MATH SOLVE

4 months ago

Q:
# Use the encrypting congruence c ≡ (7p + 12) mod 26 to code the message PARALLEL LINES.

Accepted Solution

A:

Answer: PARALLEL LINES should be coded as "TSHSRRUR RWFUO"Step-by-step explanation:Since we have given that PARALLEL LINESAs we know that according to alphabets, P is at 16A is at 1R is at 18L is at 12E is at 5N is at 14S is at 19And we have given that [tex]c \equiv(7p+12)\ mod 26[/tex]So, P becomes :[tex]c\equiv (7\times 16+12)\ mod\ 26=124\ mod\ 26=20\ mod\ 26=T[/tex]A becomes [tex]c\equiv (7\times 1+12)\ mod\ 26=19\ mod\ 26=S[/tex]S becomes [tex]c\equiv (7\times 19+12)\ mod\ 26=145\ mod\ 26=15\ mod\ 26=O[/tex]L becomes[tex]c\equiv (7\times 12+12)\ mod\ 26=96\ mod\ 26=18\ mod\ 26=R[/tex]E becomes[tex]c\equiv (7\times 5+12)\ mod\ 26=47\ mod\ 26=21\ mod\ 26=U[/tex]I becomes[tex]c\equiv (7\times 9+12)\ mod\ 26=75\ mod\ 26=23\ mod\ 26=W[/tex]N becomes[tex]c\equiv (7\times 14+12)\ mod\ 26=110\ mod\ 26=6\ mod\ 26=F[/tex]R becomes[tex]c\equiv (7\times 18+12)\ mod\ 26=138\ mod\ 26=8\ mod\ 26=H[/tex]Hence, PARALLEL LINES should be coded as "TSHSRRUR RWFUO"