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 Feb 15 comment How to find roots of equation $f(x)=0 \pmod p$, where $p$ is prime number? If the prime number is more than 192-bit, this formula will be applicable? Feb 8 comment How to find roots of equation $f(x)=0 \pmod p$, where $p$ is prime number? I agreed your answer. But how to solve the equation if degree of the polynomial greater than 2? any reference is available. Nov 3 comment how to calculate non linearity of AES S-box? i sincerely thanks for elaborated explanation... i am trying to find mathematical view for calculating SAC, non linearity? so, i can apply to any expression. could you give me any source of information? Mar 27 comment How to calculate y value from ((y*y) mod prime) efficiently In some cases (y^2) mod p does not exit. means for every (y^2) mod p there is no need to existence of y-value. In that case also it will work? Mar 19 comment Efficient algorithm for remainder calculation over prime field for ECC implementation? Aninteger c = (c13,..., c2, c1, c0) in base 2^32 with 0 ≤ c < 224-bit*224-bit OUTPUT: c mod p(224-bit) z1 = (c6, c5, c4, c3, c2, c1, c0), z2 = (c10, c9, c8, c7, 0, 0, 0), z3 = (0, c13, c12, c11, 0, 0, 0), z5 = (0, 0, 0, 0, c13, c12, c11), z4 = (c13, c12, c11, c10, c9, c8, c7),= Return(z1 + z2 + z3 − z4 − z5mod p224).this is algorithm what i supposed to explain. after 224-bit * 224-bit multiplication gives 448 -bit output. it will reduce into field range using prime number (2^224-2^96+1) using above algorithm. can you explain mathematical concept behind in this efficient reduction technique? Mar 18 comment Efficient algorithm for remainder calculation over prime field for ECC implementation? yes. i know that procedure. It is recommended by NIST standard Elliptic Curve. But if the prime number changes that formula won't work. Is any alternative way? In FIPS 186-3 , how can he able to computed the value, could you explain mathematics behind in that method? Mar 18 comment While generating a random Elliptic curve what are the conditions i have to considerd? I NPUT :Aninteger c = (c13,..., c2, c1, c0) in base 2^32 with 0 ≤ c < 224-bit*224-bit OUTPUT: c mod p(224-bit) z1 = (c6, c5, c4, c3, c2, c1, c0), z2 = (c10, c9, c8, c7, 0, 0, 0), z3 = (0, c13, c12, c11, 0, 0, 0), z5 = (0, 0, 0, 0, c13, c12, c11), z4 = (c13, c12, c11, c10, c9, c8, c7),= Return(z1 + z2 + z3 − z4 − z5mod p224).this is algorithm what i supposed to explain. after 224-bit * 224-bit multiplication gives 448 -bit output. it will reduce into field range using prime number (2^224-2^96+1) using above algorithm. can you explain mathematical concept of above? Mar 2 comment While generating a random Elliptic curve what are the conditions i have to considerd? NIST recommended standard ECC-224 bit, prime value is 2^224-2^96+1. 224 bit * 224 bit multiplication results 448 bit output. which can be converted back over field 224 bit, NIST standard has given one formula ((z1+z2+z3-z4-z5) mod prime )). what is mathematical logic beind in this formula. Mar 1 comment While generating a random Elliptic curve what are the conditions i have to considerd? i want to generate a random curve over prime field...