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THE EFFECT OF GLUCOSE 4.0 SIMPLIFICATION OPTIONS ON A 210,121-VARIABLE, 629,597-CLAUSE CNF ENCODING OF SHA-1 No such encoding optimisations have been enacted in this work. A simple, naive encoding of the SHA-1 algorithm, as described by Equation 2, results in 210,121 variables and 629,597 clauses, giving a clause-to-variable ratio of 2.996 — which is a “better” ratio than any listed in Table I. [18] focuses on longer clauses with more 2-clause bridges, giving a higher ratio. When this naive encoding is passed to the Glucose 4.0 solver! [9], [25] along with suitable simplification

Table 1 THE EFFECT OF GLUCOSE 4.0 SIMPLIFICATION OPTIONS ON A 210,121-VARIABLE, 629,597-CLAUSE CNF ENCODING OF SHA-1 No such encoding optimisations have been enacted in this work. A simple, naive encoding of the SHA-1 algorithm, as described by Equation 2, results in 210,121 variables and 629,597 clauses, giving a clause-to-variable ratio of 2.996 — which is a “better” ratio than any listed in Table I. [18] focuses on longer clauses with more 2-clause bridges, giving a higher ratio. When this naive encoding is passed to the Glucose 4.0 solver! [9], [25] along with suitable simplification

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CNF ENCODINGS, 80 ROUNDS OF SHA-1 Both [18] and [16] call out the addition step as being worthy of special effort when encoding. [16] try several approaches: using the Espresso heuristic logic minimizer [23] to express formulae using the least number of terms; using the CryptLogVer toolkit [24] for a similar reason; and using a straight Tseitin transformation. The clauses, variables, and ratios for various 80-round encodings are presented as Table I.
CNF ENCODINGS, 80 ROUNDS OF SHA-1 Both [18] and [16] call out the addition step as being worthy of special effort when encoding. [16] try several approaches: using the Espresso heuristic logic minimizer [23] to express formulae using the least number of terms; using the CryptLogVer toolkit [24] for a similar reason; and using a straight Tseitin transformation. The clauses, variables, and ratios for various 80-round encodings are presented as Table I.
THE EFFECT OF GLUCOSE 4.0 SIMPLIFICATION OPTIONS ON A 267,603-VARIABLE, 857,477-CLAUSE CNF ENCODING OF SHA-. For comparison purposes, Table III presents figures for an encoding of SHA-1 that uses bitpatterns. The figures demon- strate that the trends caused by simplification are similar, even when the initial encoding of the problem is quite different: the number of variables decreases, the number of clauses increases, and the number of 2-clauses decreases. The 2- clauses column, in particular, is interesting because of how similar it is between the encodings.
THE EFFECT OF GLUCOSE 4.0 SIMPLIFICATION OPTIONS ON A 267,603-VARIABLE, 857,477-CLAUSE CNF ENCODING OF SHA-. For comparison purposes, Table III presents figures for an encoding of SHA-1 that uses bitpatterns. The figures demon- strate that the trends caused by simplification are similar, even when the initial encoding of the problem is quite different: the number of variables decreases, the number of clauses increases, and the number of 2-clauses decreases. The 2- clauses column, in particular, is interesting because of how similar it is between the encodings.
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