1. Use the Pohlig-Hellman algorithm to compute the discrete logarithm x for 23 87 mod 421. 2. Use the baby step-giant step algorithm to solve 2 208 mod 421.
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- Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .we have 1529 MOD 83 = 2 Find the inverse to 2 by using the Euclid's algorithmLet p be an odd prime and let g be a primitive root modulo p. Prove that a has a square root modulo p if and only if its discrete logarithm logg(a) modulo p−1 is even.
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