Metadata-Version: 2.1
Name: subsets
Version: 1.0.0
Summary: Tools for cryptanalysis (binary/box subsets & transforms)
Home-page: UNKNOWN
Author: Aleksei Udovenko
Author-email: aleksei@affine.group
License: MIT
Project-URL: Source, https://github.com/CryptoExperts/AC21-DivProp-Convexity
Description: # subsets - binary/box subsets & transforms
        
        This package provides C++ implementation and Python bindings (SWIG) for dense binary/box multidimensional transformations.
        
        Example of such transform is the TruthTable-to-AlgebraicNormalForm conversion (the Möbius transform), TruthTable-to-ParitySet conversion, Lower/UpperClosure with respect to the product partial order, etc. For more details, see Section 5 of ???
        
        Box here means a set of the shape `{0,...d_1} × {0,...d_2} x ...`.
        
        
        ## Installation
        
        ```bash
        apt install swig  # or any other package manager
        pip install hackycpp
        pip install subsets
        ```
        
        Note: the build can take a few minutes.
        
        
        ## Examples
        
        Note: `subsets` uses [binteger](https://binteger.readthedocs.io/) for convenient representations of bit vectors.
        
        See also [tests](tests/) for more examples.
        
        
        ### DenseSet
        
        `DenseSet` stores a subset of n-bit vectors as a bitstring of 2^n bits. 
        
        ```python
        from subsets import DenseSet
        
        # set of 3-bit vectors
        b = DenseSet(3, [6, 7]) 
        b
        # <DenseSet hash=f502ae1f64521d04 n=3 wt=2 | 2:1 3:1>
        
        list(b)
        # [6, 7]
        
        b.to_Bins()
        # [Bin(0b110, n=3), Bin(0b111, n=3)]
        
        b.Mobius().to_Bins()
        # [Bin(0b110, n=3)] = x0x1
        
        DenseSet(3, [3]).LowerSet().to_Bins()
        # [Bin(0b000, n=3), Bin(0b001, n=3), Bin(0b010, n=3), Bin(0b011, n=3)]
        
        DenseSet(3, [3]).LowerSet().MaxSet().to_Bins()
        # [Bin(0b011, n=3)]
        ```
        
        Bitwise operations such as `^,|,&` are supported naturally:
        
        ```python
        from subsets import DenseSet
        
        list(DenseSet(3, [0, 1]) ^ DenseSet(3, [1, 7]))
        # [0, 7]
        
        list(DenseSet(3, [0, 1, 2]).Complement())
        # [3, 4, 5, 6, 7]
        
        list(DenseSet(3, [0, 1, 2]).Not())  # equiv. to xor 0xfff... each index set
        # [5, 6, 7]
        
        list(DenseSet(3, [0, 1, 2]).Not(3))  # equiv. to xor 3 each index set
        # [1, 2, 3]
        ```
        
        ### DenseBox
        
        `DenseBox` stores a subset of a set `{0,...d_1} × {0,...d_2} × ...` as a bitstring of length `(d_1 + 1) × (d_2 + 1) × ...`. It supports multidimensional transforsms similar to `DenseSet`.
        
        Each element is addressed either by a list of integers from `{0,...d_1} × {0,...d_2} × ...`, or by a packed 64-bit integer.
        
        ```python
        from subsets import DenseBox
        
        d = DenseBox([2, 3, 4])  # dimensions
        d.data.n
        # 60 = 3*4*5 bits to stored d
        
        d.set(d.pack([1, 0, 3]))
        assert [1, 0, 3] in d
        assert [0, 0, 0] not in d
        
        d
        # <DenseBox(2,3,4) hash=89366ea36f16f570 wt=1 | 4:1>
        
        list(d.LowerSet())
        # [0, 1, 2, 3, 20, 21, 22, 23]
        
        d.LowerSet().get_unpacked()
        # ((0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (1, 0, 0), (1, 0, 1), (1, 0, 2), (1, 0, 3))
        ```
        
        In addition, `DenseBox` can be converted to and from `DenseSet` with `n = d_1 + d_2 + ...`:
        the first produces set of bitstrings that have weight pattern `(l_1, l_2, ...)` for each such pattern in the given `DenseBox` (expansion);
        the second produces all weight patterns in a given `DenseSet` (compression):
        
        ```python
        from subsets import DenseSet
        
        d = DenseSet(4, [1, 2, 3, 12]).to_DenseBox([2, 2])
        
        d.get_unpacked()
        # ((0, 1), (0, 2), (2, 0))
        ```
        
        **Caution:** a convex binary set may have a non-convex weight pattern bounds:
        
        ```python
        from subsets import DenseSet
        
        d = DenseSet(4, [7, 8])
        d.to_Bins()
        # [Bin(0b0111, n=4), Bin(0b1000, n=4)]
        
        d == d.LowerSet() & d.UpperSet()
        # True  - is convex
        
        db = d.to_DenseBox([4])
        db
        # <DenseBox(4) hash=ef70011e9740ac1c wt=2 | 1:1 3:1>
        
        db.LowerSet() & db.UpperSet()  # convex hull
        # <DenseBox(4) hash=c3729f500963e25a wt=3 | 1:1 2:1 3:1>
        
        db == db.LowerSet() & db.UpperSet()
        # False - obviously non-convex
        ```
        
        ### Division Property Propagation Table
        
        Basic implementation of the (reduced) DPPT computation algorithm (Section 5 of ???).
        
        ```python
        from subsets import DenseSet
        
        sbox = [  # AES
            0x63,0x7c,0x77,0x7b,0xf2,0x6b,0x6f,0xc5,0x30,0x01,0x67,0x2b,0xfe,0xd7,0xab,0x76,
            0xca,0x82,0xc9,0x7d,0xfa,0x59,0x47,0xf0,0xad,0xd4,0xa2,0xaf,0x9c,0xa4,0x72,0xc0,
            0xb7,0xfd,0x93,0x26,0x36,0x3f,0xf7,0xcc,0x34,0xa5,0xe5,0xf1,0x71,0xd8,0x31,0x15,
            0x04,0xc7,0x23,0xc3,0x18,0x96,0x05,0x9a,0x07,0x12,0x80,0xe2,0xeb,0x27,0xb2,0x75,
            0x09,0x83,0x2c,0x1a,0x1b,0x6e,0x5a,0xa0,0x52,0x3b,0xd6,0xb3,0x29,0xe3,0x2f,0x84,
            0x53,0xd1,0x00,0xed,0x20,0xfc,0xb1,0x5b,0x6a,0xcb,0xbe,0x39,0x4a,0x4c,0x58,0xcf,
            0xd0,0xef,0xaa,0xfb,0x43,0x4d,0x33,0x85,0x45,0xf9,0x02,0x7f,0x50,0x3c,0x9f,0xa8,
            0x51,0xa3,0x40,0x8f,0x92,0x9d,0x38,0xf5,0xbc,0xb6,0xda,0x21,0x10,0xff,0xf3,0xd2,
            0xcd,0x0c,0x13,0xec,0x5f,0x97,0x44,0x17,0xc4,0xa7,0x7e,0x3d,0x64,0x5d,0x19,0x73,
            0x60,0x81,0x4f,0xdc,0x22,0x2a,0x90,0x88,0x46,0xee,0xb8,0x14,0xde,0x5e,0x0b,0xdb,
            0xe0,0x32,0x3a,0x0a,0x49,0x06,0x24,0x5c,0xc2,0xd3,0xac,0x62,0x91,0x95,0xe4,0x79,
            0xe7,0xc8,0x37,0x6d,0x8d,0xd5,0x4e,0xa9,0x6c,0x56,0xf4,0xea,0x65,0x7a,0xae,0x08,
            0xba,0x78,0x25,0x2e,0x1c,0xa6,0xb4,0xc6,0xe8,0xdd,0x74,0x1f,0x4b,0xbd,0x8b,0x8a,
            0x70,0x3e,0xb5,0x66,0x48,0x03,0xf6,0x0e,0x61,0x35,0x57,0xb9,0x86,0xc1,0x1d,0x9e,
            0xe1,0xf8,0x98,0x11,0x69,0xd9,0x8e,0x94,0x9b,0x1e,0x87,0xe9,0xce,0x55,0x28,0xdf,
            0x8c,0xa1,0x89,0x0d,0xbf,0xe6,0x42,0x68,0x41,0x99,0x2d,0x0f,0xb0,0x54,0xbb,0x16
        ]
        
        graph = DenseSet(16)
        for x, y in enumerate(sbox):
            graph.set((x << 8) | y)
        
        # do_* does the operation in place
        dppt = graph
        dppt.do_ParitySet()  # same as dppt.do_Sweep_XOR_down()
        dppt.do_UpperSet(0xff00)
        dppt.do_MinSet(0x00ff)
        dppt.do_Not(0xff00)
        
        [v.split(2) for v in dppt.to_Bins()]
        # (Bin(0b00000000, n=8), Bin(0b00000000, n=8))
        # (Bin(0b00000001, n=8), Bin(0b00000001, n=8))
        # (Bin(0b00000001, n=8), Bin(0b00000010, n=8))
        # (Bin(0b00000001, n=8), Bin(0b00000100, n=8))
        # (Bin(0b00000001, n=8), Bin(0b00001000, n=8))
        # (Bin(0b00000001, n=8), Bin(0b00010000, n=8))
        # (Bin(0b00000001, n=8), Bin(0b00100000, n=8))
        # (Bin(0b00000001, n=8), Bin(0b01000000, n=8))
        # (Bin(0b00000001, n=8), Bin(0b10000000, n=8))
        # (Bin(0b00000010, n=8), Bin(0b00000001, n=8))
        # (Bin(0b00000010, n=8), Bin(0b00000010, n=8))
        # (Bin(0b00000010, n=8), Bin(0b00000100, n=8))
        # (Bin(0b00000010, n=8), Bin(0b00001000, n=8))
        # ...
        # (Bin(0b11111101, n=8), Bin(0b10000000, n=8))
        # (Bin(0b11111110, n=8), Bin(0b00000100, n=8))
        # (Bin(0b11111110, n=8), Bin(0b00001010, n=8))
        # (Bin(0b11111110, n=8), Bin(0b00010010, n=8))
        # (Bin(0b11111110, n=8), Bin(0b00011000, n=8))
        # (Bin(0b11111110, n=8), Bin(0b00100001, n=8))
        # (Bin(0b11111110, n=8), Bin(0b00101000, n=8))
        # (Bin(0b11111110, n=8), Bin(0b00110000, n=8))
        # (Bin(0b11111110, n=8), Bin(0b01000001, n=8))
        # (Bin(0b11111110, n=8), Bin(0b01010000, n=8))
        # (Bin(0b11111110, n=8), Bin(0b01100010, n=8))
        # (Bin(0b11111110, n=8), Bin(0b10000001, n=8))
        # (Bin(0b11111110, n=8), Bin(0b10010000, n=8))
        # (Bin(0b11111111, n=8), Bin(0b11111111, n=8))
        ```
        
        ### Extra
        
        Subsets can be stored to / loaded from files, and a command line tool to view information on such files is provided:
        
        ```bash
        $ subsets.info -s data/sbox_aes/ddt.set
        INFO:subsets.setinfo:data/sbox_aes/ddt.set: <DenseSet hash=3ab8d88c8de49448 n=16 wt=32386 | 0:1 2:24 3:212 4:855 5:2205 6:3901 7:5637 8:6378 9:5746 10:4007 11:2169 12:907 13:276 14:58 15:9 16:1>
        
        $ subsets.info data/sbox_aes/ddt.set
        INFO:subsets.setinfo:set file data/sbox_aes/ddt.set
        INFO:subsets.setinfo:data/sbox_aes/ddt.set: <DenseSet hash=3ab8d88c8de49448 n=16 wt=32386 | 0:1 2:24 3:212 4:855 5:2205 6:3901 7:5637 8:6378 9:5746 10:4007 11:2169 12:907 13:276 14:58 15:9 16:1>
        INFO:subsets.setinfo:stat by weights:
        INFO:subsets.setinfo:0 : 1
        INFO:subsets.setinfo:1 : 0
        INFO:subsets.setinfo:2 : 24
        INFO:subsets.setinfo:3 : 212
        INFO:subsets.setinfo:4 : 855
        INFO:subsets.setinfo:5 : 2205
        INFO:subsets.setinfo:6 : 3901
        INFO:subsets.setinfo:7 : 5637
        INFO:subsets.setinfo:8 : 6378
        INFO:subsets.setinfo:9 : 5746
        INFO:subsets.setinfo:10 : 4007
        INFO:subsets.setinfo:11 : 2169
        INFO:subsets.setinfo:12 : 907
        INFO:subsets.setinfo:13 : 276
        INFO:subsets.setinfo:14 : 58
        INFO:subsets.setinfo:15 : 9
        INFO:subsets.setinfo:16 : 1
        INFO:subsets.setinfo:stat by pairs:
        INFO:subsets.setinfo:0 0 : 1
        INFO:subsets.setinfo:1 1 : 24
        INFO:subsets.setinfo:1 2 : 102
        INFO:subsets.setinfo:1 3 : 234
        ...
        INFO:subsets.setinfo:8 6 : 14
        INFO:subsets.setinfo:8 7 : 5
        INFO:subsets.setinfo:8 8 : 1
        INFO:subsets.setinfo:
        ```
Keywords: subsets,binary,multidimensional transforms,cryptanalysis,cryptography
Platform: UNKNOWN
Requires-Python: >=3.7,<4.0
Description-Content-Type: text/markdown
