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Absolute public key cryptographic system and method surviving private-key compromise with other advantages

  • US 20020186848A1
  • Filed: 05/03/2001
  • Published: 12/12/2002
  • Est. Priority Date: 05/03/2001
  • Status: Active Grant
First Claim
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1. In a system for sending messages over a network between first and second computing units, method comprising the following steps:

  • (a). computing r components of encrypting key e.sub.1, e.sub.2, . . . , e.sub.r and r components of decrypting key d.sub.1, d.sub.2, . . . , d.sub.r according to the following relations;

    (e.sub.1).(d.sub.1)+(e.sub.2).(d.sub.2)+ . . . +(e.sub.r).(d.sub.r)=(k.sub.1).(p−

    1).(q−

    1)+1 and (d.sub.1)+(d.sub.2)+ . . . +(d.sub.r)=(k.sub.2).(p−

    1).(q−

    1), where;

    p and q are two prime numbers;

    k.sub.1 and k.sub.2 are suitable integers; and

    encrypting a message M into r cipher versions M.sub.1, M.sub.2, . . . , M.sub.r using the r blinded components of the encrypting key e.sub.1+t, e.sub.2+t, . . . ,e.sub.r+t as follows;

    M.sub.1=(M.sup.(e.sub.1+t)) mod n M.sub.2=(M.sup.(e.sub.2+t)) mod n . . . M.sub.r=(M.sup.(e.sub.r+t)) mod n, where;

    n=p.q;

    t is a random number generated on encrypting unit and discarded after encryption is complete;

    mod represents the remainder left when left hand operand is divided by right hand operand;

    or computing the key components e.sub.1, e.sub.2, . . . , e.sub.r and d.sub.1, d.sub.2, . . . , d.sub.r according to the following relation and conditions;

    (e.sub.1).(d.sub.1)+(e.sub.2).(d.sub.2)+ . . . +(e.sub.r).(d.sub.r)=(k.sub.1).(p−

    1).(q−

    1)+1 and each of the values (e.sub.1), (e.sub.2), . . . , (e.sub.r) has a common factor with (p−

    1).(q−

    1), but there is no common factor for all (e.sub.1), (e.sub.2), . . . , (e.sub.r), (p−

    1).(q−

    1), where;

    p and q are prime numbers;

    k.sub.1 is a suitable integer; and

    encrypting a message M into r cipher versions M.sub.1, M.sub.2, . . . , M.sub.r using the r components of the encrypting key, e.sub.1, e.sub.2 . . . , e.sub.r as follows;

    M.sub.1=M.sup.(e.sub.1) mod n M.sub.2=M.sup.(e.sub.2) mod n . . . M.sub.r=M.sup.(e.sub.r) mod n, where;

    n=p.q;

    p and q are two prime numbers;

    (b). delivering all the cipher versions of the message individually to the destination unit in source routing mode, or hop-by-hop routing mode with a small time gap between every two consecutive cipher versions;

    (c). collecting all the cipher versions at the destination unit;

    (d). computing r number of values N.sub.1, N.sub.2, . . . , N.sub.r using r components d.sub.1, d.sub.2, . . . , d.sub.r of decrypting key, where;

    N.sub.1=((M.sub.1).sup.(d.sub.1)) mod n N.sub.2=((M.sub.2).sup.(d.sub.2)) mod n . . . N.sub.r=((M.sub.r).sup.(d.sub.r)) mod n, where;

    n is the same composite number as used for encryption;

    (e). reproducing the original message M as follows;

    M=(N.sub.1).(N.sub.2) . . . (N.sub.r) mod n, where;

    n is the same composite number as used for encryption.

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