Abstract. A solution of the integrity problem for arithmetic programs running on a remote computing resource is proposed. The solution is to replace the arithmetic operations such as multiplication and division by procedures of the addition machine introduced by R. Floyd and D. Knuth. The order of instructions as well as current meanings of variables are signed by dynamic digital signatures, which are homomorphic with respect to addition and subtraction. Verification of digital signatures ensures detection of any unauthorized changes to the source code of the program and to the results of calculations.
Keywords: addition machine, digital signature, homomorphic cryptography.
1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
e-mail: ava@unicyb.kiev.ua.
2 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
e-mail: andrey.novokshonov@ukr.net.