RU2014112547A - METHOD FOR FORMING S-BLOCKS WITH A MINIMUM NUMBER OF LOGIC ELEMENTS - Google Patents

Abstract

A method for generating S-blocks with a minimum number of logic elements, which consists in the following: setting an initial S-block having n inputs; forming a system of n Boolean functions according to a given S-block in the form of a truth table; multiplying the Hadamard matrix by values of Boolean functions ; get n vectors, which are the values of the coefficients of the Zhegalkin polynomials; form a set of vectors P = {p, p, ..., p}, i = 1 ... n, whose components are composed of the corresponding coefficients of the Zhegalkin polynomial by replacing a, a, ..., a, ..., a; at set the initial value k = 1; form a set of D1 {z, k, t, i} vectors of length 2 (initially empty), where each vector is additionally associated with z = 0, t = 0, where z is the number of a pair of vectors in the previous iteration k ; t is the number of a pair of vectors in the current iteration k; add the vectors d1 {z = 0, k = k, t = 0, i} = p to the set D1; set the initial valuekt = 0; find the most frequent subsequences of components in the vectors p, performing the following steps: (A1) form an initially empty set of DTMP {z, k, t = 0, i} vectors of length n, where each vector is complemented by о, the values t = 0 and k = k are compared; they form an initially empty set D2 {z, k, t, i} of vectors of length 2; they form an initially empty set of D3 {z, k, t, i} vectors of length 2; set the initial value for the pair number t = 1; (A2) if the relation | D1 {z, k, t = 0, i} | <2 holds, then we go to step A3; we determine the pair of vectors (d1 {z, k, t, i} , d1 {z, k, t, j}) in the set D1 {k}, and i ≠ j such that Nxor (ν {k, t} = d1 {z, k, t, i} & d1 {z, k, t, j}), where, wt (ν) is the Hamming weight of the vector ν; ν is an arbitrary binary vector; takes the maximum value; if Nxor = 0 and t = 1, then proceed to stage A5; until

Claims (1)

The method of forming S-blocks with a minimum number of logical elements, which consists in the fact that: set the source S-block having n inputs; form a system of n Boolean functions for a given S-block in the form of a truth table; multiplying the Hadamard matrix by the values of Boolean functions; get n vectors, which are the values of the coefficients of the Zhegalkin polynomials; form a set of vectors P = {p ₁ , p ₂ , ..., p _n }, i = 1 ... n, whose components are composed of the corresponding coefficients of the Zhegalkin polynomial by replacing a ₀ , a ₁ , ..., a _ij , ..., a _{1 ... n} on $$a_0,a_{\mathrm{one}},...,a_{2^n-\mathrm{one}}$$

; set the initial value k is 1; form the set D1 {z, k, t, i} of vectors of length 2 ⁿ (initially empty), where each vector is additionally associated with the values z = 0, t = 0, where z is the number of a pair of vectors in the previous iteration k; t is the number of a pair of vectors in the current iteration k; add vectors to the set D1 d1 {z = 0, k = k, t = 0, i} = p _i ; set the initial value kt = 0; find the most common subsequences of components in the vectors p _i by performing the following steps: (A1) form an initially empty set of DTMP {z, k, t = 0, i} vectors of length n, where the values t = 0 and k = k are additionally associated with each vector; form the initially empty set D2 {z, k, t, i} of vectors of length 2 ⁿ ; form the initially empty set D3 {z, k, t, i} of vectors of length 2 ⁿ ; set the initial value for the pair number t is 1; (A2) if the relation | D1 {z, k, t = 0, i} | <2, then proceed to step A3; define a pair of vectors (d1 {z, k, t, i}, d1 {z, k, t, j}) in the set D1 {k}, and i ≠ j, such that, the quantity Nxor _A (ν {k, t} = d1 {z, k, t, i} & d1 {z, k, t, j}), Where

, wt _H (ν) is the Hamming weight of the vector ν; ν is an arbitrary binary vector; takes the maximum value; if Nxor _A = 0 and t = 1, then proceed to step A5; vectors (d1 {z, k, t, i}, d1 {z, k, t, j}) are sequentially added to the set of DTMPs for a specific pair t DTMP = DTMP∪ {d1 {z1, k, t, i}, d1 {z, k, t, j}}; add to vector D3

remove common elements from the vectors of each pair

add both vectors to the set D2 D2 = D2∪ {d2 {z, k, t, i}, d2 {z, k, t, j}}; remove the participating pairs of vectors from the set D1 {z, k, t, i} D1 {z, k, t, i} = D1 {z, k, t, i} \ {d1 {z, k, t, i}, d1 {z, k, t, j}}; calculate t = t + 1; calculate the power of the set of vectors D1 | D1 {z, k, t = 0, i} |; proceed to stage A2; (A3) temporarily store the set of DTMP vectors (d1 {z, k, t, i}, d1 {z, k, t, j}) and the sets of vectors D2 {z, k, t, i} and D3 {z, k , t, i}; calculate kp = 2k, kν = 2k + 1; if the relation holds | D3 {z, k = kν, t, i} | <2, then proceed to step A4; calculate k = kν; assign to the elements of the set D1 {k} the values of the elements of the set D3 {kν} d1 [z, k, t, i} = d3 {z, kν, t, i}; calculate kt = 0; proceed to stage A1; (A4) if the relation holds | D2 {z, k = kp, t, i} | <2, then proceed to step A6; calculate k = kp kt = 1; assign to the elements of the set D1 {z, k, t, i} the values of the elements of the set D2 {z, kp, t, i} d1 {z, k, t, i} = d2 {z, kp, t, i}; proceed to stage A1; (A5) if kt = 1, then go to step A6, otherwise go to step A4; (A6) receive the resulting logical function by performing the following steps: calculate k is 1; form an auxiliary vector kf (n), initially having zero elements; (C1) if kf (k) = 1, then proceed to step C2; calculate k = 2k + 1; calculate the number of vectors m in iteration k; if m ≠ 0, then proceed to step C1; calculate k = (k-1) / 2; proceed to step C3; (C2) if k is even, then calculate k = k / 2; proceed to step C3; calculate k = k-1; if k = 0, then proceed to the implementation of step C7, otherwise - proceed to the implementation of step C1; (C3) calculate the number of vectors m in iteration k; if m = 1, then form a circuit for the vector d1 {z, k, t, i}; proceed to step C6; calculate t is 1; (C4) if t> m / 2, then proceed to step C6; calculate the number of vectors m ₁ in iteration 2k + 1; if m ₁ = 0, then form a circuit for the vector d1 {z, k, t, i}; form a circuit for d1 {z, k, t, j}; proceed to step C5; form a circuit for the vector d1 {z, k, t, i} from the obtained schemes for the vectors d1 {z = t, 2k, t, i} and d1 {z = t, 2k + 1, t, i = t}; form a circuit for the vector d1 {z, k, t, j} from the obtained schemes d1 {z = t, 2k, t, j} and d1 {z = t, 2k + 1, t, i = t}; (C5) calculate t = t + 1; proceed to step C4; (C6) calculate kf (k) = 1; proceed to stage C1; (C7) form, based on the resulting logic circuitry, an electronic circuitry for implementing the S-block.