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One round of Simon


General  

Designers  Ray Beaulieu, Douglas Shors, Jason Smith, Stefan TreatmanClark, Bryan Weeks, Louis Wingers NSA 
First published  2013^{[1]} 
Related to  Speck 
Cipher detail  
Key sizes  64, 72, 96, 128, 144, 192 or 256 bits 
Block sizes  32, 48, 64, 96 or 128 bits 
Structure  Balanced Feistel network 
Rounds  32, 36, 42, 44, 52, 54, 68, 69 or 72 (depending on block and key size) 
Speed  7.5 cpb (21.6 without SSE) on Intel Xeon 5640 (Simon128/128) 
Best public cryptanalysis  
Differential cryptanalysis can break 46 rounds of Simon128/128 with 2^{125.6} data, 2^{40.6} bytes memory and time complexity of 2^{125.7} with success rate of 0.632.^{[2]}^{[3]}^{[4]} 
Simon is a family of lightweight block ciphers publicly released by the National Security Agency (NSA) in June 2013.^{[5]}^{[1]} Simon has been optimized for performance in hardware implementations, while its sister algorithm, Speck, has been optimized for software implementations.^{[6]}^{[7]}
The Simon block cipher is a balanced Feistel cipher with an nbit word, and therefore the block length is 2n. The key length is a multiple of n by 2, 3, or 4, which is the value m. Therefore, a Simon cipher implementation is denoted as Simon2n/nm. For example, Simon64/128 refers to the cipher operating on a 64bit plaintext block (n=32) that uses a 128bit key.^{[1]} The block component of the cipher is uniform between the Simon implementations; however, the key generation logic is dependent on the implementation of 2, 3 or 4 keys.
Simon supports the following combinations of block sizes, key sizes and number of rounds:^{[1]}
Block size (bits)  Key size (bits)  Rounds 

32  64  32 
48  72  36 
96  36  
64  96  42 
128  44  
96  96  52 
144  54  
128  128  68 
192  69  
256  72 
The key schedule is mathematically described as
The key schedule structure may or may not be balanced. The key word count of is used to determine the structure of the key expansion, resulting in a total bit width of . The key word expansion consists of a right shift, XOR and a constant sequence, . The bit operates on the lowest bit of the key word once per round^{[7]}.
The constant sequence, , is created by a Linear Feedback Shift Register (LFSR). The logical sequence of bit constants is set by the value of the key and block sizes. The LFSR is created by a 5bit field. The constant bit operates on a key block once per round on the lowest bit in order to add nonkeydependent entropy to the key schedule. The LFSR has different logic for each sequence; however, the initial condition is the same for encryption. The initial condition of the LFSR for decryption varies on the round.
Constant Sequence 

German, Japanese and Israeli delegates to the International Organization for Standardization have opposed efforts by the NSA to standardise the Simon and Speck ciphers, citing concerns that the NSA is pushing for their standardisation with knowledge of exploitable weaknesses in the ciphers, based on partial evidence of weaknesses in the ciphers, lack of clear need for standardisation of the new ciphers, and the NSA's previous involvement in the creation and promotion of the backdoored Dual_EC_DRBG cryptographic algorithm.^{[8]}
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