes.*\n\n*[[Ste89]](https://doi.org/10.1007/BFb0019850) Jacques Stern. A method for finding codewords of small weight*\n\n*[[Pra62]](https://doi.org/10.1109/TIT.1962.1057777) Eugene Prange. The use of information sets in decoding cyclic codes*",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Code length (n)",
"placeholder": "Insert parameter",
"tooltip": "Code length of the specified code",
"validate_fields_ids": [
"k",
"w"
]
},
{
"id": "k",
"type": "number",
"display_label": "Code dimension (k)",
"placeholder": "Insert parameter",
"tooltip": "Code dimension of specified code",
"validate_fields_ids": [
"w"
],
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
}
]
},
{
"id": "w",
"type": "number",
"display_label": "Error weight (w)",
"placeholder": "Insert parameter",
"tooltip": "Hamming weight of the target solution",
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
},
{
"action": "validateLessThanOperation",
"operation": "n - k"
}
]
}
],
"optional_parameters": [
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "nsolutions",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Number of solutions",
"placeholder": "Insert value",
"caption": "Leave empty to take expected amount of solutions",
"tooltip": "Log2 of number of existing solutions of which one has to be found"
},
{
"id": "workfactor_accuracy",
"type": "slider",
"direction": "column",
"display_label": "Tilde-O accuracy",
"default_value": 1,
"tooltip": "Accuracy level of optimization",
"min": 1,
"max": 100,
"number_of_decimals": 0,
"step": 1
},
{
"id": "limit_depth",
"type": "switch",
"display_label": "Limit tree-depth",
"default_value": false,
"tooltip": "Limits the depth of May-Ozerov and BJMM algorithm to two, otherwise two and three are considered"
},
{
"id": "include_tildeo",
"type": "switch",
"display_label": "Tilde-O complexity",
"default_value": false,
"tooltip": "Include complexity estimates that disregard polynomial factors",
"dependencies": [
{
"id": "workfactor_accuracy",
"parent_value": true,
"action": "show"
}
]
},
{
"id": "hmap",
"type": "switch",
"display_label": "Hashmap",
"default_value": true,
"tooltip": "Use linear time matching between lists via hashmaps. If false, use sort-and-match"
}
],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,
"tooltip": "Show complexities as count of bit operations. If false, show number of elementary operations"
},
{
"id": "included_algorithms",
"type": "multiple_selector",
"direction": "column",
"display_label": "Included algorithms",
"tooltip": "Algorithms to include for optimization",
"default_value": [],
"excluded_algorithms": [
"BJMMdw",
"BJMMpdw"
],
"options": [],
"dependencies": [
{
"id": "limit_depth",
"parent_contains": [
"MayOzerov",
"BJMM"
],
"action": "show"
}
]
},
{
"id": "memory_access",
"type": "selector",
"direction": "column",
"display_label": "Memory access cost",
"default_value": 0,
"tooltip": "Function that takes as input the memory bit complexity and outputs the associate algorithmic cost. Example, logarithmic memory access, input M, output M+log2M.",
"options": [
"Constant",
"Logaritmic",
"Square root",
"Cube root"
]
},
{
"id": "precision",
"type": "number",
"direction": "column",
"display_label": "Decimal precision",
"default_value": 0,
"placeholder": "Insert value",
"tooltip": "Number of decimal digits to display"
}
]
},
{
"estimator_id": "MQEstimator",
"algorithm_id": "MQAlgorithm",
"display_label": "Multivariate Quadratic",
"landing_page_content": "# Multivariate Quadratic Estimator\n\n\nThis project provides an estimator for the hardness of the multivariate quadratic problem. This problem is defined as follows: \nLet $\\mathbb{F}_{q}$ be a field with $q$ elements, and let $\\mathbb{F}_{q}[x_1, x_2, \\ldots, x_n]$ be the ring of polynomials in the variables $x_1, x_2, \\ldots, x_n$ and coefficients in $\\mathbb{F}_{q}$. Given $p_1, p_2, \\ldots, p_m \\in \\; \\mathbb{F}_{q}[x_1, x_2, \\ldots, x_n]$ the multivariate quadratic problem asks to find a vector $\\mathbf a \\in \\; \\mathbb{F}_q^n$ satisfying $p_{i}(\\mathbf a ) = 0$ for all $i=1,2,\\ldots,m$. \n\nMore details on the theoretical foundations of the estimator can be found in the corresponding papers:\n\n[[BFP09]](https://www.degruyter.com/document/doi/10.1515/JMC.2009.009/html) Luk Bettale, Jean-Charles Faug\u00e8re and Ludovic Perret. Hybrid Approach for Solving Multivariate Systems over Finite Fields. [[eprint]](https://www-polsys.lip6.fr/~jcf/Papers/JMC2.pdf)\n\n\n[[BFP12]](https://dl.acm.org/doi/10.1145/2442829.2442843) Luk Bettale, Jean-Charles Faug\u00e8re and Ludovic Perret. Solving Polynomial Systems over Finite Fields: Improved Analysis of the Hybrid Approach.[[eprint]](https://inria.hal.science/hal-00776070/document)\n\n[[BFSS11]](https://pdf.sciencedirectassets.com/272569/1-s2.0-S0885064X12X00062/1-s2.0-S0885064X12000611/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBoaCXVzLWVhc3QtMSJGMEQCIBHnYYyQivq5VWZYvmhCqtMpTXyb0CrGtt7E1qyC0ZJ%2BAiBfUBVOKdbnJZzeZ%2FbgFOpYWU9l%2BQoFzOIcLVgpZZnm0yq6BQjS%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAUaDDA1OTAwMzU0Njg2NSIMwnWkvDQITUOcgAwNKo4FmSWjG8P8MVTGNxKlUW8YYmkHDWQVQB%2BVQW%2BG4jlq83XjGRCCjk0%2FDb6CjUKjBK%2FK8698eCXVZ4LJ9CVH9aRbSI8LNxJlzVah0DftlOeogKx6ARAJsmEAeKhsW55eDh3HVIaYKrgR0Ewfz3W1Vg0a19FUQUor17iqEW1RwWWKvA93ja%2FCDn26haeHuEl4Rjb%2BsQbavDeJZN%2FOAsIO60Boqe0PcmhJ8upEJRYz2Gom3W7ZoKIjKpQ7eyE90rBMoIKp94oM3yNkb5wKoYKIo6VKRR1wJ94AlyfeprmOSpFwX%2F6CMcBG43S0qyG7%2F2WRZHpTBwOM1RBKVzdR7jwj8j7LiQkaPIV1aFbpIn5Fp57TR3Iwq6YQfSmZeUtc7pJ8DRqihynCz8wR6U%2BEsg%2FUpHkZuesB5jtmLQE%2FrPsH5m4XmOiC%2BJzw3BAWpI4lqaDjW9b8eyg%2F4e2mOzZEOz0cj3Ew8ta0PhDureat9twodedu6227smjrLUySdJwOyDqqdje4WxKsBnUJ4fEteP0aSoT41x1E2BOGZw9uhVz9rxaNK23VySJ%2Bcu6n5g9JPJ2hNXB272PfephanXGRwsA2IldE9NokT22Eawg9%2B3c2E2wwcj5WJSFjTrnCaxK88y%2FBXbsYqIkztlrbFVhDs48QfzndR4wkqBX8kW6plvxLQV4RsSomuw1wUbbsBsMMBRDN0EpS6KdL4Jvt7hBuOb%2FiyboGQVDKl6c3s3kWxx%2FIkDY0SRSEKfyMX%2BumI%2FL%2FQ%2B5ob7hxxOXmUgtjfKj8tQ1Kl1VNEub2eT%2BAN4cgU9V74fbIKWKQXEGp%2Bc4zsCYk62vT8ftnhi2Pt88cl8CikAa5fZAqw8uKpdFcxi%2B%2BJ6WfyE2iMKHRjKcGOrIBLNhClwMzLz7TV7LRxsX6kFR%2BzwbMHqXWv8PpCUIYdEKP1RGHvCAT4q50xHGzfJqb5CxSkGoL56Fove9gzFqKWSRllpuUV1RZ7GZWsYtkWNpOWQuIRz8JHPK7yHCgVs94kWjD8yIS%2BrK93eYxkoDK%2BTWzSl2aMTlaCavMnNNf7frjwXiuOZbMwo1dl46JJA%2BvkK%2Fq4Ax8Q7X79JtiYjpvJ7mr82RL2oMPqsy0MpECstoIKQ%3D%3D&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20230821T101656Z&X-Amz-SignedHeaders=host&X-Amz-Expires=299&X-Amz-Credential=ASIAQ3PHCVTYTP2IJIPD%2F20230821%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Signature=e090ae1ce0cc71e9c821a3b37d14928c394ef10c0a5d6bbbcc23e6c2a051ad58&hash=b13dc44acd73359364fc817eb08d10ea6b5bc3661d7a71b501eb0ec26b56ec32&host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&pii=S0885064X12000611&tid=spdf-60dd10bd-1c4f-413d-90ee-b5f00b079ede&sid=bf3cf8d028ef4649897883c939f8845d9e60gxrqb&type=client&tsoh=d3d3LnNjaWVuY2VkaXJlY3QuY29t&ua=070652070f5d54015a5b&rr=7fa21f953c3917d7&cc=ae) Magali Bardet, Jean-Charles Faug\u00e8re, Bruno Salvy, and Pierre-Jean Spaenlehauer. On the Complexity of Solving Quadratic Boolean Systems.\n\n[[BKW19]](https://drops.dagstuhl.de/opus/volltexte/2019/10602/pdf/LIPIcs-ICALP-2019-26.pdf) Andreas Bj\u00f6rklund, Petteri Kaski, and Ryan Williams. Solving Systems of Polynomial Equations over GF(2) by a Parity-Counting Self-Reduction. [[eprint]](https://drops.dagstuhl.de/opus/volltexte/2019/10602/pdf/LIPIcs-ICALP-2019-26.pdf)\n\n[[BMSV22]](https://eprint.iacr.org/2022/708.pdf) Emanuele Bellini, Rusydi H. Makarim, Carlo Sanna, and Javier Verbel. An Estimator for the Hardness of the MQ Problem. [[eprint]](https://eprint.iacr.org/2022/708.pdf)\n\n[[BCCCNSY10]](https://www.iacr.org/archive/ches2010/62250195/62250195.pdf) Charles Bouillaguet, Hsieh-Chung Chen, Chen-Mou Cheng, Tung Chou, Ruben Niederhagen, Adi Shamir, and Bo-Yin Yang. Fast Exhaustive Search for Polynomial Systems in $\\mathbb{F}_2$.\n\n[[CKPS00]](https://link.springer.com/chapter/10.1007/3-540-45539-6_27) Nicolas Courtois, Alexander Klimov, Jacques Patarin, and Adi Shamir. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. [[eprint]](https://www.iacr.org/archive/eurocrypt2000/1807/18070398-new.pdf)\n\n[[CGMT02]](https://link.springer.com/chapter/10.1007/3-540-45664-3_15) Nicolas Courtois, Louis Goubin, Willi Meier, and Jean-Daniel Tacier. Solving Underdefined Systems of Multivariate Quadratic Equations.\n\n[[Din21a]](https://dl.acm.org/doi/abs/10.5555/3458064.3458215) Itai Dinur. Improved Algorithms for Solving Polynomial Systems over GF(2) by Multiple Parity-Counting. [[preprint]](https://arxiv.org/pdf/2005.04800.pdf)\n\n[[Din21b]](https://link.springer.com/chapter/10.1007/978-3-030-77870-5_14) Itai Dinur. Cryptanalytic Applications of the Polynomial Method for Solving Multivariate Equation Systems over GF(2). [[eprint]](https://eprint.iacr.org/2021/578.pdf)\n\n[[JV18]](https://link.springer.com/chapter/10.1007/978-3-319-76620-1_1) Antoine Joux and Vanessa Vitse. A Crossbred Algorithm for Solving Boolean Polynomial Systems. [[eprint]](https://eprint.iacr.org/2017/372.pdf)\n\n[[KPG99]](https://link.springer.com/chapter/10.1007/3-540-48910-X_15) Aviad Kipnis, Jacques Patarin, and Louis Goubin. Unbalanced Oil and Vinegar Signature Schemes. [[extended]](http://www.goubin.fr/papers/OILLONG.PDF)\n\n[[LPTWY17]](https://epubs.siam.org/doi/epdf/10.1137/1.9781611974782.143) Daniel Lokshtanov, Ramamohan Paturi, Suguru Tamaki, Ryan Williams, and Huacheng Yu. Beating Brute Force for Systems of Polynomial Equation over Finite Fields.\n\n[[MHT13]](https://link.springer.com/chapter/10.1007/978-3-642-38616-9_8) Hiroyuki Miura, Yasufumi Hashimoto, and Tsuyoshi Takagi. Extended Algorithm for Solving Underdefined Multivariate Quadratic Equations.\n\n[[TW12]](https://link.springer.com/chapter/10.1007/978-3-642-30057-8_10) Enrico Thomae and Christopher Wolf. Solving Underdetermined Systems of Multivariate Quadratic Equations Revisited.[[eprint]](https://www.iacr.org/archive/pkc2012/72930159/72930159.pdf)\n",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Number of variables (n)",
"placeholder": "Insert parameter",
"tooltip": "The number of variables of the system to solve",
"validate_fields_ids": [
"h"
]
},
{
"id": "m",
"type": "number",
"display_label": "Number of equations (m)",
"placeholder": "Insert parameter",
"tooltip": "The number of equations of the system to solve"
},
{
"id": "q",
"type": "number",
"display_label": "Field size (q)",
"placeholder": "Insert parameter",
"tooltip": "An integer of the form p^x for some integer x, where p is prime number. This value indicates the number of elements in the underlying field"
}
],
"optional_parameters": [
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "nsolutions",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Number of solutions",
"placeholder": "Insert value",
"caption": "Leave empty to take expected amount of solutions",
"tooltip": "Log2 of number of existing solutions of which one has to be found"
},
{
"id": "include_tildeo",
"type": "switch",
"display_label": "Tilde-O complexity",
"default_value": false,
"tooltip": "Include complexity estimates that disregard polynomial factors"
},
{
"id": "w",
"type": "slider",
"direction": "column",
"display_label": "Matrix multiplication constant",
"default_value": 2.81,
"tooltip": "Indicates that two square matrices of size n can be multiplied by performing O(n^w) field multiplications",
"min": 2,
"max": 3,
"number_of_decimals": 2,
"step": 0.01
},
{
"id": "h",
"type": "number",
"direction": "column",
"display_label": "Number of variables to guess",
"default_value": 0,
"placeholder": "Insert parameter",
"tooltip": "Assumes that the initial system is splited into q^h subsystems of n-h variables and m equations. In this case the time complexity is given by q^h times the complexity a given subsystem. The memory complexity is given by the memory required to solve one subsystem",
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
}
]
},
{
"id": "max_D",
"type": "number",
"direction": "column",
"display_label": "Max D for Crossbred",
"default_value": 20,
"placeholder": "Insert value",
"tooltip": "Upper bound to the parameter D "
}
],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,
"tooltip": "Show complexities as count of bit operations. If false, show number of elementary operations",
"dependencies": [
{
"id": "theta",
"parent_value": true,
"action": "show"
}
]
},
{
"id": "theta",
"type": "number",
"direction": "column",
"display_label": "Bitcomplexity exponent",
"default_value": 2,
"placeholder": "Insert value",
"tooltip": "The bitcomplexity of a field multiplication is assumed to be log_2(q)^(theta). Note that for theta = 0 the output gives the (log of the) necessary number of field multiplications."
},
{
"id": "included_algorithms",
"type": "multiple_selector",
"direction": "column",
"display_label": "Included algorithms",
"tooltip": "Algorithms to include for optimization",
"default_value": [],
"excluded_algorithms": [],
"options": [],
"dependencies": [
{
"id": "max_D",
"parent_contains": [
"Crossbred"
],
"action": "show"
}
]
},
{
"id": "memory_access",
"type": "selector",
"direction": "column",
"display_label": "Memory access cost",
"default_value": 0,
"tooltip": "Function that takes as input the memory bit complexity and outputs the associate algorithmic cost. Example, logarithmic memory access, input M, output M+log2M.",
"options": [
"Constant",
"Logaritmic",
"Square root",
"Cube root"
]
},
{
"id": "precision",
"type": "number",
"direction": "column",
"display_label": "Decimal precision",
"default_value": 0,
"placeholder": "Insert value",
"tooltip": "Number of decimal digits to display"
}
]
},
{
"estimator_id": "RegSDEstimator",
"algorithm_id": "RegSDAlgorithm",
"display_label": "Regular Syndrome Decoding",
"landing_page_content": "# Regular Syndrome Decoding Estimator\n\n\nThis project provides an estimator for the hardness of the regular syndrome decoding problem. This problem is defined as follows:\n\nLet $\\mathbf H\\in\\mathbb{F}_2^{(n-k)\\times n}$ be the parity-check matrix of a code of length $n$ and dimension $k$. Given $\\mathbf H$, a syndrome $\\mathbf{s}\\in\\mathbb{F}_2^{n-k}$ and an integer $\\omega \\mid n$ the regular syndrome decoding problem asks to find a vector $\\mathbf e=(\\mathbf e_1, \\mathbf e_2, \\ldots, \\mathbf e_\\omega)$ with $\\mathbf e_i \\in \\mathbb{F}_2^{\\frac n \\omega}$, satisfying $\\mathbf H \\mathbf e=\\mathbf s$ where each $\\mathbf e_i$ has Hamming weight exactly one.\n\nMore details on the theoretical foundations of the estimator can be found in the corresponding papers:\n\n*[[CCJ23]](https://link.springer.com/chapter/10.1007/978-3-031-30589-4_19) \nEliana Carozza, Geoffroy Couteau and Antoine Joux . Short Signatures from Regular Syndrome Decoding in the Head. [[eprint]](https://eprint.iacr.org/2023/1035.pdf)*\n\n*[[ES23]](https://eprint.iacr.org/2023/1568.pdf) Andre Esser and Paolo Santini. Not Just Regular Decoding: Asymptotics and Improvements of Regular Syndrome Decoding Attacks. [[eprint]](https://eprint.iacr.org/2023/1568.pdf)*",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Code length (n)",
"placeholder": "Insert parameter",
"tooltip": "Code length of the specified code",
"validate_fields_ids": [
"k",
"w"
]
},
{
"id": "k",
"type": "number",
"display_label": "Code dimension (k)",
"placeholder": "Insert parameter",
"tooltip": "Code dimension of specified code",
"validate_fields_ids": [
"w"
],
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
}
]
},
{
"id": "w",
"type": "number",
"display_label": "Error weight (w)",
"placeholder": "Insert parameter",
"tooltip": "Hamming weight of the target solution (must divide the code length)",
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
},
{
"action": "validateLessThanOperation",
"operation": "n - k"
}
]
}
],
"optional_parameters": [
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "nsolutions",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Number of solutions",
"placeholder": "Insert value",
"caption": "Leave empty to take expected amount of solutions",
"tooltip": "Log2 of number of existing solutions of which one has to be found"
}
],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,
"tooltip": "Show complexities as count of bit operations. If false, show number of elementary operations"
},
{
"id": "included_algorithms",
"type": "multiple_selector",
"direction": "column",
"display_label": "Included algorithms",
"tooltip": "Algorithms to include for optimization",
"default_value": [],
"excluded_algorithms": [],
"options": [],
"dependencies": []
},
{
"id": "memory_access",
"type": "selector",
"direction": "column",
"display_label": "Memory access cost",
"default_value": 0,
"tooltip": "Function that takes as input the memory bit complexity and outputs the associate algorithmic cost. Example, logarithmic memory access, input M, output M+log2M.",
"options": [
"Constant",
"Logaritmic",
"Square root",
"Cube root"
]
},
{
"id": "precision",
"type": "number",
"direction": "column",
"display_label": "Decimal precision",
"default_value": 0,
"placeholder": "Insert value",
"tooltip": "Number of decimal digits to display"
}
]
},
{
"estimator_id": "SDFqEstimator",
"algorithm_id": "SDFqAlgorithm",
"display_label": "Syndrome Decoding over Fq",
"landing_page_content": "# Syndrome Decoding Estimator over $\\mathbf F_q$\n\n\nThis project provides an estimator for the hardness of the syndrome decoding problem over $\\mathbf F_q$. This problem is defined as follows:\n\nLet $\\mathbf H\\in\\mathbb{F}_q^{(n-k)\\times n}$ be the parity-check matrix of a code of length $n$ and dimension $k$. Given $\\mathbf H$, a syndrome $\\mathbf{s}\\in\\mathbb{F}_q^{n-k}$ and an integer $\\omega < n$ the syndrome decoding problem asks to find a vector $\\mathbf e \\in \\mathbb{F}_q^n$ satisfying $\\mathbf H \\mathbf e=\\mathbf s$ while $\\mathbf e$ has a Hamming weight smaller or equal to $\\omega$.\n\nThe estimator covers Information Set Decoding (ISD) algorithms to estimate the hardness of given instances.\n\nMore details on the theoretical foundations of the complexity of included algorithms can be found in\n\n*[[Pet11]](https://link.springer.com/chapter/10.1007/978-3-642-12929-2_7) Christiane Peters. Information-set decoding for linear codes over Fq. [[eprint]](https://eprint.iacr.org/2009/589.pdf)*\n\n*[[Ste89]](https://doi.org/10.1007/BFb0019850) Jacques Stern. A method for finding codewords of small weight.*\n\n*[[LB88]](https://doi.org/10.1007/3-540-45961-8\\_25) Pil Joong Lee and Ernest Brickell. An observation on the security of McEliece\u2019s public-key cryptosystem.*\n\n*[[Pra62]](https://doi.org/10.1109/TIT.1962.1057777) Eugene Prange. The use of information sets in decoding cyclic codes.*",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Code length (n)",
"placeholder": "Insert parameter",
"tooltip": "Code length of the specified code",
"validate_fields_ids": [
"k",
"w"
]
},
{
"id": "k",
"type": "number",
"display_label": "Code dimension (k)",
"placeholder": "Insert parameter",
"tooltip": "Code dimension of specified code",
"validate_fields_ids": [
"w"
],
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
}
]
},
{
"id": "w",
"type": "number",
"display_label": "Error weight (w)",
"placeholder": "Insert parameter",
"tooltip": "Hamming weight of the target solution",
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
},
{
"action": "validateLessThanOperation",
"operation": "n - k"
}
]
},
{
"id": "q",
"type": "number",
"display_label": "Base Field Size (q)",
"placeholder": "Insert parameter",
"tooltip": "Size of the underlying base field",
"dependencies": []
}
],
"optional_parameters": [
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "nsolutions",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Number of solutions",
"placeholder": "Insert value",
"caption": "Leave empty to take expected amount of solutions",
"tooltip": "Log2 of number of existing solutions of which one has to be found, if not specified it will be fixed to the number of solutions in expectation"
},
{
"id": "is_syndrome_zero",
"type": "selector",
"direction": "column",
"display_label": "Code word search",
"default_value": 1,
"tooltip": "Indicates if a small code word is searched, i.e., if the syndrome is equal to the zero.",
"options": [
"Syndrome decoding",
"Code word search"
]
}
],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,
"tooltip": "Show complexities as count of bit operations. If false, show number of field additions"
},
{
"id": "memory_access",
"type": "selector",
"direction": "column",
"display_label": "Memory access cost",
"default_value": 0,
"tooltip": "Function that takes as input the memory bit complexity and outputs the associate algorithmic cost. Example, logarithmic memory access, input M, output M+log2M.",
"options": [
"Constant",
"Logaritmic",
"Square root",
"Cube root"
]
},
{
"id": "included_algorithms",
"type": "multiple_selector",
"direction": "column",
"display_label": "Included algorithms",
"tooltip": "Algorithms to include for optimization",
"default_value": [],
"excluded_algorithms": [],
"options": [],
"dependencies": [
{
"id": "max_D",
"parent_contains": [
"Crossbred"
],
"action": "show"
}
]
},
{
"id": "precision",
"type": "number",
"direction": "column",
"display_label": "Decimal precision",
"default_value": 0,
"placeholder": "Insert value",
"tooltip": "Number of decimal digits to display"
}
]
},
{
"estimator_id": "PKEstimator",
"algorithm_id": "PKAlgorithm",
"display_label": "Permuted Kernel",
"landing_page_content": "# Permuted Kernel Estimator\n\nThis project provides an estimator for the hardness of the permuted kernel problem. This problem is defined as follows: \n\nGiven two matrices $\\mathbf{A} \\in \\; \\mathbb{F}_{q}^{m\\times n}$ and $\\mathbf{V} \\in \\; \\mathbb{F}_{q}^{\\ell \\times n}$, the permuted kernel problem asks to find a permutation $\\mathbf{P} \\in \\mathbb{F}_{q}^{m\\times n}$ such that $\\mathbf{A}(\\mathbf{V} \\mathbf{P})^\\top = 0$\n\nMore details on the theoretical foundations of the estimator can be found in the corresponding papers: \n\n*[[SBC22]](https://eprint.iacr.org/2022/1749.pdf) Paolo Santini, Marco Baldi, and Franco Chiaraluce. Computational hardness of the permuted kernel and subcode equivalence problems. [[eprint]](https://eprint.iacr.org/2022/1749.pdf)*\n\n*[[KMP19]](https://eprint.iacr.org/2019/412.pdf) Eliane Koussa, Gilles Macario-Rat and Jacques Patarin. On the complexity of the permuted kernel problem. Cryptology ePrint Archive, Report 2019/412 (2019). [[eprint]](https://eprint.iacr.org/2019/412.pdf)*",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Number of columns (n)",
"placeholder": "Insert parameter",
"tooltip": "Number of columns of the input matrix"
},
{
"id": "m",
"type": "number",
"display_label": "Number of rows (m)",
"placeholder": "Insert parameter",
"tooltip": "Number of rows of the input matrix"
},
{
"id": "q",
"type": "number",
"display_label": "Field size (q)",
"placeholder": "Insert parameter",
"tooltip": "A prime number"
},
{
"id": "ell",
"type": "number",
"display_label": "No. of rows in the kernel (ell)",
"placeholder": "Insert value",
"default_value": 1,
"tooltip": "Number of rows of the matrix whose permutation should lie in the kernel"
},
{
"id": "use_parity_row",
"required": false,
"type": "switch",
"display_label": "Use parity row",
"default_value": true,
"tooltip": "Enables trick of appending extra (all one) row to the matrix, i.e., m -> m+1. Enable if you did not already increase m manually."
}
],
"optional_parameters": [
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "nsolutions",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Number of solutions",
"placeholder": "Insert value",
"caption": "Leave empty to take expected amount of solutions",
"tooltip": "Log2 of number of existing solutions of which one has to be found"
},
{
"id": "cost_for_list_operation",
"type": "number",
"display_label": "List operation cost (Time)",
"direction": "column",
"placeholder": "Insert value",
"tooltip": "Cost in Fq additions for one list operation in the SBC and KMP algorithms"
},
{
"id": "memory_for_list_element",
"type": "number",
"display_label": "List operation cost (Memory)",
"direction": "column",
"placeholder": "Insert value",
"tooltip": "Memory in Fq elements for one list element in the SBC and KMP algorithms"
}
],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,
"tooltip": "Show complexities as count of bit operations. If false, show number of elementary operations"
},
{
"id": "included_algorithms",
"type": "multiple_selector",
"direction": "column",
"display_label": "Included algorithms",
"tooltip": "Algorithms to include for optimization",
"default_value": [],
"excluded_algorithms": [],
"options": [],
"dependencies": []
},
{
"id": "memory_access",
"type": "selector",
"direction": "column",
"display_label": "Memory access cost",
"default_value": 0,
"tooltip": "Function that takes as input the memory bit complexity and outputs the associate algorithmic cost. Example, logarithmic memory access, input M, output M+log2M.",
"options": [
"Constant",
"Logaritmic",
"Square root",
"Cube root"
]
},
{
"id": "precision",
"type": "number",
"direction": "column",
"display_label": "Decimal precision",
"default_value": 0,
"placeholder": "Insert value",
"tooltip": "Number of decimal digits to display"
}
]
},
{
"estimator_id": "PEEstimator",
"algorithm_id": "PEAlgorithm",
"display_label": "Permutation Equivalence",
"landing_page_content": "# Permutation Equivalence Estimator\n\nThis project provides an estimator for the hardness of the permutation equivalence problem. \n\nThis problem is defined as follows: Given two matrices $\\mathbf{G}, \\mathbf{G}' \\in \\; \\mathbb{F}_{q}^{k\\times n}$, the permuted equivalence problem asks to find an invertible matrix $\\mathbf{S} \\in \\; \\mathbb{F}_{q}^{k\\times n}$ and permutation matrix $\\mathbf{P} \\in \\; \\mathbb{F}_{q}^{n\\times n}$ such that $\\mathbf{G}' = \\mathbf{S}\\mathbf{G}\\mathbf{P}$.\n\nMore details on the theoretical foundations of the estimator can be found in the corresponding papers: \n\n*[[Beu20]](https://link.springer.com/chapter/10.1007/978-3-030-81652-0_15) Ward Beullens. Not enough LESS: An improved algorithm for solving code equivalence problems over Fq. [[eprint]](https://eprint.iacr.org/2020/801.pdf)*\n\n*[[Sen99]](https://inria.hal.science/inria-00073037/document) Nicolas Sendrier. On the dimension of the hull. SIAM Journal on Discrete Mathematics 10(2), 282\u2013293 (1997). [[preprint]](https://inria.hal.science/inria-00073037/document)*\n\n*[[Leo82]](https://ieeexplore.ieee.org/document/1056498) Jeffrey Leon. Computing automorphism groups of error-correcting codes. IEEE Transactions on Information Theory 28(3), 496\u2013511 (1982).*",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Code length (n)",
"placeholder": "Insert parameter",
"tooltip": "Code length of the specified code",
"validate_fields_ids": [
"k"
]
},
{
"id": "k",
"type": "number",
"display_label": "Code dimension (k)",
"placeholder": "Insert parameter",
"tooltip": "Code dimension of specified code",
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
}
]
},
{
"id": "q",
"type": "number",
"display_label": "Field size (q)",
"placeholder": "Insert parameter",
"tooltip": "A prime number"
},
{
"id": "h",
"type": "number",
"display_label": "Hull dimension",
"placeholder": "Insert parameter",
"tooltip": "The dimension of the hull"
},
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "nsolutions",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Number of solutions",
"placeholder": "Insert value",
"caption": "Leave empty to take expected amount of solutions",
"tooltip": "Log2 of number of existing solutions of which one has to be found"
}
],
"optional_parameters": [],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,
"tooltip": "Show complexities as count of bit operations. If false, show number of elementary operations"
},
{
"id": "included_algorithms",
"type": "multiple_selector",
"direction": "column",
"display_label": "Included algorithms",
"tooltip": "Algorithms to include for optimization",
"default_value": [],
"excluded_algorithms": [],
"options": [],
"dependencies": []
},
{
"id": "memory_access",
"type": "selector",
"direction": "column",
"display_label": "Memory access cost",
"default_value": 0,
"tooltip": "Function that takes as input the memory bit complexity and outputs the associate algorithmic cost. Example, logarithmic memory access, input M, output M+log2M.",
"options": [
"Constant",
"Logaritmic",
"Square root",
"Cube root"
]
},
{
"id": "precision",
"type": "number",
"direction": "column",
"display_label": "Decimal precision",
"default_value": 0,
"placeholder": "Insert value",
"tooltip": "Number of decimal digits to display"
}
]
},
{
"estimator_id": "LEEstimator",
"algorithm_id": "LEAlgorithm",
"display_label": "Linear Equivalence",
"landing_page_content": "# Linear Equivalence Estimator\n\nThis project provides an estimator for the hardness of the linear equivalence problem. \n\nThis problem is defined as follows: Given two matrices $\\mathbf{G}, \\mathbf{G}' \\in \\; \\mathbb{F}_{q}^{k\\times n}$, the linear equivalence problem asks to find an invertible matrix $\\mathbf{S} \\in \\; \\mathbb{F}_{q}^{k\\times n}$ and monomial matrix $\\mathbf{Q} \\in \\; \\mathbb{F}_{q}^{n\\times n}$ such that $\\mathbf{G}' = \\mathbf{S}\\mathbf{G}\\mathbf{P}$.\n\nMore details on the theoretical foundations of the estimator can be found in the corresponding papers: \n\n*[[BBPS22]](https://eprint.iacr.org/2022/967.pdf) Alessandro Barenghi, Jean-Francois Biasse, Edoardo Persichetti and Paolo Santini,. On the Computational Hardness of the Code Equivalence Problem in Cryptography. [[eprint]](https://eprint.iacr.org/2022/967.pdf)*\n\n*[[Beu20]](https://link.springer.com/chapter/10.1007/978-3-030-81652-0_15) Ward Beullens. Not enough LESS: An improved algorithm for solving code equivalence problems over Fq. [[eprint]](https://eprint.iacr.org/2020/801.pdf)*\n\n*[[Leo82]](https://ieeexplore.ieee.org/document/1056498) Jeffrey Leon. Computing automorphism groups of error-correcting codes. IEEE Transactions on Information Theory 28(3), 496\u2013511 (1982).*",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Code length (n)",
"placeholder": "Insert parameter",
"tooltip": "Code length of the specified code",
"validate_fields_ids": [
"k"
]
},
{
"id": "k",
"type": "number",
"display_label": "Code dimension (k)",
"placeholder": "Insert parameter",
"tooltip": "Code dimension of specified code",
"dependencies": [
{
"id": "n",
"action": "validateLessThan"
}
]
},
{
"id": "q",
"type": "number",
"display_label": "Field size (q)",
"placeholder": "Insert parameter",
"tooltip": "A prime number"
},
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "nsolutions",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Number of solutions",
"placeholder": "Insert value",
"caption": "Leave empty to take expected amount of solutions",
"tooltip": "Log2 of number of existing solutions of which one has to be found"
}
],
"optional_parameters": [],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,
"tooltip": "Show complexities as count of bit operations. If false, show number of elementary operations"
},
{
"id": "included_algorithms",
"type": "multiple_selector",
"direction": "column",
"display_label": "Included algorithms",
"tooltip": "Algorithms to include for optimization",
"default_value": [],
"excluded_algorithms": [],
"options": [],
"dependencies": []
},
{
"id": "memory_access",
"type": "selector",
"direction": "column",
"display_label": "Memory access cost",
"default_value": 0,
"tooltip": "Function that takes as input the memory bit complexity and outputs the associate algorithmic cost. Example, logarithmic memory access, input M, output M+log2M.",
"options": [
"Constant",
"Logaritmic",
"Square root",
"Cube root"
]
},
{
"id": "precision",
"type": "number",
"direction": "column",
"display_label": "Decimal precision",
"default_value": 0,
"placeholder": "Insert value",
"tooltip": "Number of decimal digits to display"
}
]
},
{
"estimator_id": "UOVEstimator",
"algorithm_id": "UOVAlgorithm",
"display_label": "UOV Signature Scheme",
"landing_page_content": "# UOV Estimator\n\n\nThis project provides an estimator for the security of the Unbalanced Oil and Vinegar (UOV) signature scheme. This scheme is mainly based on the hardness of the MQ problem and it was submitted as a candidate to the NIST call for post-quantum signatures. \n\nMore details on the theoretical foundations of the signature scheme and the estimator can be found in the submitted specifications:\n\n[[UOV23]](https://csrc.nist.gov/csrc/media/Projects/pqc-dig-sig/documents/round-1/spec-files/UOV-spec-web.pdf) Ward Beullens, Ming-Shing Chen, Jintai Ding, Boru Gong, Matthias J. Kannwischer, Jacques Patarin, Bo-Yuan Peng, Dieter Schmidt, Cheng-Jhih Shih, Chengdong Tao and Bo-Yin Yang. UOV: Unbalanced Oil and Vinegar\nAlgorithm Specifications and Supporting Documentation. ",
"problem_parameters": [
{
"id": "n",
"type": "number",
"display_label": "Number of variables (n)",
"placeholder": "Insert parameter",
"tooltip": "The number of variables in the public key polynomials"
},
{
"id": "m",
"type": "number",
"display_label": "Number of equations (m)",
"placeholder": "Insert parameter",
"tooltip": "The number of polynomials in the public key"
},
{
"id": "q",
"type": "number",
"display_label": "Field size (q)",
"placeholder": "Insert parameter",
"tooltip": "An integer of the form p^x for some integer x, where p is prime number. This value indicates the number of elements in the underlying field"
}
],
"optional_parameters": [
{
"id": "memory_bound",
"required": false,
"type": "number",
"direction": "column",
"display_label": "Memory limit",
"default_value": null,
"placeholder": "Insert value",
"caption": "Leave empty if no limit is desired",
"tooltip": "Log2 of the maximum number of bits of memory available"
},
{
"id": "w",
"type": "slider",
"direction": "column",
"display_label": "Matrix multiplication constant",
"default_value": 2.81,
"tooltip": "Indicates that two square matrices of size n can be multiplied by performing O(n^w) field multiplications",
"min": 2,
"max": 3,
"number_of_decimals": 2,
"step": 0.01
}
],
"estimator_parameters": [
{
"id": "bit_complexities",
"type": "switch",
"display_label": "Bit complexities",
"default_value": true,